Systems, devices methods and scalable architectures for quantum computing

Abstract

Systems, devices, methods and architectures for quantum computing are disclosed. A system for controlling quantum elements includes input signal sources configured to generate signals, where each input signal source is coupled with at least one quantum element; and at least one controller configured to provide data signals comprising instructions, where the instructions are configured to cause the system to generate control sequences, where the sequences are configured to apply desired respective operation on the at least one quantum element, each control sequence includes a time-dependent series of control subsequences, and each control subsequence includes a signal generated by a single input signal source at a time interval, or defines a time interval during which the plurality of input signal sources does not generate signals; and apply the control sequences on the at least one quantum element.

Description

SYSTEMS, DEVICES METHODS AND SCALABLE ARCHITECTURES FOR QUANTUM COMPUTINGCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The present application claims the benefit of and priority to U.S. Provisional Application No. 63 / 651,080, filed May 23, 2024, U.S. Provisional Application No. 63 / 659,603, filed June 13, 2024, U.S. Provisional Application No. 63 / 695,882, filed September 18, 2024 and U.S. Provisional Application No. 63 / 724,428, filed November 25, 2024. The entire contents of each and every priority application are hereby incorporated by reference herein.FIELD

[0002] The present disclosure relates generally to quantum computing, and to designing, constructing or controlling quantum processors, in particular.BACKGROUND

[0003] One of the major bottlenecks for scaling up superconducting quantum computers is the need to control qubits individually. This leads to unacceptable overheads in cable and Radio-Frequency (RF) component counts and heat load.

[0004] The core of a superconducting quantum computer is the Quantum Processing Unit (QPU), a chip or assembly of chips hosting, among others, Quantum Elements (QEs, will be also referred to herein as “elements”) such as qubits. These qubits, consisting of elementary superconducting circuits (such as “transmon” or “fluxonium” circuits), operate using two distinct current states, representing the binary 0 and 1. Unlike classical bits, qubits can be in a superposition state of 0 and 1. The qubits in a QPU can be entangled with each other, which enables them to solve computational problems that cannot be solved efficiently with classical computers. Although current QPUs contain up to a few hundred qubits, the leap to fault-tolerant quantum computers with over a million qubits is necessary for unlocking their full potential.

[0005] The quantum computation unfolds through a series of control operations on quantum elements, such as qubits, encompassing their initialization, manipulation via quantum gates, and measurement.

[0006] Single-qubit gates, such as a bit-flip (X) or phase-flip (Z) gates are achieved by sending signals to the relevant qubit in the QPU. These signals can consist of microwave pulses, Single-Flux Quantum (SFQ) pulses, magnetic flux signals, or Direct Current (DC) pulses.

[0007] Two-qubit gates, such as controlled-Z (CZ) or controlled-X (CX) gates are used to create entanglement between qubits. Such gates can be achieved by sending microwave signals to the qubits, or as is more common in more recent QPUs, by sending DC pulses to coupling elements interconnecting the qubits.

[0008] Measurements are used at the end of the quantum computation to measure the output and, importantly, to detect errors in qubits during the computation in a process called Quantum Error Correction (QEC). Measurements are performed by sending microwave or SFQ signals to, e.g., readout resonators (herein also referred to as “resonators”), and acquiring the signals reflected or transmitted by the readout resonators. Readout resonators have different resonance frequencies to those of qubits. Those resonant frequencies are sensitive to the qubit state. As such, they can be used to non-destructively measure the qubit.

[0009] According to the state of the art, the qubits, or the qubits and the coupling elements, may be placed on a separate quantum chip. Readout resonators, wiring, and other supporting circuitry may be placed on additional interface chips placed above or below the quantum chip. This stacked-chip approach alleviates some of the integration challenges. Furthermore, it keeps the quantum chip and its fabrication as simple as possible, which is beneficial for achieving favorable qubit properties.

[0010] Superconducting QPUs are cooled to temperatures well below one Kelvin (K) (e.g., milli-Kelvin temperatures) to achieve their desired operation. This cooling can be achieved using a cryostat such as a dilution refrigerator.

[0011] In the current state of the art, the hardware for orchestrating the QPU control is outside the cryostat. Analog microwave signals from signal generators at room temperature are sent through transmission lines running through the cryostat, where they are heavily filtered and attenuated at each temperature stage to remove noise, before being routed to the qubits. Output signals from the readout resonators are amplified before being sent through other cryogenic microwave equipment, such as circulators and isolators, and are then routed to a signal acquisition setup outside the cryostat.

[0012] Microwave devices such as cables, amplifiers, attenuators, filters, amplifiers, circulators and isolators are typically bulky, costly, and present a substantial heat load to the cryostat, which has a cooling power of only about 100 micro-Watts (pW) at milli-Kelvin temperatures. The microwave control setup becomes increasingly cumbersome as the number of qubits scales, since every qubit requires at least a few cables. It is widely understood that scaling to a large quantity of qubits, e.g., millions of qubits, as may be required for usefulquantum computers, is not feasible using current control hardware. The current approach is limited to a few thousand qubits per cryostat. For realizing quantum computers with more than a few thousand qubits, a new approach for control is therefore required.

[0013] One approach taken is to place up to a few thousand qubits in every cryostat, and then to interlink the cryostats to each other. Another approach places the control hardware at an intermediate temperature stage of a few Kelvins. This hardware uses a traditional semiconductor Complementary-Metal-Oxid-Semiconductor (CMOS) architecture, which is modified to operate at low temperatures (cryo-CMOS). This hardware is relatively mature and can reduce the footprint and cost of control hardware. However, cryo-CMOS circuits still generate excessive heat. Moreover, cables and microwave equipment are still needed for connecting the cryo-CMOS controller to the QPU at the milli-Kelvin stage.SUMMARY

[0014] In accordance with aspects of the present disclosure, a quantum processing unit (QPU) includes multiple quantum elements arranged in multiple sets of quantum elements, where the quantum processing unit is configured to operate not more than a single quantum element of each set of quantum elements in parallel.

[0015] In various embodiments of the QPU, the quantum processing unit is configured to apply operations on the multiple quantum elements, where the quantum processing unit is configured to apply each operation of the operations on not more than a single quantum element of each set of quantum elements.

[0016] In various embodiments of the QPU, the QPU further includes multiple cells, where each cell of the multiple cells includes a respective set of quantum elements of the sets of quantum elements.

[0017] In various embodiments of the QPU, each cell of the plurality of cells includes up to a predefined number of quantum elements.

[0018] In various embodiments of the QPU, the multiple cells are of one or more types.

[0019] In various embodiments of the QPU, the multiple cells are arranged in a periodic pattern.

[0020] In various embodiments of the QPU, the QPU further includes multiple supercells, where the multiple cells are arranged in sets of cells, and each supercell of the multiple supercells includes a respective set of cells of the sets of cells.

[0021] In various embodiments of the QPU, each supercell of the plurality of supercells includes up to a predefined number of cells.

[0022] In various embodiments of the QPU, scaling of the quantum processing unit is performed by adding one or more additional supercells.

[0023] In various embodiments of the QPU, the QPU further includes at least one module, where the multiple supercells are arranged in one or more sets of supercells, and where the at least one module includes a respective set of supercells of the one or more sets of supercells.

[0024] In various embodiments of the QPU, scaling of the quantum processing unit is performed by adding one or more additional modules.

[0025] In various embodiments of the QPU, the QPU further includes multiple control channels configured to provide instructions for operating the multiple quantum elements, where each control channel of the multiple control channels is configured to provide instructions for operating quantum elements of a different plurality of sets of quantum elements of the multiple sets of quantum elements.

[0026] In various embodiments of the QPU, the QPU further includes multiple supercells, each supercell of the multiple supercells including a plurality of sets of quantum elements of the multiple sets of quantum elements, where each supercell of the multiple supercells is coupled with a different one or more control channels of the multiple control channels.

[0027] In various embodiments of the QPU, each supercell of the multiple supercells is coupled with a single different control channel of the multiple control channels.

[0028] In various embodiments of the QPU, the QPU further includes a predefined number of input signal sources. Each input signal source is configured to generate signals for operating the multiple quantum elements, each supercell of the multiple supercells is coupled with a predefined number of control channels, and the predefined number of control channels is determined based on the predefined number of input signal sources.

[0029] In various embodiments of the QPU, the quantum processing unit is configured to apply operations on the multiple quantum elements. Each quantum element of the multiple quantum elements is assigned to a single Quantum Element Set of OPeration (QESOP) of a plurality of QESOPs, each operation of the operations is applied on at least a plurality of quantum elements of the multiple quantum elements, each QESOP of the plurality of QESOPs comprises a plurality of quantum elements of the multiple quantum elements, and each operation of the operations is applied only to quantum elements of a single QESOP of the plurality of QESOPs.

[0030] In various embodiments of the QPU, for each set of the quantum elements of the multiple sets of quantum elements, each quantum element of the set of quantum elements is assigned to a different QESOP.

[0031] In various embodiments of the QPU, the QPU further includes at least one routing control channel configured to cause the routing of control sequences for applying each operation of the operations on its respective QESOP, where each routing control channel of the at least one routing control channel is configured to cause the routing of the control sequences for applying each operation by enabling the routing of the control sequences to at least a plurality of quantum elements of the multiple quantum elements assigned to the respective QESOP.

[0032] In various embodiments of the QPU, the QPU further includes at least one module. Each module of the at least one module including different sets of quantum elements of the multiple sets of quantum elements, each module of the at least one module is coupled with one or more routing control channels of the at least one routing control channel, and the one or more routing control channels coupled with each module of the at least one module are configured to cause the routing of the control sequences for applying an operation on the quantum elements of the respective module which are assigned to the operation’s respective QESOP.

[0033] In various embodiments of the QPU, each module of the at least one module is coupled with a single routing control channel of the at least one routing control channel.

[0034] In various embodiments of the QPU, each QESOP of the multiple QESOPs is assigned with a different address of a plurality of addresses, each quantum element is assigned with its QESOP’ s respective address, and the routing of the control sequences is based on the quantum elements assigned addresses.

[0035] In various embodiments of the QPU, each routing control channel includes a current, and the routing is based on the present value of a characteristic of the current.

[0036] In various embodiments of the QPU, the characteristic of the current is the direction of the current.

[0037] In various embodiments of the QPU, the present value of the characteristic of the current enables the branching of the presently provided control sequences towards the respective quantum elements.

[0038] In various embodiments of the QPU, each quantum element of the multiple quantum elements is assigned to a single QESOP of a plurality of QESOPs, and the quantum processingunit is configured to operate in parallel only quantum elements of the multiple quantum elements which are of the same QESOP.

[0039] In various embodiments of the QPU, the QPU is further configured to apply at least one measurement operation once in each cycle of operations, where each cycle of operations includes the application of one or more operations, and each measurement operation is configured to measure only a single quantum element of each set of quantum elements.

[0040] In various embodiments of the QPU, operating a quantum element of the multiple quantum elements is performed by applying a control sequence on the quantum element via input signal sources of a plurality of input signal sources, and each input signal source of the plurality of input signal sources is coupled with the multiple quantum elements.

[0041] In various embodiments of the QPU, the QPU further includes the plurality of input signal sources.

[0042] In various embodiments of the QPU, the control sequence includes a timedependent series of a plurality of control subsequences, and each control subsequence of the plurality of control subsequences includes a signal generated by a single input signal source of the plurality of input signal sources at a time interval, or defines a time interval during which the plurality of input signal sources does not generate signals.

[0043] In various embodiments of the QPU, the QPU further includes multiple memory elements, where each memory element of the multiple memory elements is coupled with a different set of quantum elements of the multiple sets of quantum elements and configured to store information received from its respective set of quantum elements.

[0044] In accordance with aspects of the present disclosure, a method for quantum computing is disclosed. The method includes applying operations on multiple quantum elements, where the multiple quantum elements are arranged in multiple sets of quantum elements, and each operation of the operations is applied on not more than a single quantum element of each set of quantum elements of the multiple sets of quantum elements.

[0045] In various embodiments of the method, not more than a single quantum element of each set of quantum elements of the multiple sets of quantum elements is operated in parallel.

[0046] In various embodiments of the method, the applying of operations on the multiple quantum elements includes providing instructions for operating the multiple quantum elements via multiple control channels, where each control channel of the multiple control channels is configured to provide instructions for operating quantum elements of a plurality of sets of quantum elements of the multiple sets of quantum elements.

[0047] In various embodiments of the method, the multiple sets of quantum elements are arranged in multiple supercells, each supercell of the multiple supercells includes a different plurality of sets of the multiple sets of quantum elements, and the applying of operations on the quantum elements includes providing instructions for operating the quantum elements of each supercell of the multiple supercells via a single different respective control channel of the multiple control channels.

[0048] In various embodiments of the method, each quantum element of the multiple quantum elements is assigned to a single Quantum Element Set of OPeration (QESOP) of a plurality of QESOPs. Each operation of the operations is applied on at least a plurality of quantum elements of the multiple quantum elements, each QESOP of the plurality of QESOPs includes a plurality of quantum elements of the multiple quantum elements, and each operation of the operations is applied only on quantum elements of a single respective QESOP of the plurality of QESOPs.

[0049] In various embodiments of the method, for each set of the quantum elements of the multiple sets of quantum elements, each quantum element of the set of quantum elements is assigned to a different QESOP.

[0050] In various embodiments of the method, applying each operation of the operations includes causing the routing of control sequences for applying the operation by enabling the routing of the control sequences to at least a plurality of quantum elements of the multiple quantum elements assigned to the respective QESOP.

[0051] In various embodiments of the method, each QESOP of the multiple QESOPs is assigned with a different address of a plurality of addresses, each quantum element is assigned with its QESOP’ s respective address, and enabling the routing of the control sequences of each operation is performed by enabling the routing of the control sequences to quantum elements of the multiple quantum elements assigned with the respective QESOP address.

[0052] In various embodiments of the method, applying operations on the quantum elements is performed by applying control sequences on the quantum elements generated via a plurality of input signal sources. Each input signal source of the plurality of input signal sources is coupled with the quantum elements and configured to provide signals for operating each quantum element of the quantum elements.

[0053] In various embodiments of the method, each control sequence of the control sequences includes a time-dependent series of a plurality of control subsequences, and each control subsequence of the plurality of control subsequences includes a signal generated by asingle input signal source of the plurality of input signal sources at a time interval, or defines a time interval during which the plurality of input signal sources does not generate signals, where the method further includes providing instructions for generating the control sequences.

[0054] In accordance with aspects of the present disclosure, a system for controlling quantum elements is disclosed. The system includes a plurality of input signal sources configured to generate signals including at least two different input signal sources, where each input signal source is coupled with at least one quantum element of the quantum elements. The system further includes at least one controller configured to provide data signals including instructions, where the instructions are configured to cause the system to generate one or more control sequences, where the one or more control sequences are configured to apply one or more desired respective operation on the at least one quantum element, each control sequence of the one or more control sequences includes a time-dependent series of a plurality of control subsequences, and each control subsequence of the plurality of control subsequences includes a signal generated by a single input signal source of the plurality of input signal sources at a time interval, or defines a time interval during which the plurality of input signal sources does not generate signals. The controller is further configured to apply the one or more control sequences on the at least one quantum element thereby applying the desired one or more operations on the at least one quantum element.

[0055] In various embodiments of the system, there is provided a quantum processing unit which includes the system and the quantum elements.

[0056] In various embodiments of the system, the system further includes at least one combiner coupled with the plurality of input signal sources, the at least one controller and the at least one quantum element, the combiner configured to receive the data signals from the at least one controller and temporally output control subsequences includes signals generated by one or more input signal sources of the plurality of input signal sources according to the received instructions to the at least one quantum element.

[0057] In various embodiments of the system, the at least one controller includes at least one first controller coupled with the at least one combiner, configured to provide the data signals to the at least one combiner and at least one second controller coupled with the first controller and configured to calculate the one or more control sequences, store the instructions for generating the one or more control sequences in association with the corresponding one or more operations in a storage device, and access the instructions for generating the one or more control sequences, when required.

[0058] In various embodiments of the system, the at least one quantum element is a superconducting quantum element, and the at least one first controller is kept at a cryogenic temperature and the at least one second controller is kept at room temperature.

[0059] In various embodiments of the system, the at least one combiner is configured to temporally switch on or switch off each input signal source of one or more input signal sources of the plurality of input signal sources according to the received instructions.

[0060] In various embodiments of the system, the at least one combiner is configured to select, according to the received instruction, the input signal source of the plurality of input signal sources from which a signal is output to the at least one quantum element at a specific time.

[0061] In various embodiments of the system, the plurality of input signal sources is ordered according to a predefined order, and the at least one combiner is configured, upon receiving an instruction from the controller, to output a signal generated from the next input signal source of the plurality of input signal sources, according to the predefined order.

[0062] In various embodiments of the system, one or more instructions for generating a control sequence comprise a time dependent sequence of two or more triggers.

[0063] In various embodiments of the system, at least one combiner includes at least one multiplexer.

[0064] In various embodiments of the system, the plurality of input signal sources is configured to continuously generate signals, and the at least one multiplexer is configured to output a signal from a certain input signal source of the plurality of input signal sources at a time.

[0065] In various embodiments of the system, the at least one controller is further configured to timely provide an instruction for generating each control subsequences of a control sequence to the at least one combiner, and the at least one combiner is further configured, once the instruction is received, to immediately output a signal generated by the corresponding input signal source of the plurality of input signal sources to the at least one quantum element.

[0066] In various embodiments of the system, the system further includes at least one transmission line coupled with the at least one combiner and the at least one quantum element and configured to feed the output of the at least one combiner to the at least one quantum element.

[0067] In various embodiments of the system, the received data signals vary in time synchronized with a clock, and the clock has a frequency above 10 Mega Hertz (MHz) and below 10 Giga Hertz (GHz).

[0068] In various embodiments of the system the at least one combiner includes a first combiner and at least one second combiner, the first combiner coupled with the at least one second combiner; the at least one second combiner is coupled with one or more input signal sources of the plurality of input signal sources, the first combiner is configured to temporally output the control subsequences to the at least one quantum element, and each control subsequence outputted by the first combiner includes a signal outputted by a combiner of the at least one second combiner, or each control subsequence outputted by the first combiner includes a signal outputted by a combiner of the at least one second combiner or a signal generated by an input signal source of the plurality of input signal sources other than the one or more input signal sources.

[0069] In various embodiments of the system, the at least one quantum element and the first combiner are kept at a cryogenic temperature, and at least one combiner of the at least one second combiner is kept at a cryogenic temperature.

[0070] In various embodiments of the system, the at least one quantum element, the first combiner and the at least one second combiner are kept at a cryogenic temperature

[0071] In various embodiments of the system, the instructions include addresses of the input signal sources from which a signal is to be output by the at least one combiner per time.

[0072] In various embodiments of the system, the at least one quantum element is an at least one superconducting quantum element and where the at least one quantum element, and a combiner of the at least one combiner configured to output the control signal to the at least one quantum element, are kept at a cryogenic temperature.

[0073] In various embodiments of the system, the at least one controller is further configured to calculate one or more control sequences corresponding to one or more operations of interest, and instructions for generating each control sequence of the calculated one or more control sequences are stored in a storage device.

[0074] In various embodiments of the system, the one or more control sequences are calculated offline.

[0075] In various embodiments of the system, each of the at least two different input signal sources is of a different characteristic selected from: periodicity, phase shift, time delay, or amplitude.

[0076] In various embodiments of the system, the system further includes a measurement system. The measurement system includes at least one detector configured to measure one or more parameters of the at least one quantum element, where the measurement system is coupled with the at least one controller and the at least one quantum element, and where the at least one controller is further configured to calculate the control sequence based on the measured one or more parameters of the at least one quantum element received from the measurement system.

[0077] In various embodiments of the system, the one or more parameters are measured at predefined times or when required.

[0078] In various embodiments of the system, the one or more parameters include at least one parameter selected from: resonance frequency, anharmonicity, coherence properties and drive port coupling strength.

[0079] In various embodiments of the system, the at least one controller is further configured to suppress leakage to non computational states of the at least one quantum element when calculating a control sequence of the one or more control sequences of interest.

[0080] In various embodiments of the system, the plurality of input signal sources includes a plurality of Radio-Frequency (RF) analog signal sources.

[0081] In various embodiments of the system, the plurality of input signal sources includes a plurality of microwave signal sources.

[0082] In various embodiments of the system, the plurality of input signal sources includes a plurality of Single Flux Quantum (SFQ) signal sources.

[0083] In various embodiments of the system, at least one input signal source of the plurality of input signal sources is a null input signal source.

[0084] In various embodiments of the system, the at least one null input signal source is configured to emit a zero-amplitude pulse.

[0085] In various embodiments of the system, at least one input signal source of the plurality of input signal sources is a periodic signal source.

[0086] In various embodiments of the system, the plurality of input signal sources is periodic input signal sources, and where each input signal source of the plurality of input signal sources has a different period.

[0087] In various embodiments of the system, each input signal source of the plurality of input signal sources is a periodic input signal source, and where at least one input signal sourceof the plurality of input signal sources has a frequency different from a resonance frequency associated with one or more quantum elements of the at least one quantum element.

[0088] In various embodiments of the system, the plurality of input signal sources has frequencies different from a resonance frequency associated with the at least one quantum element.

[0089] In various embodiments of the system, the difference between a second or a higher harmonic of the least one frequency of the at least one input signal source and a resonance frequency associated with one or more quantum elements of the at least one quantum element is between one kilo Hertz (kHz) and 500 Mega Hertz (MHz).

[0090] In various embodiments of the system, the difference between at least one frequency of the at least one input signal source and a resonance frequency associated with one or more quantum elements of the at least one quantum element is between one kilo Hertz (kHz) and 500 Mega Hertz (MHz).

[0091] In various embodiments of the system, the desired operation is a single-qubit gate or a two qubit gate, and where when applied, the operation has gate infidelity lower than 0.005.

[0092] In various embodiments of the system, the at least one controller is further configured to decrease discretization errors due to its finite clock frequency when providing the data signals.

[0093] In various embodiments of the system, the at least one quantum element includes at least one qubit.

[0094] In various embodiments of the system, the at least one qubit includes a quantum dot, a spin qubit or a defect in a solid-state substrate.

[0095] In various embodiments of the system, the at least one quantum element includes at least one coupler element configured to couple between at least two qubits.

[0096] In various embodiments of the system, the at least one quantum element includes at least one resonator.

[0097] In various embodiments of the system, the at least one quantum element is an at least one superconducting quantum element.

[0098] In various embodiments of the system, the desired operation is a single-qubit gate, a two-qubit gate, a qubit initialization, a qubit reset, or a qubit measurement operation.

[0099] In various embodiments of the system, the plurality of input signal sources includes not more than ten input signal sources.

[0100] In various embodiments of the system, the quantum elements are arranged in sets of quantum elements, where not more than a single quantum element of each set of quantum elements is operated in parallel.

[0101] In various embodiments of the system, each input signal source of the plurality of input signal sources is coupled with the quantum elements.

[0102] In various embodiments of the system, the sets of quantum elements are arranged in cells, each cell of the cells including a single different set of quantum elements of the sets of quantum elements, where the cells are arranged in supercells, each supercell of the supercells including a different plurality of cells of the cells. The system further includes multiple control channels configured to provide the instructions, where each supercell of the multiple supercells is coupled with a different one or more control channels of the multiple control channels, and where each control channel of the multiple control channels is configured to provide the instructions to the plurality of cells of the respective supercell.

[0103] In various embodiments of the system, each quantum element of the quantum elements is assigned to a single Quantum Element Set of OPeration (QESOP) of a plurality of QESOPs, for each set of the quantum elements of the sets of quantum elements, each quantum element of the set of quantum elements is assigned to a different QESOP of the plurality of QESOPs, and only quantum elements assigned to the same QESOP of the plurality of QESOPs are operated in parallel.

[0104] In various embodiments of the system, the system further includes at least one routing control channel configured to cause the routing of the control sequences for applying each operation of the one or more desired operations on the quantum elements of the respective QESOP, where each routing control channel of the at least one routing control channel is configured to cause the routing of the control sequences by enabling the routing of the control sequences to at least a plurality of the quantum elements assigned to the respective QESOP.

[0105] In accordance with aspects of the present disclosure, a method for controlling at least one quantum element is disclosed. The method includes providing instructions for generating a control sequence designed to apply a desired operation on the at least one quantum element. The instructions includes a time dependent series of instructions configured to generate a time dependent series of control subsequences, the time dependent series of control subsequences forming the control sequence, where each instruction causes the generation and application of a control subsequence of the time dependent series of control subsequences on the at least one quantum element at its respective time, and each control subsequence of theplurality of control subsequences includes a signal and each control sequence includes at least two different signals.

[0106] In various embodiments of the method, the method further including calculating the control sequence.

[0107] In various embodiments of the method, the method further including storing the instructions for generating the control sequence and accessing the instructions when required.

[0108] In various embodiments of the method, providing the instructions for generating the control sequence is performed by at least one first controller, and calculating the control sequence and storing it are performed by at least one second controller, coupled with the at least one first controller. The method further includes providing the instructions to the at least one first controller by the at least one second controller.

[0109] In various embodiments of the method, the at least one quantum element is a superconducting quantum element, the at least one first controller is kept at a cryogenic temperature and the at least one second controller is kept at room temperature.

[0110] In various embodiments of the method, the method further includes accessing measured values of one or more parameters of the at least one quantum element, where the calculating of the control sequence is performed based on the measured values of the one or more parameters.[oni] In various embodiments of the method, the method further includes causing a measurement system including at least one detector and coupled with the at least one quantum element to measure the one or more parameters.

[0112] In various embodiments of the method, causing the measurement system to measure the one or more parameters is repeatedly performed.

[0113] In various embodiments of the method, the one or more parameters include at least one parameter selected from: resonance frequency, anharm oni city, coherence properties and drive port coupling strength.

[0114] In various embodiments of the method, the calculating of the control sequence includes suppressing leakage to non computational states of the at least one quantum element.

[0115] In various embodiments of the method, the control sequence is calculated offline.

[0116] In various embodiments of the method, the instructions are provided to at least one combiner, coupled with the at least one quantum element.

[0117] In various embodiments of the method, each instruction of the instructions for generating the control sequence causes the at least one combiner to output a signal generatedby a specific input signal source of a plurality of input signal sources, or cease to output a signal.

[0118] In various embodiments of the method, each instruction of the instructions for generating the control sequence which causes the at least one combiner to output a signal includes the address of the respective signal source configured to generate the output signal.

[0119] In various embodiments of the method, the plurality of input signal sources is ordered according to a predefined order, where each instruction of the instructions for generating the control sequence includes a trigger causing the at least one combiner to output a signal generated by the next input signal source of the plurality of input signal sources according to the predefined order.

[0120] In various embodiments of the method, each instruction of the instructions for generating the control sequence causes the at least one combiner to switch on or switch off each input signal source of one or more input signal sources of the plurality of input signal sources.

[0121] In various embodiments of the method, the plurality of input signal sources includes at least two different input signal sources, where each input signal source of the at least two different input signal sources is of a different characteristic selected from: periodicity, phase shift, time delay, or amplitude.

[0122] In various embodiments of the method, the providing of the instructions further includes timely providing each instruction of the time dependent series of instructions for generating each corresponding control subsequence of the time dependent series of control subsequences to the at least one combiner, causing to immediately output a signal to be applied on the at least one quantum element or cease the output of signals, according of the provided instruction.

[0123] In various embodiments of the method, the instructions for generating the control sequence are provided via at least one controller and the provision of the instructions is performed such that discretization errors due to the finite frequency of a clock of the at least one controller are decreased.

[0124] In various embodiments of the method, the method is for controlling multiple quantum elements arranged in sets of quantum elements. The method further includes applying the desired operation such that not more than a single quantum element of each set of quantum elements is operated in parallel.

[0125] In various embodiments of the method, the applying of the desired operation on the multiple quantum elements includes providing instructions for operating the multiple quantum elements via multiple control channels, where each control channel of the multiple control channels is configured to provide instructions for operating quantum elements of a different plurality of sets of quantum elements of the multiple sets of quantum elements.

[0126] In various embodiments of the method each quantum element of the multiple quantum elements is assigned to a single Quantum Element Set of OPeration (QESOP) of a plurality of QESOPs, for each set of the quantum elements of the sets of quantum elements, each quantum element of the set of quantum elements is assigned to a different QESOP of the plurality of QESOPs, and only quantum elements assigned to the same QESOP of the plurality of QESOPs are operated in parallel.

[0127] In various embodiments of the method, applying the desired operation includes causing the routing of control sequences for applying the operation by enabling the routing of the control sequences to at least a plurality of quantum elements of the multiple quantum elements assigned to the respective QESOP.

[0128] In accordance with aspects of the present disclosure, a further QPU is disclosed. The QPU includes multiple quantum elements, multiple splitting devices successively interconnected in one or more separate chains of splitting devices, each splitting device of the multiple splitting devices, which is not the last splitting device in a chain of the one or more chains of splitting devices, is configured to duplicate a received triggering signal to a first triggering signal and a second triggering signal, where the first triggering signal is configured to trigger output of information relating to a respective quantum element of the multiple quantum elements and the second triggering signal is transferred to the next interconnected splitting device in the respective chain of splitting devices.

[0129] In various embodiments of the QPU, the QPU further includes multiple memory elements, each memory element of the multiple memory elements is coupled with one or more quantum elements of the multiple quantum elements and with a different splitting device of the multiple splitting devices, where each memory element of the multiple memory elements is configured to store information received from its respective one or more quantum elements, and where the first triggering signal is configured to trigger output of information by triggering the respective memory element to output its stored information.

[0130] In various embodiments of the QPU, the QPU further includes one or more merging combiners, where each merging combiner of at least one merging combiner of the one or moremerging combiners is coupled with a plurality of memory elements of the multiple memory elements, such that the plurality of memory elements is coupled with splitting devices of the multiple splitting devices which are of the same chain of splitting devices, and where each merging combiner of the at least one merging combiner of the one or more merging combiners is configured to fan in information received from its respective plurality of memory elements to a single information output line.

[0131] In various embodiments of the QPU, each merging combiner of at least one merging combiner of the one or more merging combiners is coupled with a plurality of merging combiners of the rest of the one or more merging combiners and is configured to fan in information received from its respective plurality of merging combiners to a single information output line.

[0132] In various embodiments of the QPU, the QPU further includes multiple merging combiners successively interconnected in a chain of merging combiners, each merging combiner of the multiple merging combiners is coupled with a different memory element of the multiple memory elements, where each merging combiner of the multiple merging combiners is configured to receive information from its preceding merging combiner in the chain of merging combiners or from its respective memory element, and where each merging combiner of the multiple merging combiners, except for the last merging combiner in the chain of merging combiners, is configured to transfer the received information to the successively interconnected merging combiner, and the last merging combiner in the chain of merging combiners is configured to fan in its received information to a single information output line.

[0133] In various embodiments of the QPU, the QPU further includes one or more merging combiners, where each merging combiner of the one or more merging combiners is coupled with two or more information mediums of multiple information mediums, where the multiple information mediums include the multiple memory elements or merging combiners of the one or more merging combiners, and where at least one merging combiner of the one or more merging combiners is configured to fan in information received from its respective two or more information mediums to a single information output line.

[0134] In various embodiments of the QPU, at least one of the one or more merging combiners is designed with a dual-rail configuration.

[0135] In various embodiments of the QPU, the multiple memory elements are triggered once every error correction cycle of the quantum processing unit.

[0136] In various embodiments of the QPU, the multiple quantum elements are arranged in multiple sets of quantum elements, where the quantum processing unit is configured to operate not more than a single quantum element of each set of quantum elements in parallel.

[0137] In various embodiments of the QPU, each memory element of the multiple memory elements is coupled with a different set of quantum elements of the multiple sets of quantum elements.

[0138] In accordance with aspects of the present disclosure, a method for reading out information from multiple quantum elements is disclosed. The method includes duplicating a received triggering signal by each splitting device of multiple splitting devices successively interconnected in a chain of splitting devices, except for the last splitting device of the chain of the splitting devices, to a first triggering signal and a second triggering signal, utilizing the first triggering signal to trigger output of information relating to a respective quantum element of the multiple quantum elements, and transferring the second triggering signal to the next interconnected splitting device in the chain of splitting devices.

[0139] In various embodiments of the method, the method further includes providing a triggering signal to a first splitting device of the chain of splitting devices.

[0140] In various embodiments of the method, each splitting device of the chain of splitting devices is coupled with a memory element of a plurality of memory elements which is coupled with the respective quantum element, and for each splitting device of the chain of splitting devices, except from the last splitting device, triggering output of information relating to the respective quantum element includes triggering the coupled respective memory element to output information stored in the memory element and which was received from the respective quantum element.

[0141] In various embodiments of the method, each memory element of the plurality of memory elements is coupled with a different one splitting device of the plurality of splitting devices. The method then further includes fanning in information output by the plurality of memory elements to a single information output line.

[0142] In various embodiments of the method, the fanning in of the information output by the plurality of memory elements is performed via one or more merging combiners.

[0143] In various embodiments of the method, the triggering of the memory element is performed once every error correction cycle.

[0144] In various embodiments of the method, the multiple quantum elements are arranged in multiple sets of quantum elements, where not more than a single quantum element of each set of quantum elements is operated in parallel.

[0145] In various embodiments of the method, each memory element of the multiple memory elements is coupled with a different set of quantum elements of the multiple sets of quantum elements.

[0146] In accordance with aspects of the present disclosure, a quantum computing device is disclosed. The device includes a quantum processing unit including multiple quantum elements kept at a cryogenic temperature, where the quantum computing device is configured to send input signals from a temperature higher than the cryogenic temperature to the multiple quantum elements at the cryogenic temperature and to send output signals from the multiple quantum elements at the cryogenic temperature to the higher temperature, and one or more Josephson Transmission Line (JTL) devices disposed at one or more temperature levels, where at least one JTL of the one or more JTL devices is configured to amplify the output signals at a temperature level of the one or more temperature levels.

[0147] In various embodiments of the device, at least one temperature level of the one or more temperature levels is of a temperature between the cryogenic temperature and the higher temperature.

[0148] In various embodiments of the device, the one or more JTL devices include a plurality of JTL devices, and the one or more temperature levels include a plurality of temperature levels. At least a portion of the plurality of JTL devices is then configured to generate a JTL amplifier chain for gradually amplifying the output signals along temperature levels of the plurality of temperature levels.

[0149] In various embodiments of the device, the JTL amplifier chain includes the at least portion of plurality of JTL devices interconnected in series, each JTL device in the JTL amplifier chain having a plurality of progressively higher critical currents.

[0150] In various embodiments of the device, the rest of the plurality of JTL devices are configured to generate a JTL attenuator chain for gradually attenuating the input signals at one or more temperature levels of the plurality of temperature levels.

[0151] In various embodiments of the device, each JTL stage of each JTL device includes at least one Josephson Junction (JJ) designed to have a critical current value corresponding to the temperature level at which the respective JTL device is disposed.

[0152] In various embodiments of the device, the one or more temperature levels include a plurality of temperature levels, where each temperature level of the plurality of temperature levels is of a different temperature between the cryogenic temperature and the higher temperature.

[0153] In accordance with aspects of the present disclosure, a method for transferring signals in a cryogenic environment for quantum computing is disclosed. The method includes amplifying signals output by multiple quantum elements kept at a cryogenic temperature by one or more Josephson Transmission Line (JTL) devices, where the one or more JTL devices are disposed at one or more temperature levels, each temperature level equal to or higher than the cryogenic temperature.

[0154] In various embodiments of the method, at least one temperature level of the one or more temperature levels is of a temperature higher than the cryogenic temperature.

[0155] In various embodiments of the method, the one or more JTL devices include a plurality of JTL devices, the one or more temperature levels include a plurality of temperature levels, and the amplifying of the output signals includes gradually amplifying the output signals by a JTL amplifier chain comprising at least a portion of the plurality of JTL devices interconnected in series and disposed along the respective temperature levels.

[0156] In various embodiments of the method, each JTL device in the JTL amplifier chain has a plurality of progressively higher critical currents.

[0157] In various embodiments of the method, the method further includes gradually attenuating input signals transferred to the plurality of quantum elements from a temperature higher than the cryogenic temperature by a JTL attenuator chain including the rest of the plurality of JTL devices interconnected in series and disposed along the temperature levels, where at least one temperature level of the temperature levels is between the cryogenic temperature level and the higher temperature level.

[0158] In various embodiments of the method, each JTL stage of each JTL device of the one or more JTL devices includes at least one Josephson Junction (JJ) designed to have a critical current value corresponding to the temperature level at which the respective JTL device is disposed.

[0159] In various embodiments of the method, the one or more temperature levels include a plurality of temperature levels, and each temperature level of the plurality of temperature levels is of a different temperature between the cryogenic temperature and the higher temperature.BRIEF DESCRIPTION OF THE DRAWINGS

[0160] The above and other aspects and features of the disclosure will become more apparent in view of the following detailed description when taken in conjunction with the accompanying drawings wherein like reference numerals identify similar or identical elements.

[0161] FIG. 1 is a diagram illustrating a multi-layered hierarchy, in accordance with aspects of the disclosure;

[0162] FIG. 2 is a diagram illustrating a physical layout reflecting the multi-layered hierarchy of FIG. 1, in accordance with aspects of the disclosure;

[0163] FIG. 3 is a diagram illustrating an exemplary quantum error corrected QPU subdivided into repetitions of cells, in accordance with aspects of the disclosure;

[0164] FIG. 4 is a block diagram of an exemplary system for controlling quantum elements, in accordance with aspects of the disclosure;

[0165] FIG. 5 is a block diagram of another exemplary system for controlling quantum elements, in accordance with aspects of the disclosure;

[0166] FIG. 6 is a block diagram of a further exemplary system for controlling quantum elements, in accordance with aspects of the disclosure;

[0167] FIG. 7 is an illustration of an exemplary control operation on a Bloch sphere, in accordance with aspects of the present disclosure;

[0168] FIG. 8 is an illustration of a plurality of Bloch spheres illustrating a transmon dynamics for a calibrated 7t / 2-pulse gate around the x-axis, in accordance with aspects of the present disclosure;

[0169] FIG. 9 is a schematic illustration of an exemplary RF distribution network for an input signal source, in accordance with aspects of the present disclosure;

[0170] FIG. 10 is a schematic illustration of an exemplary RF distribution network for multiple frequencies on the same network, in accordance with aspects of the present disclosure;

[0171] FIG. 11 is a diagram of an exemplary implementation of a 4: 1 multiplexer, in accordance with aspects of the present disclosure;

[0172] FIG. 12 is a diagram illustrating the flow of quantum elements control with respect to the multi-layered hierarchy of FIG. 1, in accordance with aspects of the disclosure;

[0173] FIG. 13, is a conceptual illustration of control of quantum elements in a scalable system for quantum information processing, in accordance with aspects of the present disclosure;

[0174] FIG. 14 is the diagram of FIG. 2, further illustrating a physical layout of quantum elements control according to the multi-layered hierarchy of FIG. 1, in accordance with aspects of the disclosure;

[0175] FIG. 15A is a diagram illustrating quantum elements control in a module level, in accordance with aspects of the disclosure;

[0176] FIG. 15B is a diagram illustrating quantum elements control in a supercell level, in accordance with aspects of the disclosure;

[0177] FIG. 15C is a diagram illustrating quantum elements control in a cell level, in accordance with aspects of the disclosure;

[0178] FIG. 16 is a flow diagram of a method for controlling quantum elements, in accordance with aspects of the present disclosure;

[0179] FIG. 17 is a graph showing 7t / 2-pulse infidelity results for an exemplary system for quantum information processing, in accordance with aspects of the present disclosure;

[0180] FIG. 18 is a diagram illustrating routing of quantum elements control with respect to the multi-layered hierarchy of FIG. 1, in accordance with aspects of the disclosure;

[0181] FIG. 19 is an illustration of an exemplary current control for routing control, in accordance with aspects of the present disclosure;

[0182] FIG. 20 is a diagram of the physical layout of FIG. 2, further illustrating routing quantum elements control, in accordance with aspects of the disclosure;

[0183] FIG. 21 is a diagram illustrating the multi-layered hierarchy of FIG. 1, and further illustrating an over-all control of quantum elements, in accordance with aspects of the disclosure;

[0184] FIG. 22 is a diagram illustrating the layout of FIG. 2, further illustrating a physical layout of over-all control of quantum elements at a module level, in accordance with aspects of the disclosure;

[0185] FIG. 23 is a flow diagram of methods for controlling quantum elements and for routing the control, in accordance with aspects of the present disclosure;

[0186] FIG. 24 is a graph showing a Fourier spectrum of an SFQ signal train generated by modulating a single modulated a single input signal source, in accordance with aspects of the present disclosure;

[0187] FIG. 25A is a diagram illustrating readout in a quantum processing unit, in accordance with aspects of the present disclosure;

[0188] FIG. 25B is a diagram illustrating readout multiplexing in a quantum processing unit, in accordance with aspects of the present disclosure;

[0189] FIG. 25C is a diagram illustrating another readout multiplexing in a quantum processing unit, in accordance with aspects of the present disclosure;

[0190] FIG. 25D is a diagram illustrating a further readout multiplexing in a quantum processing unit, in accordance with aspects of the present disclosure;

[0191] FIG. 26 is a diagram a diagram of the multi layered hierarchy of FIG. 1, further illustrating readout multiplexing, in accordance with aspects of the disclosure;

[0192] FIG. 27A is a diagram of an exemplary cell measurement circuitry, in accordance with aspects of the present disclosure;

[0193] FIG. 27B is a diagram of an exemplary supercell measurement circuitry, in accordance with aspects of the present disclosure;

[0194] FIG. 27C is a diagram of multiplexing readout in a module, in accordance with aspects of the present disclosure;

[0195] FIG. 28 is a flow diagram of a method for readout, in accordance with aspects of the present disclosure;

[0196] FIG. 29 is a diagram illustrating a multi layered hierarchy according to FIG. 1, further illustrating over-all quantum elements’ control and readout multiplexing, in accordance with aspects of the disclosure;

[0197] Figure 30A is a schematic illustration of JTL devices placed at an intermediate temperature stage, in accordance with aspects of the present disclosure; and

[0198] Figure 30B is a schematic illustration of an exemplary JTL device, in accordance with aspects of the present disclosure.

[0199] It will be appreciated that for simplicity and clarity of illustration, elements shown in the figures have not necessarily been drawn to scale. For example, the dimensions and / or aspect ratio of some of the elements can be exaggerated relative to other elements for clarity. Further, where considered appropriate, reference numerals can be repeated among the figures to indicate corresponding or analogous elements throughout the serial views.DETAILED DESCRIPTION

[0200] The present disclosure relates to systems, devices, methods and architectures for quantum computing. More particularly, the present disclosure relates to systems, devices, methods and architectures for designing, constructing or using in quantum computers, and insuperconducting quantum computers, in particular, or for constructing scalable quantum computers, e.g., with cryogenic control hardware that use, inter alia, extensive parallelism and multiplexing.

[0201] The disclosure simultaneously addresses crucial factors, such as cable count, heat load, footprint, and data throughput, all together while supporting high-fidelity quantum operations.

[0202] Superconducting quantum computers have demonstrated error correction beyond the fault-tolerance threshold, but running valuable quantum algorithms requires scaling to millions of physical qubits while maintaining performance. A major challenge is the inputoutput bottleneck, as each qubit, kept at millikelvin temperatures, requires connection to roomtemperature radio-frequency control and measurement equipment.

[0203] The present disclosure provides a unique architecture utilizing SFQ circuits specialized for millikelvin temperatures to realize an integrated superconducting quantum processor. Designed for quantum error correction, it features individually calibrated, massively parallel operations and a compressed instruction set operating at millikelvin (mK) temperatures. The disclosed solution dramatically reduces heat dissipation, data throughput, input / output (I / O) overhead, and component count, all while maintaining error rates below the fault-tolerance threshold. Performed simulations have demonstrated support of over one million qubits with under 500 microwatts (pW) and 10,000 input-output channels, while keeping error rates below 0.1% per quantum operation.

[0204] The key to the disclosed approach is holistic massive scaling targeted for quantum error correction. Ultra-low power logic at mK temperatures may be utilized, which drastically reduces input-output channels and data throughput.

[0205] The core of a superconducting quantum computer is the QPU, which hosts qubits (e.g., transmon or fluxonium), readout resonators, and couplers, operating at millikelvin temperatures in dilution refrigerators. Control electronics outside the cryostat generate and acquire RF signals delivered through heavy filtering, bulky components, multiple cables, and amplification generating significant heat, occupying space, and requiring complex calibration.

[0206] Currently, qubits and quantum elements are placed in the QPU, while supporting circuitry is housed on stacked interface Integrated Circuits (ICs) above or below it. This design aids integration and maintains a clean electromagnetic environment, preserving qubit performance. Despite advancements, utility-scale quantum computers remain elusive. The number of qubits per cryostat is limited to several thousand due to heating and spaceconstraints. Interconnecting multiple cryostats via quantum links is challenging and costly. Integrating cryo-CMOS at around 4 Kelvin reduces wiring between room temperature and the 4 K stage but does not solve scalability issues at millikelvin temperatures. Moreover, heat generated by cryo-CMOS still limits qubits per cryostat to a few thousand. Thus, achieving millions of qubits remains a formidable challenge.

[0207] This challenge may be tackled from a full system, massive scale perspective. A scalable architecture must holistically consider the various aforementioned problems. On the technical level, this approach entails, inter alia, using modified SFQ circuitry with ultra-low heat dissipation at millikelvin temperatures, exploiting the structure of quantum error correction codes to multiplex the control architecture and parallelize gate applications and using compressed instruction sets and decoding into control signals to allow for custom high- fidelity gate operations for each quantum element while maintaining low cable count and data throughput.

[0208] The disclosure enables a dramatic increase in the number of qubits per cryostat, e.g., to above one million, while maintaining below-threshold gate errors. The disclosed approach distinguishes itself, inter alia, by being exclusively designed for quantum error correction, enabling extensive parallelism. According to some aspects, this specialization may achieve a reduction in data throughput, e.g., by at least 40times, and may decrease the heat load, e.g., by more than 100 times, compared to conventional SFQ methods. These figures result from simulations using realistic parameters.

[0209] The disclosed approach for building a utility-scale quantum computer overcomes several significant challenges. Since utility-scale quantum computing is estimated to require approximately one million qubits, a critical question arises with respect to the feasibility of an architecture based on SFQ circuits that can significantly increase the number of qubits per cryostat. Managing excessive heat load, wiring complexity, and the vast amount of data transmission to millikelvin temperatures presents a major challenge, especially while maintaining sufficiently high-fidelity operations. The disclosed architectural and circuit designs, as well as simulations, have demonstrated that achieving this level of scaling is feasible while maintaining the necessary system performance.

[0210] Furthermore, achieving high fidelity in SFQ-based systems is a significant challenge. The high bandwidth of each pulse can cause errors due to leakage to higher qubit levels. The disclosure addresses these challenges and demonstrates fidelities below IE-3 using the disclosed optimized hardware design and an efficient optimizer for gate instruction sets.

[0211] According to some aspects, QEs control circuitry is placed in a dedicated control chip adjacent to the quantum chip at milli-Kelvin (mK) temperatures. The control chip, which in itself is managed by a co-processor at room temperature or at a warmer stage of the cryostat, may handle control pulse generation, measurement acquisition, and signal distribution to the quantum elements (e.g., qubits).

[0212] The control chip, which may be kept, for example, at 10 mK, must be energyefficient to prevent heating the cryostat or the quantum elements themselves. Thus, superconducting classical electronics may be used. Superconducting electronics may be based on Single-Flux Quantum (SFQ) logic, which uses current pulses instead of the digital voltages of semiconductor electronics. The transistor as the fundamental element in semiconductor electronics is replaced by a Josephson Junction (JJ). Unlike conventional semiconductor circuits, superconducting circuits require cryogenic temperatures. However, they can operate at significantly higher speeds (e.g., in a range of frequencies measured in tens to hundreds of Gigahertz (GHz)) and produce minimal heat, thanks to their superconducting nature.

[0213] According to some aspects, a QPU is divided into a hierarchy of levels. According to some aspects, the hierarchy of levels may include a plurality of modules, where each module includes a plurality of supercells, and each supercell includes a plurality of cells. Each cell may include a plurality of quantum elements. The hierarchy of levels may be used for streamlining the control data flow.

[0214] Large-scale quantum computers executing fault-tolerant quantum circuits need to rely on quantum error corrected logical qubits. A QEC approach encodes logical qubits redundantly in a plurality of physical qubits rather than in a single physical qubit. This is one of the main reasons useful quantum computers are required to have physical qubit counts in the millions. The redundant encoding prevents noise from corrupting the computation. QEC takes up the vast majority of the quantum computer’s operation, requiring continuous removal of errors from the QPU. However, these operations are highly repetitive and identical for small groups of qubits. While the present disclosure particularly refers to the fault-tolerant storage of quantum information, similar principles can be applied to e.g., the fault-tolerant processing of quantum information and the distillation of magic states.

[0215] According to some aspects, disclosed systems, devices, methods and architectures are compatible with Quantum Error Correction (QEC) protocols, which are highly-important for fault-tolerant quantum computers. This focus on QEC allows a high degree of parallelism in control and leads to massive reduction in data throughput.

[0216] A significant simplification of the architecture may be achieved using the self-timed nature of the control. This allows employing asynchronous circuit designs and selfsynchronizing circuit design (e.g., dual-rail) instead of utilizing a clock distribution network to synchronize the signal delivery. A clock distribution network is a difficult resource to scale, costly in terms of heat load, and architecturally complex, e.g., by requiring additional fabrication layers. According to the disclosure there is no longer need for a clock distribution network typically found in SFQ circuits, by that greatly simplifying the quantum computing architecture and its realization.

[0217] According to some aspects, the disclosure provides asynchronous SFQ circuits, thus not necessitating clock distribution.

[0218] According to some aspects, a redesigned efficient classical-quantum interface is provided, such as qubit control.

[0219] According to some aspects, a QPU including multiple quantum elements arranged in sets of quantum elements is disclosed. The QPU principle of operation may include operating not more than a single quantum element of each set of quantum elements in parallel. According to some aspects, the QPU principle of operation may include applying operations on the multiple quantum elements, such that each operation is applied on not more than a single quantum element of each set of quantum elements. According to some aspects of the disclosure, each quantum element of a QPU may be assigned to a single Quantum Elements Set of OPeration (QUESOP) of a plurality of Quantum Elements Set of Operations (QESOPs). The QPU principle of operation may then include operating in parallel only quantum elements which are of the same QESOP.

[0220] According to some aspects, an efficient readout mechanism and readout multiplexing to be utilized in a QPU, in general, and through the levels of the disclosed multilayered architecture, in particular, are further disclosed. In the current state of the art, each qubit measurement is output in a separate output cable or transmission line, preventing scaling to above a few thousand qubits. Reducing the output bottleneck is therefore equally important to reducing the input bottleneck.

[0221] According to some aspects, there are disclosed systems, devices and methods for efficiently sending signals to progressively lower temperature stages of a QPU or of a quantum computer with minimal heat dissipation and maximal noise filtration, as well as transmitting signals from the lowest temperature through progressively higher temperatures without compromising Signal to Noise Ratio (SNR).

[0222] The term “operation” as used herein with respect to quantum elements may include operations applied on quantum elements such as a qubit measurement, a qubit initialization, a qubit reset or a gate such as a single qubit gate, two-qubit gate etc..

[0223] The terms “signal generator” and “signal source” and their respective derivatives may be used interchangeably. The term “signal”, as used herein, may refer to data transmitted by a single input signal source during a time period. The term “signal”, as referred to herein, may relate to an analog signal, an SFQ signal, an analog signal converted to SFQ signal and vice versa and the like.

[0224] The terms “current control” and “control current” and their derivations may be used interchangeably. The terms “measurement” and “readout” and their derivations may be used interchangeably.

[0225] Although the disclosure is not limited in this regard, the terms “plurality” and “a plurality” as used herein may include, for example, “multiple” or “two or more.” The terms “plurality” or “a plurality” may be used throughout the specification to describe two or more components, devices, elements, units, parameters, or the like.

[0226] Although the disclosure is not limited in this regard, by using the term “or” when listing two or more items or options, it is meant that each item, and each plausible or feasible combination of the listed items including a combination of all listed items may be considered.

[0227] Unless explicitly stated, the methods described herein are not constrained to a particular order or sequence. Additionally, some of the methods described or elements thereof can occur or be performed simultaneously, at the same point in time, or concurrently.

[0228] In the following detailed description, specific details are set forth in order to provide a thorough understanding of the disclosure. However, it will be understood by those skilled in the art that the disclosure may be practiced without these specific details. In other instances, well-known methods, procedures, and components have not been described in detail so as not to obscure the present disclosure. Some features or elements described with respect to one system may be combined with features or elements described with respect to other systems. For the sake of clarity, discussion of same or similar features or elements may not be repeated.

[0229] A QPU according to the disclosure may include multiple quantum elements arranged in multiple sets of quantum elements. The QPU may be configured to operate not more than a single quantum element of each set of quantum elements in parallel. The term “operate” as used herein with respect to quantum elements may include the application of quantum operations on the quantum elements. It should be noted that while the operation isapplied to a single quantum element of each set of quantum elements, the operation may influence, may be designed to influence or may be designed with respect to another quantum element, which may be of the same set of quantum elements or of a different set of quantum elements. For example, a measurement operation may be applied on a resonator which is coupled with a qubit to be measured. The operation is applied on the resonator but is aimed to measure its coupled qubit. The qubit may be of the same set of quantum elements as its coupled resonator. As another example, a two-qubits gate operation may be applied on a coupler coupling between two qubits. Although the operation is applied on the coupler, it is designed to influence its coupled qubits. Two or more quantum elements of the coupler and the qubits may be of the same set of quantum elements or of a different set of quantum elements.

[0230] An operation may also be an identity operation (e.g., multiplying by a unit matrix) or other operations which act trivially on the quantum element. The terms “operation” and “gate” may be used interchangeably throughout the disclosure. The time during which an operation is applied to a quantum element (e.g., starting when the first signal of the operation is applied to the quantum element and ending when the last signal of the operation is applied to the quantum element) will be referred to herein as the operation time of the quantum element with respect to the specific operation. Quantum elements are operated in parallel when the quantum elements have overlapping periods of operation time, where the entire operation time of the quantum elements may not necessarily overlap. According to some aspects, the QPU is configured to apply each operation to not more than a single quantum element of each set of quantum elements.

[0231] According to some aspects, the QPU may be configured to apply at least one measurement operation once in each cycle of operations. Each cycle of operations may include the application of one or more operations, and each measurement operation may be configured to measure only a single quantum element of each set of quantum elements.

[0232] According to some aspects, each quantum element of the multiple quantum elements may be assigned to a single Quantum Elements Set of OPeration (QESOP) of a plurality of Quantum Elements Set of Operations (QESOPs). The quantum processing unit may be configured to operate in parallel only quantum elements which are of the same QESOP. According to some aspects, the quantum processing unit is configured to apply operations on the multiple quantum elements, where each operation is applied on at least a plurality of quantum elements of the multiple quantum elements. According to some aspects, each QESOP includes a plurality of quantum elements, and each operation is applied only to quantumelements of a single QESOP of the plurality of QESOPs. According to some aspects, each quantum element of each set of quantum elements is assigned to a different QESOP.

[0233] According to some aspects, a QPU according to the disclosure may include multiple cells. Each cell may include a respective set of quantum elements. According to some aspects, each cell of the QPU may include a predefined number of quantum elements or up to a predefined number of quantum elements (e.g., up to a number equal to or between 10 and 50). The multiple cells may be of one or more types, e.g., of two types. The types may be, for example, a type for applying quantum error correction, a type for applying magic state distillation, or a type for ancillary qubits. According to some aspects, the multiple cells may be arranged in a periodic pattern.

[0234] According to some aspects, a QPU according to the disclosure may further include multiple supercells. The multiple cells may be arranged in sets of cells where each supercell includes a respective set of cells. According to some aspects, each supercell may include a predefined number of cells or up to a predefined number of cells (e.g., up to a predefined number equal to or between 10 and 100).

[0235] According to some aspects, a QPU according to the disclosure may further include at least one module. The multiple supercells may be arranged in one or more sets of supercells, where each module includes a respective set of supercells.

[0236] Reference is now made to FIG. 1, which is a diagram illustrating a multi-layered hierarchy 10 of a QPU according to the disclosure. Multi-layered hierarchy 10 includes a plurality of logical or conceptual layers. Multi-layered hierarchy 10 may include a first, lowest, quantum elements layer 20, a second cells layer 14, a third supercells layer 16, a fourth modules layer 18 and a fifth, highest layer, QPU layer 20. Quantum elements layer 20 may include the multiple QEs of the QPU. Cells layer 14 may include multiple cells where each cell includes a single different set of the QEs and each set of QEs includes a plurality of QEs. Supercells layer 16 may include multiple supercells, where each supercell includes a single different set of the cells and each set of cells may include a plurality of cells. Modules layer 18 may include one or more modules. Each module may include a plurality of supercells or a set of supercells. QPU layer 20, which is the highest layer, may include one or more modules. According to some aspects, each of the modules corresponds to a single motherboard within the QPU. According to some aspects, each supercell corresponds to a single die or chip stack. According to some aspects, the cells may be unit cells in the quantum error correction operation of the QPU (e.g., the quantum elements included in a plaquette and star pair in the surface code architecture).

[0237] A person skilled in the art will recognize a variety of configurations for a hierarchy and a multi-layered hierarchy, in particular, following the disclosed QPU operation principles. For example, according to some aspects, a QPU hierarchy according to the disclosure may include only the lowest and the highest layers, e.g., QEs layer 12 and QPU layer 20. According to some aspects, a QPU hierarchy according to the disclosure may include in addition to QEs layer 12 and QPU layer 20, one or more middle layers such as cells layer 14, supercells layer 16, or modules layer 18. According to some aspects, a QPU hierarchy according to the disclosure may include middle layers, in addition to middle layers: cells layer 14, supercells layer 16 and modules layer 18.

[0238] According to some aspects scaling of a QPU constructed according to multi-layered hierarchy 10 may be performed, for example, by adding one or more additional supercells to supercells layer 16 or by adding one or more additional modules to modules layer 18.

[0239] Reference is now made to FIG. 2, which shows a diagram illustrating a physical layout 50 reflecting multi-layered hierarchy 10 of FIG. 1. According to some aspects, physical layout 50 may be a physical layout of at least a portion of a module according to hierarchy 10 of FIG. 1. Layout 50 may include multiple supercells such as supercell 58 (nine overall shown in FIG. 2). Each supercell such as supercell 58 includes three stacked chips 60 A, 60B and 60C, however any other number of stacked chips may be utilized. Stacked chips 60A-60C may include, for example, a QEs chip, a control chip, a readout chip an interposer chip, a wiring chip, and the like. Each supercell, such as supercell 58, may include a cells layout such as cell layout 62 of supercell 58. Cells layout 62 includes a plurality of cells arranged in a periodic or repeated pattern.

[0240] According to some aspects, cells of a QPU according to the disclosure may be arranged in one or more periodic patterns. A periodic pattern may refer to, for example, a spatial periodicity in the number of quantum elements or the maximal number of quantum elements in each cell, the connectivity of the cells or the function of the cells. According to some aspects, each supercell may include a predefined number of cells or up to a predefined number of cells. According to some aspects, each cell of the QPU may include a predefined number of QEs or up to a predefined number of QEs. According to some aspects, the cells may be of one or more types. Cells of different types may differ, for example, in functionality, the types of the quantum elements included in the cell or the number of quantum elements included in the cell. Reference is now made to FIG. 3 which shows a diagram illustrating an exemplary quantum error corrected layout 40 of a QPU subdivided into repetitions of cells, using a surface code.The quantum error corrected QPU is subdivided into repetitions of cells marked by rectangles, such as rectangle 44 (or cell 44). Each rectangle or cell such as cell 44 includes a plurality of QEs such as QE 42 (indicated by black dots). Each QE is included in a single cell. For example, QE 42 is included in cell 44. For example, each cell may include 16 quantum elements: 4 qubits, 4 readout resonators and 8 coupling elements, while according to some aspects of the disclosure, none of which need to be operated simultaneously. This layout of cells may represent a portion of a cells layer (cell layer 14) according to hierarchy 10 of FIG. 1. According to disclosed principles of operation, each cell may be designed to encapsulate a single operation per time instance. According to some aspects, each cell may be integrated with error correction code structure. Each cell of layout 40, such as cell 44, may include one or more units of error correction such as a Z-type stabilizer measurement unit 46A (indicated by clear plus symbol) and an X-type stabilizer measurement unit 46B (indicated by stripped plus symbol). According to some aspects, each cell tiles the entire surface.

[0241] According to some aspects, the repetitive nature of QEC across cells or in time may be leveraged to significantly simplify and parallelize the control hardware of the QPU and to reduce data throughput, cooling power, and footprint requirements. Since only one operation needs to be applied at a time within a single cell, a single controller may be used per cell and route the control sequence to the correct element within the cell at each time, as will be further discussed below.

[0242] Multiplexing control for a cell reduces the number of input signal sources (will be also referred as “signal sources” or “signal generator”) per cell. However, there is still a very large number of cells within a QPU. Moreover, the signal sequences that need to be sent to qubits are usually very complex and can differ from quantum element to quantum element or from one time to the next. Therefore, a significant amount of memory is required to store the control pulse sequences to be delivered to the quantum elements. Unfortunately, memory in SFQ circuits is a difficult resource to scale and architecturally complex. Disclosed systems and methods significantly reduce the complexity of the signal sources, requiring no memory at the lowest temperature stage and only minimal memory at elevated temperature stages, e.g., leading to a 100-fold reduction in the memory instruction set.

[0243] According to the disclosure, turning on / off or switching between a low number of fixed signal sources can be used to control a wide variety of quantum elements having different parameters. What changes is not the signal sources (or the signals), but only which signal or which signal source output is sent through to a quantum element at any given time. A relativelylow number of signals from fixed signal sources may then be used. The signals may be sent to the control chip from room temperature or from an additional processor at an intermediate temperature stage. According to some aspects, each cell may include at least one combiner (e.g., a multiplexer). According to some aspects, a sparse input-selection signal may be used to provide instructions for toggling from one signal source to another.

[0244] According to some aspects, the disclosed control sequence generation circuits reduce the data throughput required for controlling quantum elements by switching between a plurality of signal sources, thereby creating a concatenated control signal or a control signal including alternating control subsequences. The switching between the different signal sources is achieved using, e.g., a multiplexing device. The multiplexer is fed by signal source selection data for selecting the signal from a specific signal source to be transmitted at a specific time.

[0245] A control sequence according to the disclosure may include a sequence of e.g., SFQ signals or signals generated by using a plurality of signal sources. The signal source selection data can be determined using real-time calibration data, e.g., obtained from calibration measurements of the quantum element that receives the control. The calibration measurements can be performed, for example, by using spectroscopic methods or time-domain methods.

[0246] High-fidelity operations on a quantum element can be obtained using a low number of predetermined signal sources, irrespective of the precise parameters of the quantum element, by only modifying the signal source selection data. According to some aspects, each signal source of the signal sources emits a periodic signal with different periodicities. According to some aspects, the periodic signal sources may include one or more null signal sources, which, for example, emit zero-amplitude signals. A concatenated control sequence generated from a timed selection of such periodic signals can generate high-fidelity single-qubit gates, two-qubit gates, initialization, or measurement operations that are robust to variations, e.g., in the resonant frequency or anharmonicity of the quantum element.

[0247] Each periodic signal rotates the quantum state of the qubit represented by a unit vector on the qubit Bloch sphere around a specific axis with a specific rotation rate. This is the same dynamics known as Rabi oscillations. The rotation axis and rotation rate depend on the frequency detuning, the phase of the signal or the amplitude of the periodic signal. When the frequency of a signal source matches the resonance frequency of the qubit the rotation is around an equatorial axis, however this matching condition is unlikely to be met in practice for predetermined sources. Thus, sources that are arbitrarily detuned from the qubit frequency within a certain detuning window may be used. According to the disclosed systems andmethods, differences between a quantum element resonance frequency and the signal sources frequencies of magnitude of tens of MHz may be used. By using a plurality of periodic signal sources, the qubit can be made to rotate around a plurality of axes of the qubit’s Bloch sphere, thus enabling the desired target operation to be applied. It may be shown that sequential rotations around any two non-aligned axes on the Bloch sphere can bring the state from any point on the Bloch sphere to any other point. It should also be noted that a null source creates an effective rotation around the z-axis. It was found that turning on and off only two sources is sufficient to generate arbitrary operations with high fidelities, e.g., at the 99.9% level.

[0248] For a system with more levels, e.g., a transmon, the spectral content of the periodic sources will be of significance. This is because higher frequencies can coincide with a transition to the higher transmon levels. If one considers a periodic train of SFQ signals, the spectral distribution will be a sine function, that is a large spectral peak at the frequency corresponding to the period and smaller peaks at multiples of the frequency corresponding to the period, with decaying tail for each peak. The effect of these can be calculated and the time of turning on and off the different signal sources can be adjusted to suppress spectral components that are adversely affecting the gate fidelity. Although the Bloch sphere model is not valid for more than two levels, the qualitative picture of combinations of Rabi rotations around different axes remains valid.

[0249] According to some aspects, a quantum processing unit may include multiple quantum elements and a plurality of input signal sources including at least two different input signal sources. Each input signal source may be coupled with at least a plurality of the quantum elements. The quantum processing unit may be configured to generate a control sequence configured to apply a desired respective operation on at quantum elements of the multiple quantum elements. The control sequence may include a time-dependent series of a plurality of control subsequences. Each control subsequence may include a signal generated by a single input signal source of the plurality of input signal sources at a time interval or may define a time interval during which the plurality of input signal sources does not generate signals. The QPU may be further configured to apply the control sequence on the quantum elements thereby applying the desired operation on the quantum elements. According to some aspects, the control sequences may be provided to the quantum elements via combiners. According to some aspects, each combiner is coupled with a single quantum element. According to some aspects, each combiner is coupled with a set of quantum elements (e.g., a combiner per cell).

[0250] Various methods to realize signal sources or signal generators which output constant frequency SFQ signals may be used. These include on-chip signal generators, such as the various Josephson Transmission Line (JTL) ring oscillators and DC voltage-controlled oscillators. A highly heat-efficient method is to directly bring an RF / microwave signal from an external source (for example, a source kept at room temperature) and feed it into a DC to SFQ (DC2SFQ) converter at cryogenic temperatures, converting microwave signals to SFQ signals at corresponding frequencies. The downside of such a method is that if quantum elements in each cell required signals of slightly different frequency, then one would need an external RF generator for each cell, which does not scale. The disclosed architecture and specifically, the disclosed systems and methods for control sequence generation, may work with signal sources having any frequency within a certain frequency range to generate all required SFQ signal sequences. Thus, only a low number of external RF sources split into the different cells are required, without additional circuitry.

[0251] The signal source selection data or the instructions for generating a control sequence may be delivered through one control channel or one cable per supercell (chip stack). The signals delivered for each supercell may be calculated by a controller at a higher temperature. A Josephson Transmission Line (JTL) may be used for filtering and matching the input from the higher temperature before routing into the Passive Transistor Logic (PTL) that leads to the corresponding supercell.

[0252] Systems and methods for delivering control sequences to quantum elements, e.g., in quantum processors, are disclosed. According to some aspects, control sequences are formed by concatenating subsequences selected from predetermined input signals. According to some aspects, the predetermined input signals are provided in real-time by predetermined input signal sources. According to some aspects, the disclosed systems and methods utilize at least one combiner controlled by a sparse data signal over time to select the predetermined input signals at specific times for transmission to the quantum element.

[0253] The disclosed systems and methods for quantum elements control reduce the data throughput and heat dissipation required for controlling quantum elements, e.g., by switching between a plurality of signal sources, thereby creating a concatenated control signal consisting of alternating control subsequences. The switching between the different signal sources may be achieved by using a combiner or a multiplexing device. The combiner or multiplexer is fed by data signals for selecting a signal from a specific signal source to be transmitted at a specifictime. The input selection data can be determined using real-time calibration data obtained from calibration measurements of the quantum elements.

[0254] According to the disclosed systems and methods for quantum elements control, the same set of input signal sources may be used for multiple quantum elements having various resonance frequencies, as opposed to using a different signal source, corresponding to the quantum element’s resonance frequency, for each quantum element. Furthermore, according to some aspects, only switching to an input signal source, or to a specific input signal source, at the right time, may be needed for applying an operation. Thus, high-fidelity operations on a quantum element may be obtained, using a low number of predetermined input signal sources, irrespective of the precise parameters of the quantum element, by only modifying the input control data. Moreover, the disclosed systems and methods may allow sending little information or significantly less information, compared to the state of the art, for controlling a quantum element. This may be particularly advantageous when the information is provided to a cryogenic environment.

[0255] According to some aspects, each of the input signal sources emits a periodic signal with a different periodicity. According to some aspects, the input signal sources may include a null signal source, e.g., emitting a zero-amplitude signal. A concatenated control sequence generated from a timed selection of periodic signals according to the disclosure can generate high-fidelity single-qubit gates, two-qubit gates, initialization or measurement operations for a range of resonant frequencies or anharmonicities of the quantum element. Each periodic signal may rotate the quantum state of the qubit represented by a unit vector on the qubit Bloch sphere around a specific axis with a specific rotation rate, while the rotation axis and rotation rate depend on the frequency, phase and amplitude of the periodic signal. The frequencies of the signal sources do not have to match the resonance frequency of the qubit. By using a plurality of periodic signal sources, the qubit can be made to rotate around a plurality of axes of the qubit’s Bloch sphere, thus enabling the desired target operation to be applied.

[0256] The disclosed systems and methods for QEs control may provide single-qubit and two-qubit gates with gate infidelities below 0.005 or even 0.001, where the frequency difference between a periodic input signal and the qubit resonance frequency can be, for example, between one kilo Hertz (kHz) and 500 Mega Hertz (MHz). The disclosed systems and methods may also be used to generate high-fidelity operations that protect against the unwanted transitions of qubit states to non-computational quantum states.

[0257] The disclosed systems and methods may allow the generation of complex signal sequences with little data or based on minimal data. A few instructions may be used to control a quantum element in an accurate manner. Signals and control sequences, in particular, are not stored but only the instructions on how to concatenate or generate the signal sequence from subsequences provided by a given set of plurality of input signal sources are stored.

[0258] Referring to FIG. 4, there is shown a diagram of an exemplary system 100 for controlling quantum elements 140A, 140B,. . . 140M, where M is a natural number equal to or greater than one (M>1). System 100 includes a plurality of input signal sources 110A, HOB, . . . 110N, where N is a natural number greater than one (N>1). According to some aspects, at least two of the N input signal sources are different. According to some aspects, each input signal source of the N signal sources is different from the rest of the input signal sources. System 100 further includes at least one combiner 120 and at least one controller 130. Combiner 120 is coupled with input signal sources 110A-110N, controller 130 and quantum elements 140A-140M. Controller 130 is configured to provide data signals including instructions to combiner 120. Combiner 120 is configured to receive the data signals from controller 130. The data signals may include instructions for generating one or more control sequences. The control sequences may be configured to apply one or more desired operations on quantum elements 140A-140M. The operations may include a single-qubit gate, a two-qubit gate, an initialization, or a quantum measurement operation. A control sequence includes a time-dependent series of a plurality of control subsequences. A control subsequence may include a signal to be emitted or generated by a single input signal source of input signal sources 110A-110N at or during a time interval. A control subsequence may be a null subsequence. Depending on the design of system 100, a null subsequence may include a signal (e.g., a zeroamplitude signal) generated by a null input signal source of input signal sources 110A-110N or may define or may be a time interval during which input signal sources 110A-110N do not emit or generate a signal (e.g., input signal sources 110A-110N are turned off or not selected bythe combiner). Combiner 120 may then temporally output control subsequences including signals generated by one or more input signal sources of input signal sources 110A-110N according to the instructions received from controller 130 to quantum elements 140A-140M. Thus, desired operations may be applied on quantum elements 140A-140M.

[0259] According to some aspects, input signal sources 110A-110N include Radio-Frequency (RF) analog input signal sources. According to some aspects, input signalsources 110A-1 ION may include microwave input signal sources. According to some aspects, input signal sources 110A-1 ION include SFQ input signal sources.

[0260] According to some aspects, input signal sources of input signal sources 110A-1 ION may be different one from the other by including at least one different characteristic. According to some aspects, the at least one different characteristic may be periodicity, phase shift, time delay, or amplitude. According to some aspects, a set of input signal sources of the disclosed systems, such as the set of input signal sources 110A-1 ION is predetermined.

[0261] According to some aspects, at least one input signal source of input signal sources 110A-1 ION is a periodic signal source. According to some aspects, input signal sources 110A- 11 ON are periodic input signal sources, where each input signal source of input signal sources 110A-1 ION has a different period. According to some aspects, input signal sources 110A-1 ION are periodic input signal sources, where at least one input signal source of input signal sources 110A-110N has a frequency different from the resonance frequency associated with at least one quantum element of quantum elements 140A-140M. According to some aspects, input signal sources 110A-1 ION have frequencies different from the resonance frequency associated with at least one quantum element of quantum elements 140A-140M. According to some aspects, input signal sources 110A-110N have frequencies different from the resonance frequencies associated with quantum elements 140A-140M. According to some aspects, the difference between a frequency of at least one input signal source of input signal sources 110A-110N and the resonance frequency associated with at least one quantum element of quantum elements 140A-140M is equal to or greater than one kHz, 10 kHz, 100 kHz, one MHz, 10 MHz, 100 MHz or 300 MHz. According to some aspects, the above differences between the frequency of at least one input signal source of input signal sources 110A-110N and the resonance frequency associated with at least one quantum element of quantum elements 140A-140M are further equal to or below 500 MHz, 400 MHz, 300 MHz, 200 MHz or 100 MHz. According to some aspects, the difference between a second or higher harmonic of the frequency of at least one input signal source of input signal sources 110A-110N and the resonance frequency associated with at least one quantum element of quantum elements 140A-140M is between one kilo Hertz (KHz) and 500 Mega Hertz (MHz).

[0262] Controller 130 may be or may include one or more hardware processors (e.g., general -purpose or classical hardware processors), Application-Specific Integrated Circuits (ASICs), Field-Programmable Gate Arrays (FPGAs), or SFQ circuits. According to some aspects, controller 130 is further configured to calculate one or more control sequencescorresponding to one or more operations of interest. Calculation of a control sequence including a combination of control subsequences leading to a target quantum operation may be achieved using a variety of methods, as known to a person skilled in the art. One example for such a method is a computationally expensive brute-force search. According to some aspects, the one or more control sequences are calculated offline. According to some aspects, the instructions for generating each control sequence are stored in a storage device. The type of the instructions (e.g., a trigger to switch to the next input signal source, to switch to a specific input signal source or to not transmit or output signals emanating from an input signal source) may depend on the specific design of system 100. According to some aspects, the instructions may include addresses of the input signal sources from which a signal is to be output by combiner 120 per time. According to some aspects, the instructions may include a time-dependent sequence of two or more triggering pulses (may be also referred as “triggers”).

[0263] According to some aspects, controller 130 may be or may include one or more controllers. According to some aspects, controller 130 may include at least one first controller coupled with combiner 120 and configured to provide the data signals to combiner 120. Controller 130 may further include at least one second controller coupled with the first controller. The at least one second controller may be configured to calculate the one or more control sequences. According to some aspects, the at least one second controller may be further configured to store the instructions for generating the calculated one or more control sequences in association with the corresponding one or more operations in a storage device. The at least one second controller may then access the one or more instructions and provide the instructions to the at least one first controller. Alternatively, the at least one first controller may access the one or more instructions. According to some aspects, quantum elements 140A-140M are superconducting quantum elements kept at a cryogenic temperature. The at least one first controller, or a portion of it, may be also kept at a cryogenic temperature and the at least one second controller, or a portion of it, may be kept at room temperature. Alternatively, the at least one first controller and the at least one second controller may be kept at a cryogenic temperature or at room temperature.

[0264] According to some aspects, controller 130 is configured to timely provide (e.g., in real-time) an instruction for generating each control subsequence of a control sequence to combiner 120. Once the instruction is received by combiner 120, combiner 120 is configured to immediately output a signal generated by the corresponding input signal source of input signal sources 110A-110N to quantum elements 140A-140M. The corresponding input signalsource may be, for example, the next input signal source according to a predefined order or a specific input signal source according to the provided instruction.

[0265] According to some aspects, controller 130 is further configured to suppress leakage to non-computational states of quantum elements 140A-140M when calculating a control sequence of interest. According to some aspects, controller 130 is further configured to decrease discretization errors due to its finite clock frequency when providing the data signals to combiner 120.

[0266] According to some aspects, combiner 120 may be or may include one or more multiplexers. According to some aspects, combiner 120 may be or may include one or more combiners. According to some aspects, combiner 120 is configured to temporally switch on or switch off each input signal source of one or more input signal sources of input signal sources 110A-110N according to the received instructions. According to some aspects, combiner 120 is configured to select, according to the received instruction, from which input signal source of input signal sources 110A-110N a signal is output to quantum elements 140A-140M at a specific time. According to some aspects, input signal sources 110A-110N are ordered according to a predefined order. Upon receiving an instruction (e.g., a trigger) from controller 130, combiner 120 output a signal generated from an input signal source of input signal sources 110A-110N which is the next input signal source according to the predefined order.

[0267] According to some aspects, controller 130 is synchronized with a clock. The data signals received by combiner 120 vary in time synchronized with the clock. According to disclosed systems and methods, the data signals provided by controller 130 to combiner 120 are sparse or relatively sparse in time. Thus, according to some aspects, a clock having a relatively or substantially low frequency, e.g., below 10 Giga Hertz (GHz), may be used by controller 130 to further reduce the data throughput. According to some aspects, the frequency of the clock is above 10 MHz. According to some aspects, combiner 120 may include two or more combiners. According to some aspects, combiner 120, or a portion of it, may be kept at room temperature. According to some aspects, combiner 120, or a portion of it, may be kept at a cryogenic temperature.

[0268] According to some aspects, system 100 may be configured to control a quantum processor where quantum elements 140A-140M or a plurality of quantum elements 140A-140M are included in the quantum processor. According to some aspects, the quantum processor is a cryogenic quantum processor.

[0269] According to some aspects, quantum elements 140A-140M may be or may include at least one superconducting quantum element. According to some aspects, quantum elements 140A-140M may include at least one qubit. According to some aspects, quantum elements 140A-140M are qubits. According to some aspects, a qubit may be or may include a quantum dot or a spin qubit. According to some aspects, a qubit may be or may include a defect in a solid-state substrate. According to some aspects, quantum elements 140A-140M may include at least one coupler element configured to couple between at least two qubits. According to some aspects, quantum elements 140A-140M may include at least one resonator.

[0270] According to some aspects, system 100 may include a measurement system 150. Measurement system 150 may be coupled with quantum elements 140A-140M and controller 130. Measurement system 150 may include one or more detectors, e.g., one or more readout resonators coupled with quantum elements 140A-140M. The one or more detectors may be configured to measure one or more parameters of quantum elements 140A-140M. Measurement system 150 may further include one or more amplifiers, configured to amplify the signal emanating from the one or more detectors, and one or more acquisition devices, e.g., Analog to Digital Converters (ADCs), configured to acquire the amplified signals. The one or more detectors may be coupled with quantum elements 140A-140M while each detector is configured to measure one or more quantum parameters of one or more quantum elements 140A-140M. Measurement system 150 may be controlled by controller 130 or by another controller. According to some aspects, the one or more detectors (e.g., readout resonators) may be one or more quantum elements included in quantum elements 140A-140M. According to some aspects, the one or more detectors may be controlled via control sequences applying quantum measurement operations according to the disclosed systems and methods.

[0271] Controller 130 may be configured to calculate the control sequences based on the measured one or more parameters received from the measurement system. The calculation of the control sequences may include the updating of the control sequences based on updated one or more parameters. The one or more parameters may include, for example: resonance frequency, anharmonicity, coherence properties or drive port coupling strength. Such parameters can change over time (e.g., fluctuating in minutes, hours, or days) and accordingly may be remeasured. For example, characterization test measurements may be conducted, e.g., between the operations applied to the quantum elements, to identify changes which require recalibration of the disclosed control systems. Once such a change is identified, the parameters are remeasured, and the system is recalibrated accordingly. Alternatively, or additionally, theparameters may be measured from time to time or at specific, predefined, times. According to some aspects, the parameters can be measured offline or in between certain operations. The calculation of the control sequences may be updated following each measurement. For example, it is reasonable to assume that the resonance frequencies of qubits may change each day. The resonance frequency of all the qubits may be then measured at least in the beginning of each day and the control sequences may be updated accordingly.

[0272] According to some aspects, system 100 may include at least one transmission line coupled with combiner 120 and quantum elements 140A-140M (not indicated) and configured to feed the output of combiner 120 to quantum elements 140A-140M.

[0273] According to some aspects, the desired operation is a single-qubit gate or a two- qubit gate, and when applied, the operation has gate infidelity lower than 0.005. According to some aspects the gate infidelity is lower than 0.001.

[0274] According to some aspects, system 100 may be included in a quantum computing system. The quantum computing system may include a quantum processor or a plurality of quantum processors. The quantum processor may include at least one quantum element, such as quantum elements 140A-140M. The quantum computing system may further include a plurality of input signal sources such as input signal sources 110A-110N, at least one controller, such as controller 130, and at least one combiner such as combiner 120 (e.g., a multiplexer) coupled with the plurality of input signal sources and the at least one controller. The combiner may be configured to receive data signals from the at least one controller including instructions for generating control sequences, and temporally output control subsequences of the control sequences to the quantum processor or to the quantum elements, thereby applying desired operations on the quantum processor or on the quantum elements. The quantum computing system may further include a measurement system such as measurement system 150. The measurement system may be coupled with the controller and the quantum elements. The measurement system may include one or more detectors for measuring one or more parameters of at least a portion of the quantum elements and the control sequences may be calculated (e.g., by the controller) based on the measured parameters. Furthermore, the one or more detectors may be, e.g., readout resonators included in the quantum elements.

[0275] Reference is now made to FIG. 5, which is a diagram of another exemplary system 200 for controlling quantum elements. According to some aspects, system 200 is a specific example of system 100 of FIG. 4, where N=3, M=l, input signal sources 110A-110N are SFQ voltage signal sources, combiner 120 is a multiplexer and quantum elements 140A-140M area single qubit. System 200 includes an input signal source A, also indicated 210A, an input signal source B, also indicated 210B and an input signal source C, also indicated 210C. Input signal sources A and B continuously emit periodic SFQ voltage signals indicated 215A and 215B, respectively. Signal 215 A and signal 215B have different frequencies (or periodicity). Input signal source C is a null input signal source, configured to emit a zero-amplitude signal 215C. System 200 further includes a multiplexer 220 configured to receive signals from three input signal sources and output a signal from a single input signal source (e.g., 3 to 1 multiplexer) per time. System 200 also includes a controller 230 which provides instructions 235 to multiplexer 220. Multiplexer 220 outputs a control sequence 250 to a qubit 240. Multiplexer 220 is coupled with input signal sources A, B and C, controller 230, and qubit 240. According to some aspects, multiplexer 220 may be or may include one or more multiplexers, as shown, for example, in Fig. 6. According to some aspects, controller 230 may be or may include one or more controllers. According to some aspects, qubit 240 and at least multiplexer 220 of system 200 are at a cryogenic temperature.

[0276] Controller 230 may provide a set of instructions 235 to multiplexer 220 for generating control sequence 250. Control sequence 250 is designed or calculated (e.g., by controller 230) to apply a desired operation on qubit 240 (e.g., a single-qubit gate). Control sequence 250, as calculated, includes three sequential or concatenated subsequences: subsequence 250A, including a signal of input signal source A emitted for a time duration of ti-to; subsequence 250B, including a signal of input signal source C emitted for a time duration of t2-ti; and subsequence 250C, including a signal of input signal source B emitted for a time duration of t3-t2. Instructions 235 may include three time-dependent instructions, each including an instruction to multiplexer 220 to switch to another input signal source of input signal sources 210A, 210B and 210C. At a time to controller 230 may send an instruction to multiplexer 220 to switch to input signal source 210A. Accordingly multiplexer 220 outputs signal 215 A, thereby beginning the generation of subsequence 250A. At a time ti controller 230 may send an instruction to multiplexer 220 to switch to input signal source 210C. Accordingly multiplexer 220 outputs signal 215C, thereby completing the generation of subsequence 250A and beginning the generation of subsequence 250B. At a time t2 controller 230 may send an instruction to multiplexer 220 to switch to input signal source 210B. Accordingly multiplexer 220 outputs signal 215B, thereby completing the generation of subsequence 250B and beginning the generation of subsequence 250C. At a time t3, controller 230 completes the generation of control sequence 250. For example, controller 230 may thenimmediately initiate another control sequence or send an instruction to multiplexer 220 to switch to the null input signal source, input signal source C (not shown), thereby completing the generation of subsequence 250C. Thus, by sequentially generating three subsequences 250A, 250B and 250C, target control sequence 250 is generated. As one can see, although the input signal of multiplexer 220 (e.g., as emitted from input signal sources A, B or C) is periodic, the output may not be periodic, such as control sequence 250.

[0277] According to some aspects, multiplexer 220 may be configured to switch between input signal sources A, B and C or output a signal generated by input signal sources A, B and C according to a predefined order. Referring to the specific example of FIG. 5, the predefined order would be: input signal source A, input signal source C and input signal source B. Thus, instructions 235 would only need to include a trigger indicating multiplexer 220 to immediately switch to the next input signal source or immediately output a signal from the next input signal source according to the predefined order. Controller 230 would send the switch triggers of instructions 235 in a timely manner according to the calculation of control sequence 250. Although such a design may be more limiting in terms of control sequence generation, it may significantly reduce data throughput.

[0278] According to some aspects, multiplexer 220 may be a combiner configured to “turn on / off ’ input signal sources A and B e.g., by not outputting signals emanating from these input signal sources. In such a case, there is no need for input signal source C, which is a null input signal source. Referring specifically to the generation of control sequence 250, and assuming input signal sources A and B are turned off, controller 230 may provide an instruction to combiner 220 at time to to turn on signal source 210A. Accordingly combiner 220 outputs signal 215 A therefore beginning the generation of subsequence 250A. At a time ti controller 230 may provide an instruction to combiner 220 to turn off input signal source 210A. Accordingly combiner 220 stops outputting a signal, therefore completing the generation of subsequence 250A and beginning the generation of subsequence 250B. At a time t2 controller 230 may provide an instruction to combiner 220 to turn on input signal source 210B. Accordingly combiner 220 outputs signal 215B, thereby completing the generation of subsequence 250B and beginning the generation of subsequence 250C. At a time t2, controller 230 may provide an instruction to combiner 220 to turn off input signal source B, thereby completing the generation of subsequence 250C.

[0279] According to some aspects, a combiner of the disclosed systems such as system 100 of FIG. 4 and system 200 of FIG. 5 (e.g., combiner 120 or multiplexer 220) may include a firstcombiner and at least one second combiner, where the first combiner is coupled with the at least one second combiner. The at least one second combiner may be coupled with one or more input signal sources of the plurality of input signal sources (e.g., input signal sources 110A- 11 ON of FIG. 4 or input signal sources 210A-210C of FIG. 5). The first combiner may be configured to temporally output the control subsequences to the at least one quantum element (e.g., quantum elements 140A-140M of FIG. 4 or qubit 240 of FIG. 5). Depending on the specific design of the system, each control subsequence output by the first combiner may include a signal outputted by a combiner of the at least one second combiner, or each control subsequence output by the first combiner may include a signal output by a combiner of the at least one second combiner or a signal generated by an input signal source of the plurality of input signal sources other than the one or more input signal sources coupled with the at least one second combiner.

[0280] According to some aspects, a system according to the disclosed systems may utilize a cryogenic platform and the at least one quantum element may be kept at a cryogenic temperature. According to some aspects, the combiner or at least the first combiner (e.g., for a system including a first combiner and at least one second combiner) is also kept at a cryogenic temperature. According to some aspects, at least one combiner of the at least one second combiner is also kept at a cryogenic temperature. According to some aspects, the at least one second combiner is also kept at a cryogenic temperature.

[0281] Reference is now made to FIG. 6, which shows a diagram of a further exemplary system 300 for controlling quantum elements including multiple combiners. According to some aspects, system 300 is a specific example of system 100 of FIG. 4, where N=5, M=l, input signal sources 110A-110N are SFQ voltage signal sources, combiner 120 includes three multiplexers and quantum elements 140A-140M are a qubit. According to some aspects, system 300 is similar to system 200 of FIG. 5, having five input signal sources instead of three while multiplexer 220 includes three multiplexers.

[0282] System 300 includes an input signal source A, also indicated 310A, an input signal source B, also indicated 310B, an input signal source C, also indicated 310C, an input signal source D, also indicated 310D, and an input signal source E, also indicated 310E. Input signal sources A, B, D, E continuously emit periodic SFQ voltage signals indicated 315A, 315B, 315D and 315E, respectively. Signals 315 A, 315B, 315D, and 315E have different frequencies (or periodicities). Input signal source C is a null input signal source, e.g., configured to emit a zero-amplitude signal 315C. System 300 further includes multiplexers 320A, 320B and 320C.Multiplexer 320B is configured to receive signals from input signal sources A and B and output a signal from a single input signal source (e.g., 2 to 1 multiplexer) per time to multiplexer 320A. Multiplexer 320C is configured to receive signals from input signal sources D and E and output a signal from a single input signal source (e.g., 2 to 1 multiplexer) per time to multiplexer 320A. System 300 also includes at least one controller (not shown) which provides instructions 335A to multiplexer 320A, instructions 335B to multiplexer 320B, and instructions 335C to multiplexer 320C. Multiplexer 320A outputs a control sequence 350 to a qubit 340. Multiplexer 320A is coupled with multiplexers 320A and 320B, input signal source C, the at least one controller, and qubit 340. Multiplexer 320B is further coupled with input signal sources A and B and with the at least one controller. Multiplexer 320C is further coupled with input signal sources D and E and with the at least one controller. According to some aspects, the at least one controller may be or may include multiple controllers, e.g., two or three controllers, while each controller is coupled with at least one different multiplexer of multiplexers 320A, 320B and 320C. Any and all variations, and any combinations thereof, are contemplated to be within the scope of the present disclosure. According to some aspects, qubit 340 and at least multiplexer 320A of system 300 are kept at a cryogenic temperature.

[0283] The at least one controller may provide a set of instructions 335A, 335B, and 335C to multiplexers 320A, 320B, and 320C, respectively, for generating a control sequence 350. Control sequence 350 is designed or calculated (e.g., by the at least one controller) to apply a desired or target operation on qubit 340 (e.g., a single-qubit gate). Control sequence 350, as calculated, includes three sequential or concatenated subsequences: subsequence 350 A, including a signal of input signal source D emitted for a time duration of ti-to; subsequence 350B, including a signal of input signal source C emitted for a time duration of t2-ti; and subsequence 350C, including a signal of input signal source B emitted for a time duration of t3-t2-

[0284] Instructions 335 A may include time-dependent instructions, each including an instruction to multiplexer 320A to switch to one of multiplexer 320B, input signal source C or multiplexer 320C. Instructions 335B may include time-dependent instructions to multiplexer 320B to switch to one of input signal sources A or B. Instructions 335C may include timedependent instructions to multiplexer 320C to switch to one of input signal sources D or E.

[0285] In order to generate control sequence 350, at a time to the at least one controller may send an instruction to multiplexer 320C to switch to input signal source D and an instruction to multiplexer 320A to switch to multiplexer 320C. Accordingly, multiplexer 320C outputssignal 315D to multiplexer 320A which then outputs signal 315D, thereby beginning the generation of subsequence 350A. At a time ti the at least one controller may send an instruction to multiplexer 320A to switch to input signal source C. Accordingly multiplexer 320A outputs signal 315C, thereby completing the generation of subsequence 350A and beginning the generation of subsequence 350B. At a time t2 the at least one controller may send an instruction to multiplexer 320B to switch to input signal source B and an instruction to multiplexer 320A to switch to multiplexer 320B. Accordingly multiplexer 320B outputs signal 315B to multiplexer 320A which then outputs signal 315B, thereby completing the generation of subsequence 350B and beginning the generation of subsequence 350C. At a time t3 the generation of control sequence 350 is completed. For example, the at least one controller may then immediately initiate the generation of another control sequence or, send an instruction to multiplexer 320A to switch to the null input signal source, input signal source C, thereby completing the generation of subsequence 350C. By sequentially generating subsequences 350A, 350B and 350C, target control sequence 350 is formed.

[0286] According to some aspects, multiplexer 320A may be configured to switch between multiplexer 320B, input signal source C and multiplexer 320C according to a predefined order. Referring to control sequence 350, the predefined order would be: multiplexer 320C, input signal source C, and multiplexer 320B. Thus, instructions 335A would only need to include a trigger indicating multiplexer 320A to immediately switch to the next input source (e.g., an input signal source or a multiplexer) or immediately output a signal from the next input source according to the predefined order. The at least one controller provides the switch triggers of instructions 335A in a timely manner and according to the design of control sequence 350.

[0287] According to some aspects, multiplexer 320A may be a combiner configured to turn on / off multiplexer 320B and multiplexer 320C. In such a case, there is no need in input signal source C, which is a null input signal source. According to some aspects, multiplexer 320B may be a combiner configured to turn on / off input signal source A and input signal source B. According to some aspects, multiplexer 320C may be a combiner configured to turn on / off input signal source D and input signal source E.

[0288] According to some aspects, multiplexers 320A, 320B and 320C are combiners configured to turn on / off their respective input sources. Referring specifically to the generation of control sequence 350, and assuming combiners 320B and 320C are turned off, the at least one controller may provide an instruction 335 A to combiner 320 A at time to to turn on combiner 320C and an instruction 335C to combiner 320C to turn on input signal source D. Accordinglycombiner 320C outputs signal 315D to combiner 320A, which in turn outputs signal 315D, thereby beginning the generation of subsequence 350A. At a time ti the at least one controller may provide an instruction 335A to combiner 320A to turn off combiner 320C. Accordingly combiner 320A stops outputting a signal, therefore completing the generation of subsequence 350A and beginning the generation of subsequence 350B. At atime t2 the at least one controller may provide an instruction 335A to combiner 320A to turn on combiner 320B and provide an instruction 335B to combiner 320B to turn on input signal source B. Accordingly combiner 320B outputs signal 315B to combiner 320A, which in turn outputs signal 315B thereby completing the generation of subsequence 350B and beginning the generation of subsequence 350C. At a time t2, the at least one controller may provide an instruction to combiner 320A to turn off combiner 320B, thereby completing the generation of subsequence 350C.

[0289] According to some aspects, multiplexer (or combiner) 320B and multiplexer (or combiner) 320C are input signal sources for multiplexer (or combiner) 320A. According to some aspects, the input signal sources of a multiplexer configured to output a control sequence to a quantum element, such as multiplexer 320A, may include a set of multiplexed input signal sources, such as input signal sources A, B, D and E. According to some aspects, a system according to disclosed systems including a set of concatenated combiners, as shown, for example, in FIG. 6, may be designed such that only turning on / off the input signal sources is required and there is no need in turning on / off the concatenated combiners.

[0290] According to some aspects, a system for controlling quantum elements, such as system 100 of FIG. 4, system 200 of FIG. 5 or system 300 of FIG. 6 may include a set of combiners arranged in layers (e.g., concatenated layers), while each layer includes one or more combiners. The first layer of combiners includes a single combiner, such as multiplexer 320A of system 300, configured to output the control sequence to the one or more quantum elements. The second layer of combiners, such as multiplexers 320B and 320C of system 300, outputs signals to the first layer (e.g., multiplexer 320A), the third layer outputs signals to the second layer and so on. According to some aspects, where a cryogenic quantum computing platform is used, all the layers of combiners can be kept at cryogenic temperatures. According to some aspects, only the first layer of combiners (e.g., a single combiner) is kept at a cryogenic temperature, and the rest of the layers of combiners may be kept at room temperature. According to some aspects multiple concatenated layers of combiners, starting at the first layer, may be kept at cryogenic temperatures (e.g., a first and a second, first to third and so on) while the rest of the layers of combiners are kept at room temperature.

[0291] Reference is now made to FIG. 7, which is an illustration of an exemplary operation according to the disclosed systems and methods on a Bloch sphere 400. A Bloch sphere, such as sphere 400, is a unit two-sphere which is a geometrical representation of the state space of a two-level quantum element, such as a qubit. Antipodal points 410A and 410B correspond to a pair of mutually orthogonal state vectors, specifically the standard basis vectors |0> (zero state) and |1> (one state), respectively.

[0292] An exemplary desired quantum operation aims to transfer the quantum element from an initial state 420 on sphere 400, which is the zero state (410A), to a target state 430, which is located on the equator of sphere 400, e.g., by applying a rotation to the state vector. Trajectories between points (states) on sphere 400 may represent or may be implemented by control signals applied to the quantum element to achieve the desired operation. An exemplary trajectory 460 extending between the origin zero state and target state 430 may be represented by a single specific rotation of the state vector along a particular axis and by a particular angle. However, in order to implement such a trajectory, it may be required to know the exact value of the resonance frequency of the quantum element and use an input signal source or a signal having a frequency equal to the resonance frequency of the quantum element.

[0293] According to the disclosed systems and methods, a trajectory which includes multiple segments having different characteristics, such as trajectory 440, may be calculated and applied. Trajectory 440 also allows the transfer from initial state 420 to target state 430. However, trajectory 440 includes two different segments on sphere 400: a segment 440 A and a segment 440B. Trajectory 440 represents or may be implemented as a control sequence, and each segment of the trajectory is represented by or may be implemented as a control subsequence of the control sequence according to the disclosed systems and methods. Vector 450A represents the rotation axis of segment 440A and vector 450B represents the rotation axis of segment 440B. Each segment of a trajectory may represent or may be implemented by a signal having at least one different characteristic (e.g., frequency). Trajectory 440, as opposed to trajectory 460, does not require a signal source with a frequency corresponding to the resonance frequency of the quantum element.

[0294] Reference is now made to FIG. 8, which shows a plurality of Bloch spheres 460A- 460F illustrating a simulation of transmon qubit dynamics for a calibrated 7t / 2-pulse gate around the x-axis. Dynamics are shown for initial states at the six cardinal points 462A-462F on the Bloch sphere 460A-460F, respectively. Paths 464A-464F indicate the path of the transmon for each initial state indicated by cardinal points 462A-462F, respectively. Thetransmon |0> to |1> transition frequency is 4.9409 GHz, the two signal sources used are Sl=4.97GHz and S2=5.03GHz with durations of [0,7,9,0,10,14,0,0] nano second (ns). This shown dynamics is for the specific case of driving a transmon using a multiplexer with four inputs, inputs 1 and 3 are null, and inputs 2 and 4 are connected to signal sources SI and S2 giving SFQ signals at constant frequencies. The multiplexer operates such that each subsequent pulse in the selector port switches to the next input. Specifically, the cycle will be repetitions of: Null, SI, Null and S2.

[0295] The distribution network of the input signals is further described. Reference is now made to FIG. 9, which shows a schematic illustration of an exemplary input signal channel (will be also referred herein as “signal channel”) distribution 480 for an RF input signal source. Signal channel distribution 480 is implemented in a splitter tree configuration or an H-tree configuration, composed of matched RF splitters (not shown). A signal 482 of the signal channel emanating from the input signal source, is split by the RF splitters into signals 482A and 482B. Signal 482A is then split into signals 482C and 482D. Signal 482B is then split into signals 482E and 482F. At each final node, a respective DC2SFQ component of DC2SFQ components 484A-484H is placed which converts the respective incoming RF signal into SFQ signals. Since the signals originate from the same source, it is ensured they are all phase locked. Though their phases may differ and, in general, are not known a priori due to variations in signal path lengths and minor differences in path impedance, the disclosure is ignorant of such issues since the operations are calibrated on each quantum element within every cell.

[0296] According to some aspects, the number of DC2SFQ elements may be reduced. In principle, every type of quantum element may require its own plurality of signal sources, requiring a set of DC2SFQ elements for each type of quantum element. Instead, all the required RF frequencies are considered to be turned on and phase-locked to the room temperature electronics. These are fed to a room temperature multiplexer that can choose which frequencies to pass to the distribution network. Thus, it is feasible to switch the input of the main RF signal. This way only a portion of the signal sources may be used, e.g., for QE control, qubit coupling (2-qubit gates), and readout resonator driving for QE measurement. For example, two RF frequencies required for qubit driving may be applied when qubit operation is applied, then the distribution network may be switched to a pair of frequencies relevant to measurement and the qubit readout may be applied. Thus, the RF signal sources at room temperature do not switch on and off and retain their locked phases. This may be performed, for example, by using a set of concatenated combiners, as shown, for example, in FIG. 6.

[0297] A multi -frequency signal channel distribution suitable for certain applications is also disclosed. In the description above the RF splitting and distribution was described as carrying a single frequency, split along designated paths. This approach necessitates fabricating a separate distribution network for each input signal source. An adaptation of this network to multiple frequencies per splitting network is exemplified in FIG. 10. FIG. 10 is a schematic illustration of an RF signal channel distribution 490 for multiple frequencies on the same channel. Signal channel distribution 490 is implemented, as well, in a splitter tree configuration or an H-tree configuration, composed of matched RF splitters (now shown). A multi-frequency signal 492 of a signal channel emanating from multiple input signal sources having multiple different frequencies, is split by the RF splitters such that signal 492 is split into signals 492A and 492B. Signal 492 A is then split into signal 492C and signal 492D. Signal 492B is split into signal 492E and signal 492F. Signals 492C-492F are then passed through RF filters 494A- 494H which output respective signals 496A-496H, each having a single frequency. Singlefrequency signals 496A-496H are then fed to respective DC2SFQ components 498A-498H which convert the signals into SFQ signals.

[0298] This setup allows multiple signals to traverse the splitter network, with edge filters ensuring that only the frequencies permitted by the filter reach and activate the DC2SFQ. Filters, such as filters 494A-494H may be designed to allow one or several specific frequencies, or even a band of frequencies, to pass. An advantage of this modified configuration is its potential to reduce the number of distribution networks needed. However, the filters may be fixed or tunable. The former means the frequency is being predetermined and fixed during fabrication. This introduces the limitation that a node can only output the frequency of the filter and frequencies may not change during run-time. This can be alleviated by using tunable resonators as RF filters. However, this may require an additional current control network for frequency adjustment.

[0299] Reference is now made to FIG. 11, which shows a diagram of an exemplary implementation for a 4: 1 MUX (multiplexer) 500. MUX 500 is configured to select an input signal source of input signal sources 502A-502N from which a signal is output to be applied on a quantum element at each time interval. MUX 500 selects signals or subsequences produced by signal sources 502A-502N, dependent on input selection data 503, thereby producing a sequence for controlling quantum elements.

[0300] MUX 500 operates by connecting an input selection data port (not shown) to a tree of Toggle Flip Flops (TFFs) including TFFs such as TFF 504A which is coupled with TFFs504Bi and 504B2. TFFs 504B1 and 504B2 are coupled with further TFFs which are then coupled with the edge TFFs, TFFs 504NI-504NN. Each TFF, upon receiving an input pulse or signal via input selection data 503, toggles the output port (not shown) to which the incoming signal is diverted. As a result, each signal is diverted to a different output of the TFF tree. The TFF tree is connected to an array of NDROs (Non-Destructive Readout) elements indicated 506A- 506N, each of which outputs their respectively connected signal source of signal sources 502A- 502N, if it is set. The connections between the TFF tree and the NDROs array are such that each pulse received via input selection data 503 sets one NDRO from the array, the next pulse resets that NDRO, and then the next pulse sets another NDRO from the array, and so on, until every one of the NDROs in the arrays has been set once.

[0301] According to some aspects, the data flow for a QPU control is organized and streamlined by introducing a hierarchy of control levels for a quantum processor kept at a cryogenic temperature (e.g., at lOmk), corresponding to multi-layered hierarchy 10 of FIG. 1. Each type of data is then associated with a particular layer in hierarchy 10 at which it interacts with the QPU. Reference is now made to FIG. 12, which shows a diagram illustrating the flow of quantum elements control (as shown, for example, in FIGs. 4-6), with respect to multi-layered hierarchy 10 of FIG. 1.

[0302] QPU layer or control level 20 is the upper or highest level in the hierarchy. It may include all the quantum circuitry of the QPU, separated across multiple boards. A relatively small or substantially small quantity of cables, e.g., far smaller than the number of quantum elements of the QPU, carrying a few input signals 22 (e.g., RF input signals) for QEs control, interfaces with QPU level 20, where it is then split into branches indicated by arrows 22A-22C to lower levels in the hierarchy, modules layer 18, supercells layer 16 and until cells layer 14, respectively. An illustration of a distribution of the input signals is shown, for example, in FIG. 9.

[0303] According to some aspects, each of the modules of layer 18 corresponds to a single motherboard within the QPU. According to some aspects, each of the supercells of layer 16 corresponds to a single die or chip stack. Each supercell may receive one or more cables or channels with signal source selection data 24 providing instructions for generating QE control sequences. According to some aspects, each supercell may receive a single cable or channel with signal source selection data 24 providing instructions for generating QE control. Data or instructions 24A are provided to cells layer 14. The input signals are decoded to form decodedsignal or control sequences 26 at cells control level 14 to be provided to or applied on quantum elements of QE layer 12.

[0304] Reference is now made to FIG. 13, which shows a conceptual illustration of an exemplary scalable system 510 for quantum information processing according to the disclosure. System 510 includes high-level hardware structure featuring room-temperature electronics delivering, e.g., up to 32 GS / s optical signals per fiber 518. The high-level hardware structure may include a classic computing system 512 coupled with a controller 514, such as an Application Specific Integrated Circuit (ASIC) at room temperature. The Compressed instruction sets may be transmitted via a plurality of optical fibers to the 4K stage, indicated515, and converted into SFQ pulses 520, which are then sent to the millikelvin stage 522 through SFQ-based noise filters. 4K stage 515 and 10 mK stage 522 are located at a cryostat516. At 10 mK stage 522, signals may be demultiplexed, decoded, and routed to quantum elements according to the disclosure.

[0305] Measurement outcomes 523 from the QPU are digitized at the mK stage and routed through SFQ-based pulse amplification stages to 4K, then further amplified to room temperature (indicated as signals 524). The maximum required output rate per cable may be, for example, 5 Giga Samples per second (GS / s), which is well within the capabilities of current SFQ circuits. 4K stage 515 may also include SFQ circuitry for non-computationally heavy rapid feedback tasks.

[0306] A zoom-in of a portion 522’ of mK stage 522 shows instructions or signal source selection data 526 fed to supercells 528 of a module (e.g., at supercells layer or control level 16 of layout 10). Each supercell 528 includes a plurality of cells such as cell 530. A zoom-in of a cell or of a portion of cell 530’ representing QE control within the cells or at cells control layer or control level 14 of layout 10 is also shown.

[0307] The disclosed systems and methods, from a holistic perspective, increase qubit count and cost-effectiveness to enable the construction of a large-scale, fault-tolerant quantum computer, achieving utility scale. Instructions or selection data 532 is fed into a combiner 534 which outputs decoded signals 536 to be applied on quantum elements 538 (e.g., to a single quantum element of each cell per operation).

[0308] The disclosed scheme may result, inter alia, in compatibility with all superconducting qubits: transmons, fluxonium, flux qubits and the like; fully digital control which may provide, for example: control of quantum elements with resonant lower than 10 GHz, fast and static flux control which is with a frequency bandwidth lower than 1 GHz anddigital qubit readout (no analog amplification); and individually calibrated, massively parallel operations, which allow each quantum element (e.g., qubit, coupler, or resonator) to receive its own control pulses, while being applied simultaneously across many QEs within the QPU.

[0309] The disclosed architectural approach enables the design of diverse systems, maintaining a similar overall structure while allowing for modifications to target specific quantum element types and support to various error correction codes (e.g., surface and QLDPC codes). The core components are designed to be robust to timing jitter and fabrication variance.

[0310] According to a simulations of a system such as system 510, the system may include fixed frequency transmons with tunable couplers for surface codes. The exemplary system may exhibit or may include: 1.048M qubits; dissipation @10mK: < 450uW (from Simulation Program with Integrated Circuit Emphasis (SPICE) simulation and analysis); cable count: < 10K; single qubit gate error: < 4e-4 (as shown, for example, in FIG. 17); two qubit gate error: < 8e-4 (simulated); readout fidelity: < le-2); and up to 250K simultaneous individually calibrated operations.

[0311] Reference is now made to FIG. 14, which shows layout 50 (a module layout) of FIG. 2, further illustrating a physical layout of quantum elements control according to the multi-layered hierarchy of FIG.12. A controller 70 provides instruction or input signal selection data to each supercell, such as supercell 58 of the module (corresponding to supercells control level 16). As shown in FIG. 14, a single control channel is used to provide instructions, indicated 53, for generating control sequences per supercell, at the supercell level. Each supercell includes a demultiplexing (demux) device, such as demux 66 of supercell 58, configured to fan out the instructions between the cells, such as between cells 62 of supercell 58. For example, for a specific operation, a single QE is operated from each cell and thus the control channel providing instructions to supercell 58 would provide at the relevant time period instructions for generating a plurality of sequences for a plurality of QEs (a QE of each cell of cells 62), e.g., in parallel, or quasi-parallel, according to a predefined order (e.g., in a cyclic manner). For the sake of simplification, only a single signal source 52 is illustrated. Signal source 52 may be ab RF input signal source which provide signals, indicated 54, which enter at the upper, QPU control level 20. The signal is then split to modules (illustrated by arrows 22A of FIG. 12), and at the modules layer (e.g., layer 18) is split to the supercells (e.g., supercell 58; illustrated by arrows 22B) of each module by a splitter such as splitter 56. At the supercells layer 16, a further splitter, such as splitter 64 of supercell 58, is used to further split the input signals to the cells at cells layer 14 (illustrated by arrows 22C). At the cells level 14, the signalis fed into a combiner which outputs decoded signal (illustrated by arrows 26A) to the QEs level 12 (not shown in FIG. 14).

[0312] Reference is now made to FIGs. 15A-15C. FIG. 15A is a diagram illustrating a quantum elements control in a module level. FIG. 15B is a diagram illustrating quantum elements control in a supercell level. FIG. 15C is a diagram illustrating quantum elements control in a cell level. Referring to FIG. 15 A, a module 550 includes a plurality of supercells, where each supercell includes control circuitry indicated 552A-552D. Instructions or input source selection signal 554 may be fed to each supercell control circuitry 552A-552D by a separate control channel.

[0313] Reference is now made to FIG. 15B. A supercell control circuitry 552A includes a demultiplexer 556, e.g., a single demultiplexer 556, which receives instructions 554 directly from a higher temperature to be fan out or distribute to the cells of the respective supercell. The instructions are then fed to combiners or cell decoders 560 via transmission lines 558 at the cells level. Demultiplexer 556 may be implemented using, e.g., a dual-rail demultiplexer. According to some aspects, a simple tree of TFF cells and an additional signal source to synchronize the outputs may be utilized. The edge of each demultiplexer output may be coupled with a PTL or a JTL configured to send each output to its respective cell.

[0314] Reference is now made to FIG. 15C which shows a block diagram of an exemplary cell control circuitry 562. Cell control circuitry 562 includes input signals 564A-564N from N respective input signal sources (e.g., RF constant frequency signal generators), a combiner 560A receiving input selection data 554 and input signals 564A-564N, a passive transmission line (Feeder PTL) 568 and a demultiplexer 572 receiving a routing control channel 566 routing the control sequences output by combiner 560Ato QEs 570A-570M. Input signals 564A-564N may be converted into constant-frequency SFQ signal sources using a DC to SFQ converter and then fed to combiner 560A. Combiner 560A then, selects one of the inputs according to signal source selection data 554.

[0315] Reference is now made to FIG. 16, which is a flow diagram of a method 580 for controlling quantum elements. Method 580 may be applied by the disclosed systems, layouts or architectures including layout 10 (e.g., of FIG. 12), layout 50 (e.g., of FIG. 14), system 100 of FIG. 4, system 200 of FIG. 5, system 300 of Fig. 6 AND system 510 of FIG. 13. More specifically, the controllers of the disclosed systems, layouts and architecture such as the at least one controller of system 100, 200 and 300, layout 50 or system 510 may be configured to perform the steps of method 580, e.g., by executing code or instructions.

[0316] At a step 586, instructions for generating a control sequence designed to apply a desired operation on at least one quantum element (e.g., quantum elements 140A-M of system 100, qubit 240 of system 200, qubit 340 of system 300, quantum elements of layer 12 of layout 10 or quantum elements 538 of system 510) are provided. The instructions may include a time dependent series of instructions configured to generate a time dependent series of control subsequences, where the time dependent series of control subsequences form the control sequence. Each instruction may cause the generation and application of a control subsequence on the at least one quantum element at its respective time. According to some aspects, each control subsequence includes a signal. According to some aspects, each control sequence includes at least two different signals. According to some aspects, a control sequence is generated for each quantum element or for a plurality of quantum elements having the same relevant characteristics for a specific desired operation.

[0317] The subsequences or the signals of the subsequences may be generated by a plurality of input signal sources (e.g., signal sources 110A-C of system 100, signal sources 210A-C of system 200, signal sources 310A-E of system 300, or signal source 52 of layout 50) coupled with the at least one quantum element. According to some aspects, each signal source of the plurality of the signal sources is coupled with each quantum element of the at least one quantum element.

[0318] According to some aspects, the method may include a step 584, at which the control sequence may be calculated. According to some aspects, the method may further include storing the instructions for generating the control sequence in a storage device and accessing the instructions when required.

[0319] According to some aspects, providing the instructions for generating the control sequence is performed by at least one first controller (e.g., controller 130 of system 100, controller 230 of system 200, controllers 335A-C of system 300 or controller 70 of layout 50). Calculating the control sequence and storing it in a storage device may be then performed by at least one second controller, coupled with the at least one first controller. The method may then further include providing the instructions to the at least one first controller by the at least one second controller. According to some aspects, the at least one quantum element is a superconducting quantum element. According to some aspects, the at least one first controller is kept at cryogenic temperatures and the at least one second controller is kept at room temperature.

[0320] According to some aspects, the method further includes a step 582 which includes accessing measured values of one or more parameters of the at least one quantum element. The calculating of the control sequence may be then performed based on the measured values of one or more parameters. According to some aspects, the method may further include causing a measurement system (e.g., measurement system 150 of system 100) including at least one detector coupled with the at least one quantum element to measure the one or more parameters. According to some aspects, causing the measurement system to measure the one or more parameters may be performed repeatedly, at predefined times. Alternatively, or additionally, causing the measurement system to measure the one or more parameters may be performed on the fly, e.g., when calibration is required. The one or more parameters may include resonance frequency, anharmonicity, coherence properties and drive port coupling strength.

[0321] According to some aspects, the calculating of the control sequence includes suppressing leakage to non-computational states of the at least one quantum element. According to some aspects, the one or more control sequences are calculated offline.

[0322] According to some aspects, the instructions may be provided to at least one combiner (e.g., combiner 120 of system 100, combiner 220 of system 200 or combiners 320A- C of system 300) which is coupled with the at least one quantum element. According to some aspects, the at least one combiner is coupled with the plurality of signal sources. According to some aspects, each instruction of the instructions for generating the control sequence may cause the at least one combiner to output a signal generated by a specific input signal source of the plurality of input signal sources, or to cease or halt the output of signals. According to some aspects, an instruction for generating the control sequence which causes the at least one combiner to output a signal may include the address of the specific signal source configured to generate the output signal.

[0323] According to some aspects, the plurality of input signal sources is ordered according to a predefined order. Each instruction of the instructions for generating the control sequence may then include a trigger. The trigger may cause the at least one combiner to output a signal generated by the next input signal source of the plurality of input signal sources according to the predefined order.

[0324] According to some aspects, each instruction of the instructions for generating the control sequence causes the at least one combiner to switch on or switch off each input signal source of one or more input signal sources of the plurality of input signal sources.

[0325] According to some aspects, providing the instructions may further include timely providing each instruction of the time-dependent series of instructions to the at least one combiner, to generate each corresponding control subsequence of the time-dependent series of control subsequences. The providing of the instruction causes the at least one combiner to immediately output a signal or cease the output of signals, according of the provided instruction.

[0326] According to some aspects, providing of instructions for generating the control sequence to the at least one combiner may be performed such that discretization errors due to the finite frequency of the clock of the at least one controller are decreased.

[0327] Reference is now made to FIG. 17, which is a graph 590 showing 7t / 2-pulse infidelity results for an exemplary system for quantum information processing according to the disclosure. The graph shows a single qubit operation or gate (7t / 2-pulse) infidelity vs qubit frequency for a circuit setting designed to give high fidelity between 4.675GHz and 4.825GHz. The exemplary system is optimized for high-fidelity operations for qubits within the 4.675 to 4.825 GHz frequency range, thus any qubit within the -150 MHz band can be controlled. This range can be tuned in situ on a nanosecond timescale, enabling control of all qubits, even those in different frequency bands (separated by over 150 MHz), though qubits in separate bands cannot be operated simultaneously.

[0328] Simulations of the exemplary system indicate a fabrication tolerance to overall variations of 5% in inductance and Josephson junction parameters. Notably, state-of-the-art SFQ fabrication techniques can achieve parameter variances as low as approximately 1% (e.g., MIT Lincoln Laboratory, IMEC), which is well within the disclosed system's tolerance levels. Furthermore, fidelity simulations show that gate fidelities remain above 0.999 for timing jitter up to 12 picosecond (ps) and above 0.996 for timing jitter up to 40 ps, which is already well within the capabilities of state-of-the-art control electronics. This robustness may be attributed to, inter alia, jitter-insensitive circuits, optimized control instructions, and specifically designed SFQ pulse sequences and shapes provided by the disclosure.

[0329] Such results significantly exceed the error correction threshold. The heat dissipated by the control systems provided by the disclosure at the cryogenic temperature is within the cooling capacity of a single very large cryostat. High fidelities are observed despite using transmons, which typically present challenges due to their low anharmonicity. Even higher fidelities may be achieved with alternative qubit modalities, such as fluxoniums.

[0330] According to some aspects, the disclosed QPU may include multiple control channels configured to provide instructions for operating the multiple quantum elements, as shown, for example, in FIG. 14. Each control channel may be configured to provide instructions for operating the quantum elements of the QPU. The instructions may include instructions for generating the control sequences to be applied on the quantum elements.

[0331] According to some aspects, each supercell of the QPU may be coupled with a different one or more control channels of the multiple control channels. According to some aspects, each supercell may be coupled with a single different control channel of the multiple control channels. According to some aspects, each supercell is coupled with a predefined number of control channels. The predefined number of control channels may be determined based on the number of input signal sources. For example, the number of control channels may be equal to Log 2 of the number of input signal sources. Furthermore, the control sequence generation scheme may also influence the required number of control channels per supercell. Each supercell may be coupled with a single different control channel, for example, in a configuration according to which only a trigger is required for providing one or more control signals or for generating a control sequence to be applied on a quantum element (e.g., in a predefined cyclic input signal selection scheme).

[0332] Since a plurality of cells in an error-corrected QPU may require the same sequence of operations, a single joint instruction for all the cells, directing control sequences to the desired quantum element across all the cells in parallel, may be used. Thus, a highly efficient method benefiting from this synchronization may be generated. According to some aspects, a routing control channel, e.g., a current control, may be used to realize this scheme.

[0333] A QPU operating according to a disclosed principle of operation may include at least one routing control channel. The routing control channel may be configured to cause the routing of control sequences for applying each operation on its respective QESOP. The routing control channel may be configured to cause the routing of the control sequences for applying an operation by enabling the routing of the control sequences to at least a plurality of quantum elements assigned to the respective QESOP.

[0334] According to some aspects, the QPU includes at least one module. Each module may include different sets of quantum elements of multiple sets of quantum elements of the QPU. Each module may be coupled with one or more routing control channels configured to cause the routing of the control sequences for applying an operation on the quantum elementsof the respective module which are assigned to the operation’s respective QESOP. According to some aspects, each module is coupled with a single routing control channel.According to some aspects, each QESOP is assigned with a different address of a plurality of addresses. Each quantum element is assigned with its QESOP’ s respective address. The term “address” should be interpreted in a broad manner and may be defined by e.g., a characteristic of a current such as the direction of the current. The routing of the control sequences may be then based on the quantum elements assigned addresses. According to some aspects, each routing control channel may include a current, and the routing of the control sequences is based on the present value of a characteristic of the current. According to some aspects, the characteristic of the current is its direction. According to some aspects, the present value of the characteristic of the current may enable the branching of the presently provided control sequences towards the respective quantum elements.

[0335] Reference is now made to FIG. 18, which shows the diagram of the multi-layered hierarchy of FIG. 1, further illustrating routing of quantum elements control. The significance of the module level in the hierarchy is in the control current distribution. Modules level of control 14, each module receives, among others, a small number of cables or routing currents 28, which may carry switchable control currents for determining the routing of QE control sequences to the correct QE. The current control of a module may then progress along the supercells of the module at supercells layer 16, indicated by arrows 28 A, and then along the cells within each supercell at cells layer 14, indicated by arrows 28B, as exemplified in FIG. 19.

[0336] According to some aspects, the control current distribution may include N wires whose current can be controlled at a higher temperature stage, e.g., 4K. According to some aspects, one or more current control wires may interconnect demultiplexers of plurality of cells in the module, e.g., serially, such that it makes the same selection, as described herein. Due to their serial nature, there are no splits in the wires, and each wire has an uninterrupted serial flow. This may simplify the control. However, if required, the current may be split by balancing the inductive paths and / or using the methods disclosed herein with respect to the distribution network.

[0337] Reference is now made to FIG. 19, which shows an illustration of an exemplary current control 602 (or current 602) of a routing control channel for routing control in e.g., a supercell 600 including multiple cells such as cell 604. Current control 602 determines to which branch control, such as branch 606, signals are sent. Since the cells, such as cell 604, require asynchronized operation, current control 602 can be shared among cells. The control signal from a signal source is split into a few branches per cell, each branch routing the signal to a different quantum element of the cell such as quantum element 608 of cell 604 (e.g., a splitter tree). However, only the appropriate current for the branch to the element that needs to be controlled is applied. Only the branch with the appropriate current present can transmit the signal to the desired quantum element. Current control 602 is shared across branches for multiple cells, allowing routing the signals to the correct elements in parallel for all the cells connected to the same routing control channel or current control.

[0338] Reference is now made to FIG. 20, which shows a diagram of the physical layout 50 of FIG. 2, further illustrating routing quantum elements control. In this example, module 50 includes three current control channels or currents, such as current control 68. Current 68, for example, flows into module 50 and rapidly, substantially at once, progresses through supercells of module 50. For example, as shown, current 68 flows through supercell 58, including cells 62, and through two additional supercells of module 50.

[0339] Reference is also made to FIG. 15C which shows the control circuitry of a cell. Concatenated sequence of SFQ signals according to the disclosure may be fed into demultiplexer 572 which is controlled by current control 566. Demultiplexer 572 selects which quantum-classical interface the sequence of SFQ signals will be routed to. The selection may be done by switching control currents, indicated 67 in FIG. 20 (one direction is indicated by a continuous arrow while the other direction is indicated by a dotted arrow). According to some aspects, demultiplexer 572 may be referred herein as “parallelized demultiplexer” to emphasize that the control currents are parallelized over multiple cells, such that the selected quantum element that the control sequence is being routed to at a time instance is the same in all the cells controlled by the same current.

[0340] According to some aspects, disclosed control circuitries may include a control sequence generation circuit (multiplexed drive), and a current control demultiplexer, as shown, for example, in FIG. 15C. The combination of these two components together may allow generating required signals on-chip while sending a minimal amount of control commands, and to route them to the corresponding quantum-classical interface element, that in turn controls the corresponding quantum element.

[0341] Various implementations for a parallelized demultiplexer for routing control sequences to the desired quantum element may be used. A first, exemplary, implementation includes a tree of (toggle flip-flop) TFF-like cells. Each TFF-like cell is a non-flux trappingcell, meaning that there is no internal state that determines to which side an incoming pulse is routed to. Instead, the routing direction is determined by an externally applied flux which may be provided by, e.g., a DC current line. The DC current control line is shared among at least a plurality of cells within a supercell or within a plurality of supercells.

[0342] A second implementation employs the bias currents themselves as control currents to direct the signals into the intended path. It includes a demultiplexer made up of a tree of splitters, with an escape Josephson Junction (JJ) placed before the JJs in each branch. At such a split, an incoming pulse will travel down both paths. The path with the control current turned off will cause the pulse to activate the escape junction, preventing further propagation along that path; meanwhile, the path with the current on allows the pulse to continue. This approach may permit multiple paths to be used simultaneously, should the need arise. However, it may increase the heat dissipation and the requirement for twice as many control currents compared to the previous approach. For example, for a 1 : 16 split, the first implementation would need four control currents, while the latter would need eight. However, it should be noted that the first implementation still requires the bias current in addition to the control currents. These differences are relatively minor, and the choice between them may depend on the specific requirements of the architecture.The above-described implementations require fixing the phase imbalance due to pulse propagation. This can be done, e.g., by a dual-rail design or a JTL-feeding network. Applying these methods does not affect the performance but should be performed when building or simulating such devices.

[0343] Reference is now made to FIG. 21, which shows the multi-layered hierarchy of FIG. 1, illustrating an overall control of quantum elements. Input signals 22 are provided at QPU control level 20 and split into branches to the modules of module layer 28 (signals 22A), into branches to the supercells of supercells layer 16 (signals 22B) and to cells layer 14 (signals 22C). One or more routing currents are provided at modules control level 18 and then progress through the supercells of supercells layer 16 (indicated by arrows 28 A). Signal source selection data or instructions 24 are provided at supercells control level 16. The instructions are then fanned out to the cells (indicated by arrows 24A) at the cells control level 14. Input signals 22 are decoded at cells control level 14 to form decoded signal or control sequences 26 to be provided to or applied on quantum elements at QE control level 12 (indicated by arrows 26A).

[0344] Reference is now made to FIG. 22, which shows layout 50 of FIG. 2, further illustrating a physical layout of overall control of quantum elements at a module level. Signalsource 52 (e.g., an RF input signal source) provides signals to a QPU including module 50. The signals are then split to modules, and at the modules level (indicated as signals 54) are split to the supercells of each module by a splitter such as splitter 56 of module 50. At the supercells level, a further splitter, such as splitter 64 of supercell 58, is used to further split the input signals to the cells of the supercell (e.g., cells 62). At the cells level the signals are fed into a combiner which outputs decoded signals to be applied on the QEs of the cell.

[0345] Controller 70 provides instruction or input signal selection data to each supercell, such as supercell 58 of module 50. As shown in the figure, a single control channel is used to provide instructions, indicated 53, per supercell, at the supercell level. The instructions include instructions for generating control sequences at the cells level based on input signals 54 to be applied to the quantum elements to achieve desired operations. Each supercell includes a demultiplexing (demux) device, such as demux 66 of supercell 58, controlled by a current control, such as current control 68 to fan out the instructions between the cells, such as between cells 62 of supercell 58.

[0346] According to some aspects, operating a quantum element of multiple quantum elements of a QPU is performed by applying a control sequence on the quantum element via input signal sources of a plurality of input signal sources. Each input signal source of the plurality of input signal sources is coupled with the multiple quantum elements. According to some aspects, each input signal source of the plurality of input signal sources is configured to apply operations on each quantum elements of the multiple quantum elements. According to some aspects, the QPU includes the plurality of input signal sources. According to some aspects, the control sequence includes a time-dependent series of a plurality of control subsequences. Each control subsequence includes a signal generated by a single input signal source of the plurality of input signal sources at a time interval or defines a time interval during which the plurality of input signal sources does not generate signals.

[0347] According to some aspects, a QPU operation according to a disclosed operation principle includes multiple sets of quantum elements and multiple memory elements, where each memory element is coupled with a different set of quantum elements and configured to store information received from its respective set of quantum elements.

[0348] Reference is now made to FIG. 23, which shows a flow diagram of methods 610 for controlling quantum elements and for routing the control.

[0349] At a step 612, operations are applied on multiple quantum elements, where the multiple quantum elements are arranged in multiple sets of quantum elements or assigned toQESOPs (or both). The operations are applied according to one or more principles of operations. According to a principle of operation, each operation is applied on not more than a single quantum element of each set of quantum elements. According to a principle of operation, only a single quantum element of each set of quantum elements is operated in parallel. According to s principle of operation, each operation is applied only on quantum elements of the same QESOP.

[0350] According to some aspects, each quantum element of the multiple quantum elements may be assigned to a single QESOP of a plurality of QESOPs. Each operation may be applied on at least a plurality of quantum elements of the multiple quantum elements. Each QESOP may include a plurality of quantum elements of the multiple quantum elements, and each operation may be applied only on quantum elements of a single respective QESOP of the plurality of QESOPs. According to some aspects, for each set of the quantum elements, each quantum element may be assigned to a different QESOP.

[0351] At a step 614, the applying of operations on the multiple quantum elements may include providing instructions for operating the multiple quantum elements via multiple control channels. Each control channel may be configured to provide instructions for operating quantum elements of a plurality of sets of quantum elements of the multiple sets of quantum elements.

[0352] According to some aspects, the multiple sets of quantum elements are arranged in multiple supercells, where each supercell includes a different plurality of sets of the multiple sets of quantum elements. The applying of operations on the quantum elements may then include providing instructions for operating the quantum elements of each supercell via a single different respective control channel of the multiple control channels.

[0353] At a step 616, applying operations on the quantum elements is performed by applying control sequences on the quantum elements generated via a plurality of input signal sources. Each input signal source of the plurality of input signal sources is coupled with the quantum elements and configured to provide signals for operating each quantum element of the quantum elements. According to some aspects, a QPU may include quantum elements which are not coupled with an input signal source. According to some aspects, each control sequence includes a time-dependent series of a plurality of control subsequences. Each control subsequence includes a signal generated by a single input signal source at a time interval or defines a time interval during which the plurality of input signal sources does not generatesignals. Method 610 may then further includes providing instructions for generating the control sequences.

[0354] At a step 618, applying each operation of the operations may include causing the routing of control sequences for applying the operation by enabling the routing of the control sequences to at least a plurality of quantum elements of the multiple quantum elements assigned to the respective QESOP.

[0355] According to some aspects, each QESOP may be assigned with a different address of a plurality of addresses and each quantum element may be assigned with its QESOP’ s respective address. Enabling the routing of the control sequences of each operation may be then performed by enabling the routing of the control sequences to quantum elements of the multiple quantum elements assigned with the respective QESOP address.

[0356] Each of steps 614-616 may be performed in conjunction with step 612 or further in conjunction with one or more of the other steps.

[0357] Several known methods exist for reading out or measuring the state of a superconducting qubit. The most commonly used method involves pure RF analog control, which represents the current state-of-the-art. In this approach, a microwave signal drives a resonator coupled to a qubit. The reflected or transmitted signal is then amplified and forwarded to room-temperature electronics for processing, with the qubit information encoded in the phase and / or amplitude of the microwave signal. Such methods have their respective challenges.

[0358] Devices and methods for readout which may be also based on driving a readout resonator coupled to the qubit are disclosed. The readout resonator may be driven such that the readout interface operates as desired.

[0359] The readout resonators on the quantum chip have different frequencies, yet the frequencies are distributed in a relatively narrow range. Fabrication tolerance allows to predict the circuit parameters, and specifically the resonator frequency and its coupling to the qubit to within a few percent, e.g., less than 10%. This suggests that a scale of tens of MHz detuning of the resonator frequencies from the signal sources frequencies is required. This scale is the same as with qubit frequency spread. As opposed to the qubit system, the readout resonator can be regarded as a linear classical system, rather than an anharmonic quantum system.

[0360] To drive the circuit for readout, the signal sources in the control sequence generation mechanism may be initially adjusted to frequencies that align with the spread of the readout resonator frequencies. Consequently, each cell receives the same frequencies from thecontrol sequence generation mechanism, and although each resonator operates at a unique frequency, its frequency is within a few tens of MHz detuned from at least one of the signal sources. One of the pulse generators may be then used, selecting a frequency as close as possible to that of the resonator. Next, employing the disclosed multiplexer (e.g., multiplexer 120 of FIG. 4, 230 of FIG. 5, or 33 of FIG. 6) the incoming signals are toggled on and off at a frequency nearly matching the detuning between the signal source's frequency and the resonator. This modulation results in constructive interference at the readout frequency and partial destructive interference at other frequencies. This partial destructive interference is critical for the readout scheme to work, as the resonator frequency shifts when the qubit is in |1> (one state) compared to its value for |0> (zero state). A minimal frequency component of the drive is desired at the shifted resonator frequency.

[0361] The measurement fidelity may depend on the ratio of amplitudes between the bare (qubit in |0>) and shifted (qubit in |1>) resonator frequencies. For example, if the modulated SFQ signal train is too short, then the width of each peak in the spectrum broadens. If the peak that is tuned to the bare readout resonator frequency now partially overlaps with the shifted frequency, then power may reside in the resonator, potentially leading to a false reading of the state of the qubit. On the other hand, if the modulated SFQ signal train is too long, then qubit decay can occur during the readout, potentially leading again to a false reading.

[0362] Reference is now made to FIG. 24, which includes a graph 640 showing a Fourier spectrum of an SFQ signal train generated by modulating a single modulated a single input signal source. The graph shows the sinc-like distribution. The aim is to have a peak coincide or nearly coincide with the bare readout resonator frequency, while the shifted frequency falls in a region with reduced peak amplitude.

[0363] In general, even more efficient pulses or signals can be generated using the disclosed control sequence generation method (e.g., method 580 of FIG. 16), yet the described method already yields fidelities on par with the state of the art. Using two signal sources and not just one can improve fidelity. Using more than two signal sources may also facilitate improving readout fidelity.

[0364] Systems and method for redout are further disclosed. After the QE (e.g., a qubit) is measured, the measurement signal waits in the memory element, e.g., a D Flip Flop (DFF) or Non-Destructive Readout (NDRO) element, to be triggered and sent to merging combiners. The memory elements may be triggered, e.g., once every error correction cycle of theprocessor. This may trigger a chain reaction which sequentially triggers each memory element, whose signal gets routed to the output of the corresponding module.

[0365] Measurement in general may include two parts, the first is the input signal causing the quantum measurement to occur. The second is transduction of the quantum information into a classical SFQ signal, and then passing to memory and further levels in the multi-layered hierarchy. A mechanism showing how to generate the input signal and a mechanism by which the transduction occurs are described hereinbelow.

[0366] A QPU including multiple quantum elements and multiple splitting devices successively interconnected in one or more separate chains of splitting devices, is disclosed. Each splitting device of the multiple splitting devices, which is not the last splitting device in a chain of splitting devices, may be configured to duplicate a received triggering signal to a first triggering signal and a second triggering signal. The first triggering signal may be configured to trigger output of information relating to a respective quantum element of the multiple quantum elements. The second triggering signal may be transferred to the next interconnected splitting device in the respective chain of splitting devices.

[0367] According to some aspects, the QPU may further include multiple memory elements. Each memory element may be coupled with one or more quantum elements of the multiple quantum elements and with a different splitting device of the multiple splitting devices. Each memory element may be configured to store information received from its respective one or more quantum elements. The first triggering signal may be configured to trigger output of information by triggering the respective memory element to output its stored information.

[0368] Reference is now made to FIG. 25A, which shows a diagram illustrating a readout scheme 620 in a quantum processing unit. According to scheme 620, a QPU includes QEs 622A-622D coupled with memory devices 624A-624D. The QPU further includes a chain of splitting devices 626A-626D coupled with memory devices 624A-624D, respectively. A triggering signal 625 enters splitting device 626A, which duplicates or splits the signal into two triggering signals. The first triggering signal 625A triggers the output of information relating to QE 622A by triggering its respective memory 624A. The second triggering signal 625B is transferred to trigger the next interconnected splitting device in the chain of splitting devices, splitting device 626B. This triggering mechanism repeats itself along the chain of splitting devices with each splitting device receiving a triggering signal output by its preceding splitting device and until the last splitting device in the chain of splitting devices.

[0369] According to some aspects, the QPU may further include one or more merging combiners. Each merging combiner of at least one merging combiner may be coupled with a plurality of the memory elements, such that the plurality of memory elements is coupled with splitting devices which are of the same chain of splitting devices. Each merging combiner of the at least one merging combiner may be configured to fan in information received from its respective plurality of memory elements to a single information output line.

[0370] According to some aspects, each merging combiner of at least one merging combiner may be coupled with a plurality of merging combiners of the rest of the one or more merging combiners and may be configured to fan in information received from its respective plurality of merging combiners to a single information output line.

[0371] Reference is now made to FIG. 25B which shows a diagram illustrating an exemplary readout multiplexing scheme 621 in a quantum processing unit. According to scheme 621, a QPU includes QEs 622A-622H coupled with memory devices 624A-624H, respectively. The QPU further includes a chain of splitting devices 626A-626H coupled with memory devices 624A-624H, respectively. The QPU also includes merging combiners 628A- 628D, 630 A and 630B configured to fan in the data received from memory devices 624 A- 624H. Merging combiners 628A-628D, 630 A and 630B are arranged in two layers of a hierarchy of merging combiners, as shown in the Figure. A triggering signal 625 enters splitting device 626A and initiates the triggering mechanism disclosed hereinabove along the chain of splitting devices. The output of memory devices 624A-624H is then provided to the first layer of merging combiners, merging combiners 628A-628D, respectively. In the specific example of FIG. 25B, each merging combiner of merging combiners 628A-628D is coupled with two memory devices and configured to fan in the output of the respective memory devices to a respective merging combiner of the second layer of merging combiners (e.g., merging combiners 630A and 630B). For example, splitting device 626A triggers memory device 624A which in response outputs its stored data to merging combiner 628A. Merging combiner 628A is coupled with merging combiner 630A and outputs its data to merging combiner 630A, which in turn outputs its received data to a single information output line, e.g., line 629 A. Other configurations or schemes may be contemplated by a person skilled in the art, including merging combiners hierarchy, number of memory devices coupled with a singe merging combiner and the like.

[0372] According to some aspects, the QPU may further include multiple merging combiners successively interconnected in a chain of merging combiners. Each mergingcombiner may be coupled with a different memory element of the multiple memory elements, where each merging combiner may be configured to receive information from its preceding merging combiner in the chain of merging combiners or from its respective memory element. Each merging combiner, except for the last merging combiner in the chain of merging combiners, may be configured to transfer the received information to the successively interconnected merging combiner. The last merging combiner in the chain of merging combiners may be configured to fan in its received information to a single information output line. The merging combiner can be configured to be clocked, asynchronous, or to use a dualrail configuration.

[0373] Reference is now made to FIG. 25C which shows a diagram illustrating another readout multiplexing scheme 632 in a quantum processing unit. According to scheme 632, a QPU includes QEs 622A-622D coupled with memory devices 624A-624D, respectively. The QPU further includes a chain of splitting devices 626A-626D coupled with memory devices 624A-624D, respectively. The QPU also includes merging combiners 636A-636D successively interconnected in a chain of merging combiners. Each merging combiner of merging combiners 636A-636D is coupled with a memory device (or memory element) of memory devices 624A- 624D, respectively. A triggering signal 625 enters splitting device 626A, which duplicates or splits signal 625 into two triggering signals, triggering signals 625 A and 625B. Triggering signals 625 A triggers the output of information relating to QE 622A by triggering its respective memory 624A and triggering signal 625B is transferred to trigger the next interconnected splitting device in the chain of splitting devices, splitting device 626B.

[0374] Each merging combiner of merging combiners 636A-636D is configured to receive information from its preceding merging combiner in the chain of merging combiners or from its respective memory element. For example, merging combiner 636B is configured to receive information from merging combiner 636 A or from memory element 624 A. Each merging combiner, except for the last merging combiner in the chain of merging combiners, may be configured to transfer the received information to the successively interconnected merging combiner. The last merging combiner in the chain of merging combiners is configured to fan in its received information to a single information output line 637. The merging combiner may be implemented using a dual-rail configuration.

[0375] According to some aspects, a QPU may include multiple quantum elements and multiple splitting devices successively interconnected in one or more separate chains of splitting devices, as disclosed hereinabove. The QPU may further include multiple informationmediums. The multiple information mediums may include the multiple memory elements or merging combiners. Each merging combiner may be coupled with two or more information mediums. At least one merging combiner may be configured to fan in information received from its respective two or more information mediums to a single information output line.

[0376] According to some aspects, at least one of the one or more merging combiners is designed with a dual-rail configuration. According to some aspects, the memory elements are triggered once every error correction cycle of the quantum processing unit.

[0377] According to some aspects the QPU may operate according to the disclosed principles of operation. According to some aspects, the multiple quantum elements are arranged in multiple sets of quantum elements, where the quantum processing unit is configured to operate not more than a single quantum element of each set of quantum elements in parallel. According to some aspects, each memory element may be then coupled with a different set of quantum elements of the multiple sets of quantum elements.

[0378] Reference is now made to FIG. 25D which shows a diagram illustrating a further readout multiplexing scheme 634 in a QPU. The QPU operates according to a disclosed principle of operation or applies QEs control according to the disclosure. The QPU includes QEs 622A(1)-622C(6) arranged in three sets of QEs(or cells): a first set of QEs 622A(1)- 622 A(6), a second set of QEs 622B(1)-622B(6), and a third set of QEs 622C(1)-622C(6). The QPU further includes memory devices 624A-624C and a chain of splitting devices 626A-626C coupled with memory devices 624A-624C, respectively. Each set of QEs is coupled with a single memory device of memory devices 624A-624C. The coupling may be performed via merging combiners (e.g., merging combiners 638A-638C). Since the principle of operation of the QPU may allow, for example, operating not more than a single quantum element of each set of quantum elements in parallel, each memory device of memory devices 624A-624C may store, at a time instance, data from only one quantum element of its coupled set of quantum elements.

[0379] Reference is now made to FIG. 26 which shows a diagram of the multi layered hierarchy of FIG. 1, further illustrating readout multiplexing. Measurement output at QE level 12 may be merged, e.g., by a layout, chain or hierarchy of merging combiners, as shown, for example, in FIGs. 25A-25D, along the hierarchy levels up to modules level 18. Measurement data 30A received at QE level 12 may be then merged at cells level 14, forming merged data 30B, which is then merged at supercells level 16 to form merged data 30C at the modules level 18, which is then output from the QPU, indicated measurement output 30.

[0380] Reference is now made to FIGs. 27A-27C which show illustrations of readout in a QPU operating according to a disclosed principle of operation. For example, the QPU may include multiple QEs arranged in sets of QEs where the QPU is configured to operate not more than a single quantum element of each set of quantum elements in parallel, as shown for example in FIG. 25D. Accordingly, a transduced SFQ signal including information on a qubit state can arrive from one of each of readout interface elements on a cell, but never simultaneously from more than one.

[0381] FIG. 27A is a diagram of an exemplary cell measurement circuitry 660. FIG. 27B is a diagram of an exemplary supercell measurement circuitry 676. FIG. 27C is a diagram of multiplexing readout in a module 685.

[0382] Reference is now made to FIG. 27A which shows a cell 660 including four DC to SFQ (DC2SFQ) converters 662. An SFQ signal 664 is output to a merging combiner 668 (e.g., 4: 1 merging combiner), such that regardless of which readout element the pulse arrived from, it will exit at the same channel. The exit channel leads to a memory device or element 670 which is D flip flop (DFF). The DFF can be replaced with a similar cell like a non-destructive readout (NDRO) element. The SFQ bit stays stored in the DFF until a trigger pulse arrives to release it and empty the DFF.

[0383] According to some aspects, a built-in maj ority vote implementation may be utilized. In some implementations the DFF or NDRO may have a multi-flux loop. Accordingly, the storage loop can trap N fluxons. Thus, the stored signal is not a 0 or 1 flux, but 0 or 1 or 2 or 3 etc. up to N, where N is a natural number larger than 1. The emptying mechanism, which may differ from a simple signal of a signal source as in the simpler case, will then release an SFQ signal only if the number of stored fluxons is above a certain defined number. Such an emptying mechanism may be devised by tuning the signal to a specific amplitude by adjusting the JJ at a JTL stage preceding the signal source input port. This enhanced implementation may allow to perform a majority vote on the qubit measurement data, and in appropriate cases enhance the qubit measurement fidelity.

[0384] Reference is now made to FIG. 27B. Readout circuitry of a supercell 676 may include a chain of splitters 673, one for each cell of cells 674 of the supercell. Where for the Nth splitter, one splitter output propagates to the input of the (N+l)thsplitter, and the other output goes to the memory device of the respective cell (such as memory 670 of FIG. 27A). The output of each memory device goes to a merging combiner 680. The scheme or structure of merging combiner 680 is similar to the scheme or structure of the merging according to FIG.25B. This structure works such that an incoming pulse 672 at the input of the first splitter causes a sequential triggering of all the respective memory devices, which in turn causes the sequential release of the data stored in the memory devices to output 682 of merging combiner 680, e.g., to be further combiner or merged in the modules level. The pulse from the last splitter, pulse 678, is routed to the input of the next supercell to trigger a sequential release in that supercell.

[0385] Referring to FIG. 27C, a merging combiner 686 may be employed, where each input is directly connected to the output or readout of a corresponding supercell, such as supercell 676 (triggered by signal 684). Given that the output data from the supercells is sequential, the output data 688 from the module may also be sequential, thereby alleviating timing issues. Data 688 is then output to room temperature. According to some aspects, merging combiner 686 may be designed with a dual-rail configuration to ensure robust performance.

[0386] Reference is now made to FIG. 28, which shows a flow diagram of a method 690 for reading out information from multiple quantum elements, e.g., of a QPU. At a step 692, a received triggering signal is duplicated by each splitting device of multiple splitting devices successively interconnected in a chain of splitting devices, except for the last splitting device of the chain of the splitting devices. The received triggering signal is duplicated to a first triggering signal and a second triggering signal.

[0387] At a step 694, the first triggering signal is utilized to trigger output of information relating to a respective quantum element of the multiple quantum elements.

[0388] At a step 696, the second triggering signal is transferred to the next interconnected splitting device in the chain of splitting devices.

[0389] According to some aspects, the method may further include providing a triggering signal to a first splitting device of the chain of splitting devices.

[0390] According to some aspects, each splitting device of the chain of splitting devices may be coupled with a memory element of a plurality of memory elements which is coupled with the respective quantum element. For each splitting device of the chain of splitting devices, except from the last splitting device, the triggering of output of information relating to the respective quantum element may include triggering the coupled respective memory element to output information stored in the memory element which was received from the respective quantum element.

[0391] According to some aspects, each memory element of the plurality of memory elements may be coupled with a different one splitting device of the plurality of splittingdevices. Method 690 may then further include fanning in information output by the plurality of memory elements to a single information output line (e.g., as shown in FIGs. 25B or 25C). According to some aspects, the fanning in of the information output by the plurality of memory elements may be performed via one or more merging combiners.

[0392] According to some aspects, the triggering of the memory element is performed once every error correction cycle.

[0393] According to some aspects, the multiple quantum elements may be arranged in multiple sets of quantum elements, where not more than a single quantum element of each set of quantum elements may be operated in parallel. Each memory element of the multiple memory elements may be then coupled with a different set of quantum elements of the multiple sets of quantum elements.

[0394] FIG. 29 is a diagram illustrating a multi layered hierarchy according to FIG. 1, further illustrating over-all quantum elements’ control and readout multiplexing according to the disclosure. Input signals 22 are provided at OPU control level 20 and split into branches to the modules of module layer 28 (signals 22A), into branches to the supercells of supercells layer 16 (signals 22B) and to cells layer 14 (signals 22C). One or more routing currents are provided at modules control level 18 and then progress through the supercells of supercells layer 16 (indicated by arrows 28 A). Signal source selection data or instructions 24 are provided at supercells control level 16. The instructions are then fanned out or distributed to the cells (indicated by arrows 24A) at the cells control level 14. Input signals 22 are decoded at cells control level 14 to form decoded signal or control sequences 26 to be provided to or applied on quantum elements at QE control level 12 (indicated by arrows 28A). Measurement output at QE level 12 may be then merged, e.g., by a layout, chain or hierarchy of merging combiners, as shown, for example, in FIGs. 25A-25D, along the hierarchy levels up to modules level 18. Measurement data 30A received at QE level 12 may be then merged or multiplexed at cells level 14, e.g., according to the configuration of FIG. 25D, forming data 30B, which is then merged at supercells level 16 to form merged data 30C at the modules level 18, which is then output from the QPU, indicated measurement output 30.

[0395] Systems, devices and methods for efficiently sending signals to progressively lower temperature stages with minimal heat dissipation and maximal noise filtration, as well as transmitting signals from the lowest temperature through progressively higher temperatures without compromising Signal to Noise Ratio (SNR) in a cryogenic quantum computing scheme are further disclosed.

[0396] Sending analog RF signals down multiple temperature stages is a well-known practice. Each temperature stage includes an attenuator. The function of the attenuator is to dissipate part of the signal, thereby thermalizing it in accordance with the dissipated portion. For instance, a signal arriving from 300K and attenuated by a factor of 100 at 4K, will carry noise of 300K / 100 + 4K = 7K. Sending RF signals from low temperatures to higher temperatures is also known in the art and requires low noise RF amplifiers, isolators, and sometimes circulators. These are configured to minimize SNR loss as the signal travels to room temperature.

[0397] Systems and methods for efficiently sending or transferring signals, and digital signals, in particular, such as SFQ signals, through different temperature stages, are hereby disclosed. Given the digital nature of SFQ signals, the disclosed approach enables a more efficient process than RF, particularly for output signals. For input signals the supplied control current is lowered at every temperature stage, thus creating a noise-lowering thermalizing effect with minimal attenuation. For the output, instead of using RF amplification, a JTL amplifier chain may be employed.

[0398] The disclosed technique involves positioning receiver JTL and transmitter JTL components (e.g., a JTL device including such) at each temperature stage. These JTLs are designed with differing critical currents of JJs to appropriately match the requirements for receiving and transmitting SFQ signals between the successive temperature stages. For input signals, the JTL receiver is linked to the JTL transmitter either directly or through a plurality of additional JTL stages.

[0399] On the output side, the connection between the receiver JTL and the transmitter JTL may include a JTL amplifying chain. This chain may include a series of JTLs (or JTL devices), each with a progressively higher critical current, thereby amplifying the amplitude of the SFQ signal. This strategic placement and configuration of JTLs throughout different temperature stages optimizes the transmission and amplification of SFQ signals.

[0400] According to some aspects, a quantum computing device may include a quantum processing unit including multiple quantum elements kept at a cryogenic temperature and one or more Josephson Transmission Line (JTL) devices disposed at one or more temperature levels. The quantum computing device may be configured to send input signals from a temperature higher than the cryogenic temperature to the multiple quantum elements at the cryogenic temperature and to send output signals from the multiple quantum elements at the cryogenic temperature to the higher temperature. At least one JTL of the one or more JTLdevices may be configured to amplify the output signals at a temperature level of the one or more temperature levels.

[0401] According to some aspects, at least one temperature level of the one or more temperature levels is of a temperature between the cryogenic temperature and the higher temperature.

[0402] According to some aspects, the one or more JTL devices include a plurality of JTL devices, and the one or more temperature levels include a plurality of temperature levels. At least a portion of the plurality of JTL devices may be then configured to generate a JTL amplifier chain for gradually amplifying the output signals along temperature levels of the plurality of temperature levels.

[0403] According to some aspects, the JTL amplifier chain includes the at least portion of plurality of JTL devices interconnected in series, where each JTL device in the JTL amplifier chain has a plurality of progressively higher critical currents. According to some aspects, the rest of the plurality of JTL devices may be configured to generate a JTL attenuator chain for gradually attenuating the input signals at one or more temperature levels of the plurality of temperature levels.

[0404] According to some aspects, each JTL stage of each JTL device includes at least one Josephson Junction (JJ) designed to have a critical current value corresponding to the temperature level at which the respective JTL device is disposed.

[0405] According to some aspects, the one or more temperature levels include a plurality of temperature levels, and each temperature level is of a different temperature between the cryogenic temperature and the higher temperature.

[0406] According to some aspects, a quantum computing device including a quantum processing unit which includes multiple quantum elements kept at a cryogenic temperature TQE, and one or more Josephson Transmission Line (JTL) devices disposed at one or more temperature levels is hereby disclosed. The quantum computing device may be configured to send input signals from a temperature T higher than the cryogenic temperature T > TQE to quantum elements disposed at the cryogenic temperature TQE and to send output signals from quantum elements disposed at the cryogenic temperature TQE to the higher temperature T. The one or more Josephson Transmission Line (JTL) devices may be disposed at one or more temperature levels, where each temperature level is of a temperature TLI, while i represents the index of the level, and such that TLI> TQE or T > TLI> TQE. According to some aspects, at least one temperature level is of a temperature TLI between the cryogenic temperature TQE and thehigher temperature T, e.g., T > Tu > TQE. According to some aspects, at least one JTL is configured to amplify the output signals at a temperature level of the one or more temperature levels. The temperature T higher than the cryogenic temperature TQE may be, for example, a higher cryogenic temperature (e.g., TQE < T < 4K, TQE < T < 10K, or TQE < T < 77K) or up to room temperature. The term cryogenic temperature as referred to herein relates to any temperature below 77K. According to some aspects, a cryogenic temperature at which the quantum elements are kept may be below 100 milli-Kelvin (mK). According to some aspects, a cryogenic temperature at which the quantum elements are kept may be between or equal to 5mK and 50mK. According to some aspects, a temperature level at which JTL devices may be disposed is of cryogenic temperature such as 100 mK, IK, or 4K. According to some aspects, each JTL stage of each JTL device comprises at least one Josephson Junction (JJ) designed to have a critical current value corresponding to the temperature level at which the respective JTL device is disposed.

[0407] Reference is now made to Figures 30A and 30B. Figure 30A is a schematic illustration of JTL devices placed at an intermediate temperature stage. Figure 30B is a schematic illustration of an exemplary JTL device 700.

[0408] Referring to Figure 30A, illustrates JTL devices 704 and 710 placed in a cryostat including temperature plates 706A-706C of different temperatures. JTL devices 704 and 710 are placed at an intermediate temperature stage, at temperature plates 706B of the cryostat. JTL device 704 is designed to amplify an output SFQ signal 702. Portion 702A of signal 702 enters JTL device 704 and amplified signal portion 702B of signal 702 is output by JTL device 704. JTL device 710 is designed to attenuate input SFQ signals 708 propagating between the temperature stages. Portion 708 A of signal 708 enters JTL device 710 and attenuated signal portion 708B of signal 708 is output by JTL device 710.

[0409] Referring now to Fig. 30B, JTL device 700 includes a chain of JTL stages. JTL device 700 includes a receiver stage 722 configured to receive input signal 728A, at least one intermediate stage indicated 724 and a final, transmitter stage 726, configured to output signal 728B which is signal 728A amplified or attenuated, depending on the specific configuration of JTL device 700.

[0410] Each JTL stage, such as JTL stages 722, 724 and 726, may include, inter alia, respective current sources 730A, 730B and 730C, respective inductors 732A, 732B and 732C and respective JJs 734A, 734B and 734C. JTL device 700 is configured with gradually increasing or gradually decreasing critical currents L1, Ic2, and Ic3, of respective JJs 734A, 734Band 734C of respective stages 722, 724 and 726, with the first, receiver stage 722, designed to match the incoming SFQ signal from the previous temperature stage, and the final, transmitter stage 726, designed to match the requirements for the next temperature stage.

[0411] The design of the JTL device, including number of stages and values of critical currents may vary according to the requirement of the specific quantum computing system and may be contemplated by a person skilled in the art.

[0412] According to some aspects, a method for transferring signals in a cryogenic environment for quantum computing is disclosed. The method may include amplifying signals output by multiple quantum elements kept at a cryogenic temperature by one or more Josephson Transmission Line (JTL) devices. The JTL devices are disposed at one or more temperature levels, where each temperature level is equal to or higher than the cryogenic temperature. According to some aspects, at least one temperature level is of a temperature higher than the cryogenic temperature.

[0413] According to some aspects, the one or more JTL devices include a plurality of JTL devices, the one or more temperature levels include a plurality of temperature levels, and the amplifying of the output signals includes gradually amplifying the output signals by a JTL amplifier chain including at least a portion of the plurality of JTL devices interconnected in series and disposed along the respective temperature levels.

[0414] According to some aspects, each JTL device in the JTL amplifier chain has a plurality of progressively higher critical currents.

[0415] According to some aspects, the method further includes gradually attenuating input signals transferred to the plurality of quantum elements from a temperature higher than the cryogenic temperature by a JTL attenuator chain. The JTL attenuator chain may include the rest of the plurality of JTL devices interconnected in series and disposed along the temperature levels, where at least one temperature level is between the cryogenic temperature level and the higher temperature level.

[0416] According to some aspects, each JTL stage of each JTL device includes at least one Josephson Junction (JJ) designed to have a critical current value corresponding to the temperature level at which the respective JTL device is disposed.

[0417] According to some aspects, the one or more temperature levels include a plurality of temperature levels, where each temperature level is of a different temperature between the cryogenic temperature and the higher temperature.

[0418] According to some aspects, the disclosed systems and methods for transferring signals through different temperature stages may be also utilized or adapted (e.g., by a person of ordinary skill in the art) to transfer non-digital signals (e.g., analog signals), such as RF signals.

[0419] The disclosed systems, devices and methods may be used separately or solely, e.g., with other components or may be embedded in other architectures known to a person skilled in the art or may be used in combination.

[0420] The illustrated components of the drawings are exemplary, and variations are contemplated to be within the scope of the present disclosure. For example, the types of components may be different than as described.

[0421] The aspects described above are exemplary and variations are contemplated to be within the scope of the present disclosure.

[0422] For purposes of explanation, specific configurations and details are set forth in order to provide a thorough understanding of aspects of the disclosed technologies. However, it is apparent to one skilled in the art that the disclosed technologies can be practiced without using every aspect presented herein.

[0423] Different aspects are disclosed herein. Features of certain aspects can be combined with features of other aspects; thus, certain aspects can be combinations of features of multiple aspects.

[0424] While several embodiments of the disclosure have been described herein or shown in the drawings, it is not intended that the disclosure be limited thereto, as it is intended that the disclosure be as broad in scope as the art will allow and that the specification be read likewise. Therefore, the above description should not be construed as limiting, but merely as exemplifications of particular embodiments. Those skilled in the art will envision other modifications within the scope and spirit of the claims appended hereto.

Claims

CLAIMS1. A quantum processing unit, comprising multiple quantum elements arranged in multiple sets of quantum elements, wherein the quantum processing unit is configured to operate not more than a single quantum element of each set of quantum elements in parallel.

2. The quantum processing unit according to claim 1, wherein the quantum processing unit is configured to apply operations on the multiple quantum elements, and wherein the quantum processing unit is configured to apply each operation of the operations on not more than a single quantum element of each set of quantum elements.

3. The quantum processing unit according to claim 1, further comprising multiple cells, wherein each cell of the multiple cells comprises a respective set of quantum elements of the sets of quantum elements.

4. The quantum processing unit according to claim 3, wherein each cell of the plurality of cells comprises up to a predefined number of quantum elements.

5. The quantum processing unit according to claim 3, wherein the multiple cells are of one or more types.

6. The quantum processing unit according to claim 3, wherein the multiple cells are arranged in a periodic pattern.

7. The quantum processing unit according to claim 3, further comprising multiple supercells, wherein the multiple cells are arranged in sets of cells, and wherein each supercell of the multiple supercells comprises a respective set of cells of the sets of cells.

8. The quantum processing unit according to claim 7, wherein each supercell of the plurality of supercells comprises up to a predefined number of cells.

9. The quantum processing unit according to claim 7, wherein scaling of the quantum processing unit is performed by adding one or more additional supercells.

10. The quantum processing unit according to claim 7, further comprising at least one module, wherein the multiple supercells are arranged in one or more sets of supercells, and wherein the at least one module comprises a respective set of supercells of the one or more sets of supercells.

11. The quantum processing unit according to claim 10, wherein scaling of the quantum processing unit is performed by adding one or more additional modules.

12. The quantum processing unit according to any of claims 1 to 11, further comprising multiple control channels configured to provide instructions for operating the multiple quantum elements, wherein each control channel of the multiple control channels is configured to provide instructions for operating quantum elements of a different plurality of sets of quantum elements of the multiple sets of quantum elements.

13. The quantum processing unit according to claim 12, further comprising multiple supercells, each supercell of the multiple supercells comprising a plurality of sets of quantum elements of the multiple sets of quantum elements, wherein each supercell of the multiple supercells is coupled with a different one or more control channels of the multiple control channels.

14. The quantum processing unit according to claim 13, wherein each supercell of the multiple supercells is coupled with a single different control channel of the multiple control channels.

15. The quantum processing unit according to claim 13, further comprising a predefined number of input signal sources, each input signal source is configured to generate signals for operating the multiple quantum elements, wherein each supercell of the multiple supercells is coupled with a predefined number of control channels, and wherein the predefined number of control channels is determined based on the predefined number of input signal sources.

16. The quantum processing unit according to any of claims 1 to 11, wherein: the quantum processing unit is configured to apply operations on the multiple quantum elements,each quantum element of the multiple quantum elements is assigned to a single Quantum Element Set of OPeration (QESOP) of a plurality of QESOPs, each operation of the operations is applied on at least a plurality of quantum elements of the multiple quantum elements, each QESOP of the plurality of QESOPs comprises a plurality of quantum elements of the multiple quantum elements, and each operation of the operations is applied only to quantum elements of a single QESOP of the plurality of QESOPs.

17. The quantum processing unit according to claim 16, wherein for each set of the quantum elements of the multiple sets of quantum elements, each quantum element of the set of quantum elements is assigned to a different QESOP.

18. The quantum processing unit according to claim 16, further comprising at least one routing control channel configured to cause the routing of control sequences for applying each operation of the operations on its respective QESOP, wherein each routing control channel of the at least one routing control channel is configured to cause the routing of the control sequences for applying each operation by enabling the routing of the control sequences to at least a plurality of quantum elements of the multiple quantum elements assigned to the respective QESOP.

19. The quantum processing unit according to claim 18, further comprising at least one module, each module of the at least one module comprising different sets of quantum elements of the multiple sets of quantum elements, wherein each module of the at least one module is coupled with one or more routing control channels of the at least one routing control channel, and wherein the one or more routing control channels coupled with each module of the at least one module are configured to cause the routing of the control sequences for applying an operation on the quantum elements of the respective module which are assigned to the operation’s respective QESOP.

20. The quantum processing unit according to claim 19, wherein each module of the at least one module is coupled with a single routing control channel of the at least one routing control channel.

21. The quantum processing unit according to claim 18, wherein: each QESOP of the multiple QESOPs is assigned with a different address of a plurality of addresses, each quantum element is assigned with its QESOP’ s respective address, and the routing of the control sequences is based on the quantum elements assigned addresses.

22. The quantum processing unit according to claim 18, wherein each routing control channel comprises a current, and wherein the routing is based on the present value of a characteristic of the current.

23. The quantum processing unit according to claim 22, wherein the characteristic of the current is the direction of the current.

24. The quantum processing unit according to claim 22, wherein the present value of the characteristic of the current enables the branching of the presently provided control sequences towards the respective quantum elements.

25. The quantum processing unit according to any of claims 1 to 11, wherein each quantum element of the multiple quantum elements is assigned to a single QESOP of a plurality of QESOPs, and wherein the quantum processing unit is configured to operate in parallel only quantum elements of the multiple quantum elements which are of the same QESOP.

26. The quantum processing unit according to any of claims 1 to 11, further configured to apply at least one measurement operation once in each cycle of operations, wherein each cycle of operations comprises the application of one or more operations, and wherein each measurement operation is configured to measure only a single quantum element of each set of quantum elements.

27. The quantum processing unit according to any of claims 1 to 11, wherein operating a quantum element of the multiple quantum elements is performed by applying a control sequence on the quantum element via input signal sources of a plurality of input signalsources, and wherein each input signal source of the plurality of input signal sources is coupled with the multiple quantum elements.

28. The quantum processing unit according to claim 27, further comprising the plurality of input signal sources.

29. The quantum processing unit according to claim 27, wherein the control sequence comprises a time-dependent series of a plurality of control subsequences, and each control subsequence of the plurality of control subsequences comprises a signal generated by a single input signal source of the plurality of input signal sources at a time interval, or defines a time interval during which the plurality of input signal sources does not generate signals.

30. The quantum processing unit according to any of claims 1 to 11, further comprising multiple memory elements, wherein each memory element of the multiple memory elements is coupled with a different set of quantum elements of the multiple sets of quantum elements and configured to store information received from its respective set of quantum elements.

31. A method for quantum computing, the method comprising applying operations on multiple quantum elements, wherein the multiple quantum elements are arranged in multiple sets of quantum elements, and wherein each operation of the operations is applied on not more than a single quantum element of each set of quantum elements of the multiple sets of quantum elements.

32. The method according to claim 31, wherein not more than a single quantum element of each set of quantum elements of the multiple sets of quantum elements is operated in parallel.

33. The method according to claim 31 or 32, wherein the applying of operations on the multiple quantum elements comprises providing instructions for operating the multiple quantum elements via multiple control channels, wherein each control channel of the multiple control channels is configured to provide instructions for operating quantum elements of a plurality of sets of quantum elements of the multiple sets of quantum elements.

33. The method according to claim 33, wherein the multiple sets of quantum elements are arranged in multiple supercells, each supercell of the multiple supercells comprising a different plurality of sets of the multiple sets of quantum elements, and wherein the applying of operations on the quantum elements comprises providing instructions for operating the quantum elements of each supercell of the multiple supercells via a single different respective control channel of the multiple control channels.

34. The method according to claim 31 or 32, wherein: each quantum element of the multiple quantum elements is assigned to a single Quantum Element Set of OPeration (QESOP) of a plurality of QESOPs, each operation of the operations is applied on at least a plurality of quantum elements of the multiple quantum elements, each QESOP of the plurality of QESOPs comprises a plurality of quantum elements of the multiple quantum elements, and each operation of the operations is applied only on quantum elements of a single respective QESOP of the plurality of QESOPs.

35. The method according to claim 34, wherein for each set of the quantum elements of the multiple sets of quantum elements, each quantum element of the set of quantum elements is assigned to a different QESOP.

36. The method according to claim 34, wherein applying each operation of the operations comprises causing the routing of control sequences for applying the operation by enabling the routing of the control sequences to at least a plurality of quantum elements of the multiple quantum elements assigned to the respective QESOP.

37. The method according to claim 36, wherein: each QESOP of the multiple QESOPs is assigned with a different address of a plurality of addresses, each quantum element is assigned with its QESOP’ s respective address, and enabling the routing of the control sequences of each operation is performed by enabling the routing of the control sequences to quantum elements of the multiple quantum elements assigned with the respective QESOP address.

38. The method according to claim 31, wherein applying operations on the quantum elements is performed by applying control sequences on the quantum elements generated via a plurality of input signal sources, and wherein each input signal source of the plurality of input signal sources is coupled with the quantum elements and configured to provide signals for operating each quantum element of the quantum elements.

39. The quantum processing unit according to claim 38, wherein each control sequence of the control sequences comprises a time-dependent series of a plurality of control subsequences, and each control subsequence of the plurality of control subsequences comprises a signal generated by a single input signal source of the plurality of input signal sources at a time interval, or defines a time interval during which the plurality of input signal sources does not generate signals, and wherein the method further comprises providing instructions for generating the control sequences.

40. A system for controlling quantum elements, the system comprising: a plurality of input signal sources configured to generate signals and comprising at least two different input signal sources, wherein each input signal source of the plurality of input signal sources is coupled with at least one quantum element of the quantum elements; and at least one controller configured to provide data signals comprising instructions, wherein the instructions are configured to cause the system to: generate one or more control sequences, wherein: the one or more control sequences are configured to apply one or more desired respective operation on the at least one quantum element, each control sequence of the one or more control sequences comprises a timedependent series of a plurality of control subsequences, and each control subsequence of the plurality of control subsequences comprises a signal generated by a single input signal source of the plurality of input signal sources at a time interval, or defines a time interval during which the plurality of input signal sources does not generate signals; andapply the one or more control sequences on the at least one quantum element thereby applying the desired one or more operations on the at least one quantum element.

41. A quantum processing unit comprising: the system according to claim 40, and the quantum elements.

42. The system according to claim 33, further comprising at least one combiner coupled with the plurality of input signal sources, the at least one controller and the at least one quantum element, the combiner configured to: receive the data signals from the at least one controller; and temporally output control subsequences comprising signals generated by one or more input signal sources of the plurality of input signal sources according to the received instructions to the at least one quantum element.

43. The system according to claim 42, wherein the at least one controller comprises: at least one first controller coupled with the at least one combiner, configured to provide the data signals to the at least one combiner; and at least one second controller coupled with the first controller and configured to: calculate the one or more control sequences, store the instructions for generating the one or more control sequences in association with the corresponding one or more operations in a storage device, and access the instructions for generating the one or more control sequences, when required.

44. The system according to claim 43, wherein the at least one quantum element is a superconducting quantum element, and wherein the at least one first controller is kept at a cryogenic temperature and the at least one second controller is kept at room temperature.

45. The system according to claim 42, wherein the at least one combiner is configured to temporally switch on or switch off each input signal source of one or more input signal sources of the plurality of input signal sources according to the received instructions.

46. The system according to claim 42, wherein the at least one combiner is configured to select, according to the received instruction, the input signal source of the plurality of input signal sources from which a signal is output to the at least one quantum element at a specific time.

47. The system according to claim 42, wherein the plurality of input signal sources is ordered according to a predefined order, and wherein the at least one combiner is configured, upon receiving an instruction from the controller, to output a signal generated from the next input signal source of the plurality of input signal sources, according to the predefined order.

48. The system according to claim 47, wherein one or more instructions for generating a control sequence comprise a time-dependent sequence of two or more triggers.

49. The system according to claim 42, wherein the at least one combiner comprises at least one multiplexer.

50. The system according to claim 49, wherein the plurality of input signal sources is configured to continuously generate signals, and wherein the at least one multiplexer is configured to output a signal from a certain input signal source of the plurality of input signal sources at a time.

51. The system according to claim 42, wherein the at least one controller is further configured to timely provide an instruction for generating each control subsequences of a control sequence to the at least one combiner, and wherein the at least one combiner is further configured, once the instruction is received, to immediately output a signal generated by the corresponding input signal source of the plurality of input signal sources to the at least one quantum element.

52. The system according to claim 42, further comprising at least one transmission line coupled with the at least one combiner and the at least one quantum element and configured to feed the output of the at least one combiner to the at least one quantum element.

53. The system according to claim 42, wherein the received data signals vary in time synchronized with a clock, and wherein the clock has a frequency above 10 Mega Hertz (MHz) and below 10 Giga Hertz (GHz).

54. The system according to any of claim 35 to 53, wherein: the at least one combiner comprises a first combiner and at least one second combiner, the first combiner coupled with the at least one second combiner; the at least one second combiner is coupled with one or more input signal sources of the plurality of input signal sources, the first combiner is configured to temporally output the control subsequences to the at least one quantum element, and each control subsequence outputted by the first combiner comprises a signal outputted by a combiner of the at least one second combiner, or each control subsequence outputted by the first combiner comprises a signal outputted by a combiner of the at least one second combiner or a signal generated by an input signal source of the plurality of input signal sources other than the one or more input signal sources.

55. The system according to claim 54, wherein the at least one quantum element and the first combiner are kept at a cryogenic temperature, and wherein at least one combiner of the at least one second combiner is kept at a cryogenic temperature.

56. The system according to claim 54, wherein the at least one quantum element, the first combiner and the at least one second combiner are kept at a cryogenic temperature57. The system according to claim 42, wherein the instructions comprise addresses of the input signal sources from which a signal is to be output by the at least one combiner per time.

58. The system according to claim 42, wherein the at least one quantum element is an at least one superconducting quantum element and wherein the at least one quantum element, and a combiner of the at least one combiner configured to output the control signal to the at least one quantum element, are kept at a cryogenic temperature.

59. The system according to claim 40, wherein the at least one controller is further configured to calculate one or more control sequences corresponding to one or more operations of interest, and wherein instructions for generating each control sequence of the calculated one or more control sequences are stored in a storage device.

60. The system according to claim 59, wherein the one or more control sequences are calculated offline.

61. The system according to claim 40, wherein each of the at least two different input signal sources is of a different characteristic selected from: periodicity, phase shift, time delay, or amplitude.

62. The system according to claim 40, further comprising a measurement system, the measurement system comprising at least one detector configured to measure one or more parameters of the at least one quantum element, wherein the measurement system is coupled with the at least one controller and the at least one quantum element, and wherein the at least one controller is further configured to calculate the control sequence based on the measured one or more parameters of the at least one quantum element received from the measurement system.

63. The system according to claim 62, wherein the one or more parameters are measured at predefined times or when required.

64. The system according to claim 62, wherein the one or more parameters comprise at least one parameter selected from: resonance frequency, anharmonicity, coherence properties and drive port coupling strength.

65. The system according to claim 43, wherein the at least one controller is further configured to suppress leakage to non-computational states of the at least one quantum element when calculating a control sequence of the one or more control sequences of interest.

66. The system according to claim 40, wherein the plurality of input signal sources comprises a plurality of Radio-Frequency (RF) analog signal sources.

67. The system according to claim 40, wherein the plurality of input signal sources comprises a plurality of microwave signal sources.

68. The system according to claim 40, wherein the plurality of input signal sources comprises a plurality of Single Flux Quantum (SFQ) signal sources.

69. The system according to claim 40, wherein at least one input signal source of the plurality of input signal sources is a null input signal source.

70. The system according to claim 69, wherein the at least one null input signal source is configured to emit a zero-amplitude pulse.

71. The system according to claim 40, wherein at least one input signal source of the plurality of input signal sources is a periodic signal source.

72. The system according to claim 40, wherein the plurality of input signal sources is periodic input signal sources, and wherein each input signal source of the plurality of input signal sources has a different period.

73. The system according to claim 40, wherein each input signal source of the plurality of input signal sources is a periodic input signal source, and wherein at least one input signal source of the plurality of input signal sources has a frequency different from a resonance frequency associated with one or more quantum elements of the at least one quantum element.

74. The system according to claim 73, wherein the plurality of input signal sources has frequencies different from a resonance frequency associated with the at least one quantum element.

75. The system according to claim 73, wherein the difference between a second or a higher harmonic of the least one frequency of the at least one input signal source and a resonancefrequency associated with one or more quantum elements of the at least one quantum element is between one kilo Hertz (kHz) and 500 Mega Hertz (MHz).

76. The system according to claim 73, wherein the difference between at least one frequency of the at least one input signal source and a resonance frequency associated with one or more quantum elements of the at least one quantum element is between one kilo Hertz (kHz) and 500 Mega Hertz (MHz).

77. The system according to claim 76, wherein the desired operation is a single-qubit gate or a two-qubit gate, and wherein when applied, the operation has gate infidelity lower than 0.005.

78. The system according to claim 40, wherein the at least one controller is further configured to decrease discretization errors due to its finite clock frequency when providing the data signals.

79. The system according to claim 40, wherein the at least one quantum element comprises at least one qubit.

80. The system according to claim 79, wherein the at least one qubit comprises a quantum dot, a spin qubit or a defect in a solid-state substrate.

81. The system according to claim 40, wherein the at least one quantum element comprises at least one coupler element configured to couple between at least two qubits.

82. The system according to claim 40, wherein the at least one quantum element comprises at least one resonator.

83. The system according to claim 40, wherein the at least one quantum element is an at least one superconducting quantum element.

84. The system according to claim 40, wherein the desired operation is a single-qubit gate, a two-qubit gate, a qubit initialization, a qubit reset, or a qubit measurement operation.

85. The system according to claim 40, wherein the plurality of input signal sources comprises not more than ten input signal sources.

86. The system according to claim 40, wherein the quantum elements are arranged in sets of quantum elements, wherein not more than a single quantum element of each set of quantum elements is operated in parallel.

87. The system according to claim 86, wherein each input signal source of the plurality of input signal sources is coupled with the quantum elements.

88. The system according to claim 86, wherein the sets of quantum elements are arranged in cells, each cell of the cells comprising a single different set of quantum elements of the sets of quantum elements, and wherein the cells are arranged in supercells, each supercell of the supercells comprising a different plurality of cells of the cells, the system further comprising multiple control channels configured to provide the instructions, wherein each supercell of the multiple supercells is coupled with a different one or more control channels of the multiple control channels, and wherein each control channel of the multiple control channels is configured to provide the instructions to the plurality of cells of the respective supercell.

89. The system according to claim 86, wherein: each quantum element of the quantum elements is assigned to a single Quantum Element Set of OPeration (QESOP) of a plurality of QESOPs, for each set of the quantum elements of the sets of quantum elements, each quantum element of the set of quantum elements is assigned to a different QESOP of the plurality of QESOPs, and only quantum elements assigned to the same QESOP of the plurality of QESOPs are operated in parallel.

90. The system according to claim 89, further comprising at least one routing control channel configured to cause the routing of the control sequences for applying each operation of the one or more desired operations on the quantum elements of the respective QESOP, wherein each routing control channel of the at least one routing control channel is configured to causethe routing of the control sequences by enabling the routing of the control sequences to at least a plurality of the quantum elements assigned to the respective QESOP.

91. A computerized method for controlling at least one quantum element, the method comprising providing instructions for generating a control sequence designed to apply a desired operation on the at least one quantum element, the instructions comprising a time-dependent series of instructions configured to generate a time-dependent series of control subsequences, the time-dependent series of control subsequences forming the control sequence, wherein each instruction causes the generation and application of a control subsequence of the time-dependent series of control subsequences on the at least one quantum element at its respective time, and wherein each control subsequence of the plurality of control subsequences comprises a signal and each control sequence comprises at least two different signals.

92. The method according to claim 91, further comprising calculating the control sequence.

93. The method according to claim 92, further comprising storing the instructions for generating the control sequence and accessing the instructions when required.

94. The method according to claim 93, wherein providing the instructions for generating the control sequence is performed by at least one first controller, and calculating the control sequence and storing it are performed by at least one second controller, coupled with the at least one first controller, and wherein the method further comprises providing the instructions to the at least one first controller by the at least one second controller.

95. The method according to claim 94, wherein the at least one quantum element is a superconducting quantum element, and wherein the at least one first controller is kept at a cryogenic temperature and the at least one second controller is kept at room temperature.

96. The method according to claim 92, further comprising accessing measured values of one or more parameters of the at least one quantum element, wherein the calculating of the control sequence is performed based on the measured values of the one or more parameters.

97. The method according to claim 96, further comprising causing a measurement system comprising at least one detector and coupled with the at least one quantum element to measure the one or more parameters.

98. The method according to claim 97, wherein causing the measurement system to measure the one or more parameters is repeatedly performed.

99. The method according to claim 96, wherein the one or more parameters comprise at least one parameter selected from: resonance frequency, anharmonicity, coherence properties and drive port coupling strength.

100. The method according to claim 92, wherein the calculating of the control sequence comprises suppressing leakage to non-computational states of the at least one quantum element.

101. The method according to claim 92, wherein the control sequence is calculated offline.

102. The method according to any of claim 91 to 101, wherein the instructions are provided to at least one combiner, coupled with the at least one quantum element.

103. The method according to claim 102, wherein each instruction of the instructions for generating the control sequence causes the at least one combiner to: output a signal generated by a specific input signal source of a plurality of input signal sources, or cease to output a signal.

104. The method according to claim 103, wherein each instruction of the instructions for generating the control sequence which causes the at least one combiner to output a signal comprises the address of the respective signal source configured to generate the output signal.

105. The method according to claim 103, wherein the plurality of input signal sources is ordered according to a predefined order, and wherein each instruction of the instructions for generating the control sequence comprises a trigger causing the at least one combiner tooutput a signal generated by the next input signal source of the plurality of input signal sources according to the predefined order.

106. The method according to claim 103, wherein each instruction of the instructions for generating the control sequence causes the at least one combiner to switch on or switch off each input signal source of one or more input signal sources of the plurality of input signal sources.

107. The method according to claim 103, wherein the plurality of input signal sources comprises at least two different input signal sources, and wherein each input signal source of the at least two different input signal sources is of a different characteristic selected from: periodicity, phase shift, time delay, or amplitude.

108. The method according to claim 91, wherein the providing of the instructions further comprises timely providing each instruction of the time-dependent series of instructions for generating each corresponding control subsequence of the time-dependent series of control subsequences to the at least one combiner, causing to immediately output a signal to be applied on the at least one quantum element or cease the output of signals, according of the provided instruction.

109. The method according to claim 91, wherein the instructions for generating the control sequence are provided via at least one controller and the provision of the instructions is performed such that discretization errors due to the finite frequency of a clock of the at least one controller are decreased.

110. The method according to claim 91, wherein the method is for controlling multiple quantum elements arranged in sets of quantum elements, the method further comprising applying the desired operation such that not more than a single quantum element of each set of quantum elements is operated in parallel.

111. The method according to claim 110, wherein the applying of the desired operation on the multiple quantum elements comprises providing instructions for operating the multiple quantum elements via multiple control channels, wherein each control channel of the multiplecontrol channels is configured to provide instructions for operating quantum elements of a different plurality of sets of quantum elements of the multiple sets of quantum elements.

112. The method according to claim 110, wherein: each quantum element of the multiple quantum elements is assigned to a single Quantum Element Set of OPeration (QESOP) of a plurality of QESOPs, for each set of the quantum elements of the sets of quantum elements, each quantum element of the set of quantum elements is assigned to a different QESOP of the plurality of QESOPs, and only quantum elements assigned to the same QESOP of the plurality of QESOPs are operated in parallel.

113. The method according to claim 112, wherein applying the desired operation comprises causing the routing of control sequences for applying the operation by enabling the routing of the control sequences to at least a plurality of quantum elements of the multiple quantum elements assigned to the respective QESOP.

114. A quantum processing unit comprising: multiple quantum elements; multiple splitting devices successively interconnected in one or more separate chains of splitting devices, each splitting device of the multiple splitting devices, which is not the last splitting device in a chain of the one or more chains of splitting devices, is configured to duplicate a received triggering signal to a first triggering signal and a second triggering signal, wherein the first triggering signal is configured to trigger output of information relating to a respective quantum element of the multiple quantum elements and the second triggering signal is transferred to the next interconnected splitting device in the respective chain of splitting devices.

115. The quantum processing unit according to claim 114, further comprising multiple memory elements, each memory element of the multiple memory elements is coupled with one or more quantum elements of the multiple quantum elements and with a different splitting device of the multiple splitting devices, wherein each memory element of the multiple memory elements is configured to store information received from its respective oneor more quantum elements, and wherein the first triggering signal is configured to trigger output of information by triggering the respective memory element to output its stored information.

116. The quantum processing unit according to claim 115, further comprising one or more merging combiners, wherein each merging combiner of at least one merging combiner of the one or more merging combiners is coupled with a plurality of memory elements of the multiple memory elements, such that the plurality of memory elements is coupled with splitting devices of the multiple splitting devices which are of the same chain of splitting devices, and wherein each merging combiner of the at least one merging combiner of the one or more merging combiners is configured to fan in information received from its respective plurality of memory elements to a single information output line.

117. The quantum processing unit according to claim 116, wherein each merging combiner of at least one merging combiner of the one or more merging combiners is coupled with a plurality of merging combiners of the rest of the one or more merging combiners, and is configured to fan in information received from its respective plurality of merging combiners to a single information output line.

118. The quantum processing unit according to claim 115, further comprising multiple merging combiners successively interconnected in a chain of merging combiners, each merging combiner of the multiple merging combiners is coupled with a different memory element of the multiple memory elements, wherein each merging combiner of the multiple merging combiners is configured to receive information from its preceding merging combiner in the chain of merging combiners or from its respective memory element, and wherein: each merging combiner of the multiple merging combiners, except for the last merging combiner in the chain of merging combiners, is configured to transfer the received information to the successively interconnected merging combiner, and the last merging combiner in the chain of merging combiners is configured to fan in its received information to a single information output line.

119. The quantum processing unit according to claim 115, further comprising one or more merging combiners, wherein each merging combiner of the one or more merging combinersis coupled with two or more information mediums of multiple information mediums, wherein the multiple information mediums comprise the multiple memory elements or merging combiners of the one or more merging combiners, and wherein at least one merging combiner of the one or more merging combiners is configured to fan in information received from its respective two or more information mediums to a single information output line.

120. The quantum processing unit according to any of claims 116-119, wherein at least one of the one or more merging combiners is designed with a dual-rail configuration.

121. The quantum processing unit according to any of claims 115-119, wherein the multiple memory elements are triggered once every error correction cycle of the quantum processing unit.

122. The quantum processing unit according to claim 115, wherein the multiple quantum elements are arranged in multiple sets of quantum elements, wherein the quantum processing unit is configured to operate not more than a single quantum element of each set of quantum elements in parallel.

123. The quantum processing unit according to claim 122, wherein each memory element of the multiple memory elements is coupled with a different set of quantum elements of the multiple sets of quantum elements.

124. A method for reading out information from multiple quantum elements, the method comprising: duplicating a received triggering signal by each splitting device of multiple splitting devices successively interconnected in a chain of splitting devices, except for the last splitting device of the chain of the splitting devices, to a first triggering signal and a second triggering signal; utilizing the first triggering signal to trigger output of information relating to a respective quantum element of the multiple quantum elements; and transferring the second triggering signal to the next interconnected splitting device in the chain of splitting devices.

125. The method according to claim 124, further comprising providing a triggering signal to a first splitting device of the chain of splitting devices.

126. The method according to claim 124, wherein each splitting device of the chain of splitting devices is coupled with a memory element of a plurality of memory elements which is coupled with the respective quantum element, and for each splitting device of the chain of splitting devices, except from the last splitting device, triggering output of information relating to the respective quantum element comprises triggering the coupled respective memory element to output information stored in the memory element and which was received from the respective quantum element.

127. The method according to claim 126, wherein each memory element of the plurality of memory elements is coupled with a different one splitting device of the plurality of splitting devices, the method further comprising fanning in information output by the plurality of memory elements to a single information output line.

128. The method according to claim 127, wherein the fanning in of the information output by the plurality of memory elements is performed via one or more merging combiners.

129. The method according to claim 126, wherein the triggering of the memory element is performed once every error correction cycle.

130. The method according to claim 126, wherein the multiple quantum elements are arranged in multiple sets of quantum elements, and wherein not more than a single quantum element of each set of quantum elements is operated in parallel.

131. The method according to claim 130, wherein each memory element of the multiple memory elements is coupled with a different set of quantum elements of the multiple sets of quantum elements.

132. A quantum computing device comprising: a quantum processing unit comprising multiple quantum elements kept at a cryogenic temperature, wherein the quantum computing device is configured to send input signals froma temperature higher than the cryogenic temperature to the multiple quantum elements at the cryogenic temperature and to send output signals from the multiple quantum elements at the cryogenic temperature to the higher temperature; and one or more Josephson Transmission Line (JTL) devices disposed at one or more temperature levels, wherein at least one JTL of the one or more JTL devices is configured to amplify the output signals at a temperature level of the one or more temperature levels.

133. The quantum computing device of claim 132, wherein at least one temperature level of the one or more temperature levels is of a temperature between the cryogenic temperature and the higher temperature.

134. The quantum computing device of claim 132, wherein the one or more JTL devices comprise a plurality of JTL devices, and the one or more temperature levels comprise a plurality of temperature levels, and wherein at least a portion of the plurality of JTL devices is configured to generate a JTL amplifier chain for gradually amplifying the output signals along temperature levels of the plurality of temperature levels.

135. The quantum computing device of claim 134, wherein the JTL amplifier chain comprises the at least portion of plurality of JTL devices interconnected in series, each JTL device in the JTL amplifier chain having a plurality of progressively higher critical currents.

136. The quantum computing device of claim 134, wherein the rest of the plurality of JTL devices are configured to generate a JTL attenuator chain for gradually attenuating the input signals at one or more temperature levels of the plurality of temperature levels.

137. The quantum computing device of claim 132, wherein each JTL stage of each JTL device comprises at least one Josephson Junction (JJ) designed to have a critical current value corresponding to the temperature level at which the respective JTL device is disposed.

138. The quantum computing device of claim 132, wherein the one or more temperature levels comprise a plurality of temperature levels, and wherein each temperature level of the plurality of temperature levels is of a different temperature between the cryogenic temperature and the higher temperature.

139. A method for transferring signals in a cryogenic environment for quantum computing, the method comprising amplifying signals output by multiple quantum elements kept at a cryogenic temperature by one or more Josephson Transmission Line (JTL) devices, wherein the one or more JTL devices are disposed at one or more temperature levels, each temperature level equal to or higher than the cryogenic temperature.

140. The method according to claim 139, wherein at least one temperature level of the one or more temperature levels is of a temperature higher than the cryogenic temperature.

141. The method according to claim 139, wherein: the one or more JTL devices comprise a plurality of JTL devices, the one or more temperature levels comprise a plurality of temperature levels, and the amplifying of the output signals comprises gradually amplifying the output signals by a JTL amplifier chain comprising at least a portion of the plurality of JTL devices interconnected in series and disposed along the respective temperature levels.

142. The method according to claim 141, wherein each JTL device in the JTL amplifier chain has a plurality of progressively higher critical currents.

143. The method according to claim 141, further comprising gradually attenuating input signals transferred to the plurality of quantum elements from a temperature higher than the cryogenic temperature by a JTL attenuator chain comprising the rest of the plurality of JTL devices interconnected in series and disposed along the temperature levels, wherein at least one temperature level of the temperature levels is between the cryogenic temperature level and the higher temperature level.

144. The method according to claim 139, wherein each JTL stage of each JTL device of the one or more JTL devices comprises at least one Josephson Junction (JJ) designed to have a critical current value corresponding to the temperature level at which the respective JTL device is disposed.

145. The method according to claim 139, wherein the one or more temperature levels comprise a plurality of temperature levels, and wherein each temperature level of the plurality of temperature levels is of a different temperature between the cryogenic temperature and the higher temperature.

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