Coupling a data qubit to an ancillary qubit

Abstract

A device comprising a data qubit, a first qubit coupler, a second qubit coupler, and an auxiliary qubit. The first qubit coupler is coupled to the data qubit. The second qubit coupler is coupled to the first qubit coupler. The auxiliary qubit is coupled to the second qubit coupler. The first qubit coupler is configured to operate in a state to suppress interaction between the data qubit and the auxiliary qubit. The first qubit coupler and the second qubit coupler are each configured to operate in a respective state to enable interaction between the data qubit and the auxiliary qubit, entangling the state of the data qubit with the state of the auxiliary qubit.

Description

[Background technology]

[0001] The present disclosure relates generally to superconducting quantum computing, and more particularly to superconducting quantum systems and devices implemented using superconducting quantum bits (qubits). Superconducting quantum computing systems are implemented using circuit quantum electrodynamics (QED) devices that exploit the quantum dynamics of electromagnetic fields in superconducting circuits, including superconducting qubits, to generate and process quantum information. Generally, a superconducting qubit is an electronic circuit, implemented using components such as superconducting tunnel junctions (e.g., Josephson junctions), inductors, and / or capacitors, that, when cryogenically cooled, behaves as a quantum mechanical anharmonic (nonlinear) oscillator with quantized states. Due to the anharmonicity imparted by the qubit's nonlinear inductor element (e.g., Josephson inductance), the qubit can effectively operate as a two-level system with the qubit's ground state and first excited state, allowing the ground state and first excited state to be uniquely addressed at the qubit's transition frequency without significantly perturbing the qubit's higher-order excited states.

[0002] Superconducting quantum processors comprising multiple superconducting qubits can be used to perform various types of quantum information processing operations, where the superconducting qubits can be coherently controlled, placed in quantum superposition states (e.g., via single gate operations), exhibit quantum interference effects, and be entangled with one another (e.g., via entanglement gate operations). The fidelity of quantum gate operations can be adversely affected by undesired crosstalk (e.g., residual static ZZ interactions) between adjacent superconducting qubits. For example, undesired crosstalk between superconducting qubits can cause the transition frequency of one superconducting qubit to depend on the states of one or more nearby superconducting qubits. As quantum processors scale with increased numbers of superconducting qubits and higher integration densities, such undesired crosstalk becomes increasingly problematic. Summary of the Invention

[0003] Example embodiments of the present disclosure include techniques for coupling data qubits to ancillary qubits to facilitate operations such as quantum error correction.

[0004] An illustrative embodiment includes a device comprising a first data qubit, a first qubit coupler, a second qubit coupler, and an ancillary qubit. The first qubit coupler is coupled to the first data qubit. The second qubit coupler is coupled to the first qubit coupler. The ancillary qubit is coupled to the second qubit coupler. The first qubit coupler is configured to operate in a state to suppress interaction between the first data qubit and the ancillary qubit. The first qubit coupler and the second qubit coupler are each configured to operate in a respective state to enable interaction between the first data qubit and the ancillary qubit, entangling the state of the first data qubit with the state of the ancillary qubit.

[0005] Advantageously, using the first and second qubit couplers to control the interaction between the data qubit and the ancillary qubit enables reduced crosstalk between the first data qubit and the ancillary qubit, and between the first data qubit and other data qubits coupled to the same ancillary qubit, when at least the first qubit coupler is configured to operate in a given state. Furthermore, using the first and second qubit couplers to control the interaction between the first data qubit and the ancillary qubit provides strong exchange coupling between the first data qubit and the ancillary qubit when the first and second qubit couplers are each configured in their respective operating states to entangle the state of the first data qubit with the state of the ancillary qubit.

[0006] Another exemplary embodiment includes a system comprising a quantum processor having an array of qubits and a control system configured to generate control signals to control the quantum processor. The array of qubits includes a first data qubit, a first qubit coupler, a second qubit coupler, and an ancillary qubit. The first qubit coupler is coupled to the first data qubit and configured to operate in one of a first state and a second state in response to a first control signal applied to the first qubit coupler by the control system. The second qubit coupler is coupled to the first qubit coupler and configured to operate in one of the first state and the second state in response to a second control signal applied to the second qubit coupler by the control system. The ancillary qubit is coupled to the second qubit coupler. The first qubit coupler is configured to operate in the first state to suppress interaction between the first data qubit and the ancillary qubit. The first qubit coupler and the second qubit coupler are each configured to operate in a second state to enable an interaction between the first data qubit and the ancillary qubit and to entangle the state of the first data qubit with the state of the ancillary qubit.

[0007] In another exemplary embodiment, which may be combined with the preceding paragraph, the first qubit coupler and the second qubit coupler may each include a flux-tunable transmon qubit.

[0008] In another exemplary embodiment, which may be combined with the preceding paragraph, the first qubit coupler has a first multi-mode qubit having a first mode and a second mode, and the second qubit coupler has a second multi-mode qubit having the first mode and the second mode.

[0009] In another exemplary embodiment, which may be combined with the preceding paragraph, the first data qubit is capacitively coupled to the first mode of the first multi-mode qubit; the ancillary qubit is capacitively coupled to the first mode of the second multi-mode qubit; the second mode of the first multi-mode qubit is capacitively coupled to the second mode of the second multi-mode qubit; and the first qubit coupler is configured to operate with the first data qubit exchange coupled to only the first mode of the first multi-mode qubit. the first qubit coupler is configured to operate with the first data qubit exchange coupled to both the first mode and the second mode of the first multi-mode qubit; the second qubit coupler is configured to operate with the ancillary qubit exchange coupled to only the first mode of the second multi-mode qubit; and the second qubit coupler is configured to operate with the ancillary qubit exchange coupled to both the first mode and the second mode of the second multi-mode qubit.

[0010] Another exemplary embodiment includes a device comprising a data qubit, a qubit coupler, a transmission line resonator, and an auxiliary qubit. The qubit coupler is coupled to the data qubit. The transmission line resonator is coupled to the qubit coupler. The auxiliary qubit is coupled to the transmission line resonator. The qubit coupler is configured to operate in a state to suppress interaction between the data qubit and the auxiliary qubit. The qubit coupler is configured to operate in a state to allow interaction between the data qubit and the auxiliary qubit through the qubit coupler and the transmission line resonator, entangling the state of the data qubit with the state of the auxiliary qubit.

[0011] Advantageously, utilizing a qubit coupler and a transmission line resonator to control the interaction between the data qubit and the auxiliary qubit enables suppression of crosstalk between the data qubit and the auxiliary qubit, as well as suppression of crosstalk between the data qubit and other data qubits coupled to the same auxiliary qubit, when at least a first qubit coupler is configured in a given operational state. The transmission line resonator enables relatively long-range coupling of the data qubit and the auxiliary qubit. Furthermore, because the transmission line resonator has a relatively large capacitance to ground, which serves to reduce crosstalk between data qubits coupled to the same auxiliary qubit, the transmission line resonator eliminates the need for a dedicated qubit coupler to couple to the auxiliary qubit.

[0012] Another exemplary embodiment includes a system comprising a quantum processor having an array of qubits and a control system configured to generate control signals to control the quantum processor. The array of qubits includes data qubits, a qubit coupler, a transmission line resonator, and an auxiliary qubit. The qubit coupler is coupled to the data qubits. The transmission line resonator is coupled to the qubit coupler. The auxiliary qubit is coupled to the transmission line resonator. The qubit coupler is configured to operate in a state to suppress interaction between the data qubits and the auxiliary qubits. The qubit coupler is configured to operate in a state to enable interaction between the data qubits and the auxiliary qubits through the qubit coupler and the transmission line resonator, entangling the state of the data qubits with the state of the auxiliary qubits.

[0013] In another exemplary embodiment, which may be combined with the preceding paragraph, the qubit coupler includes a multi-mode qubit having a first mode and a second mode; the data qubit is capacitively coupled to the first mode of the multi-mode qubit; the transmission line resonator is capacitively coupled to the second mode of the multi-mode qubit; the qubit coupler is configured to operate with the data qubit exchange coupled to only the first mode of the multi-mode qubit; and the qubit coupler is configured to operate with the data qubit exchange coupled to both the first mode and the second mode of the multi-mode qubit.

[0014] Another exemplary embodiment includes a method comprising: initializing a state of an ancillary qubit; placing a first qubit coupler coupled to the ancillary qubit in an activated state; placing a second qubit coupler coupled to a data qubit in an activated state to allow interaction between the data qubit and the ancillary qubit through the first and second qubit couplers in the activated states and entangle the state of the first data qubit with the state of the ancillary qubit; placing each of the first qubit coupler and the second qubit coupler in a deactivated state; reading out the state of the ancillary qubit after each of the first qubit coupler and the second qubit coupler are placed in the deactivated state; and determining a presence of a quantum error based on the reading of the ancillary qubit.

[0015] Other embodiments are described in the following detailed description of exemplary embodiments, which is to be read in conjunction with the accompanying drawings. [Brief explanation of the drawings]

[0016] [Figure 1] The Bloch sphere is shown, which graphically represents the various states of a qubit.

[0017] [Figure 2A] 1A and 1B illustrate schematic diagrams of superconducting transmon qubits utilized to implement data qubits and ancillary qubits, according to exemplary embodiments of the present disclosure. [Figure 2B] 1A and 1B illustrate schematic diagrams of superconducting transmon qubits utilized to implement data qubits and ancillary qubits, according to exemplary embodiments of the present disclosure.

[0018] [Figure 3A] 1A-1C show schematic diagrams of superconducting multi-mode qubits that can be configured to implement superconducting multi-mode qubit couplers for coupling data qubits to ancillary qubits, in accordance with exemplary embodiments of the present disclosure. [Figure 3B] 1A-1C show schematic diagrams of superconducting multi-mode qubits that can be configured to implement superconducting multi-mode qubit couplers for coupling data qubits to ancillary qubits, in accordance with exemplary embodiments of the present disclosure.

[0019] [Figure 3C] 3C and 3D schematically illustrate two distinct excitation modes of the superconducting multi-mode qubit of FIGS. 3A and 3B, according to an exemplary embodiment of the present disclosure.

[0020] [Figure 4A] 1A-1C show schematic diagrams of tunable superconducting multi-mode qubit couplers utilized to couple superconducting data qubits and superconducting ancillary qubits, in accordance with exemplary embodiments of the present disclosure. [Figure 4B] 1A-1C show schematic diagrams of tunable superconducting multi-mode qubit couplers utilized to couple superconducting data qubits and superconducting ancillary qubits, in accordance with exemplary embodiments of the present disclosure.

[0021] [Figure 5]1A-1C show schematic diagrams of quantum devices comprising superconducting data qubits coupled to superconducting annular qubits using tunable superconducting multi-mode qubit couplers, in accordance with exemplary embodiments of the present disclosure.

[0022] [Figure 6] 1A-1C show schematic diagrams of quantum devices comprising superconducting data qubits coupled to superconducting ancillary qubits using tunable superconducting multi-mode qubit couplers and superconducting transmission line resonators, in accordance with exemplary embodiments of the present disclosure.

[0023] [Figure 7A] 1A-1C illustrate schematically a method of utilizing a tunable superconducting multi-mode qubit coupler to control the interaction between a superconducting data qubit and a superconducting ancillary qubit, according to an exemplary embodiment of the present disclosure.

[0024] [Figure 7B] 1A-1C diagrammatically illustrate a method for utilizing a tunable superconducting multi-mode qubit coupler to control the interaction between a superconducting data qubit and a superconducting annular qubit, according to an exemplary embodiment of the present disclosure. [Figure 7C] 1A-1C diagrammatically illustrate a method for utilizing a tunable superconducting multi-mode qubit coupler to control the interaction between a superconducting data qubit and a superconducting annular qubit, according to an exemplary embodiment of the present disclosure.

[0025] [Figure 8] 1A-1C show schematic diagrams of quantum devices comprising an array of superconducting qubits with superconducting data qubits coupled to superconducting ancillary qubits using superconducting qubit couplers, in accordance with exemplary embodiments of the present disclosure.

[0026] [Figure 9]1A-1C show schematic diagrams of quantum devices comprising an array of superconducting qubits with superconducting data qubits coupled to superconducting ancillary qubits using superconducting qubit couplers and transmission line resonators, in accordance with exemplary embodiments of the present disclosure;

[0027] [Figure 10] 10A-B schematically illustrate quantum devices comprising an array of superconducting qubits having superconducting data qubits coupled to superconducting ancillary qubits using superconducting qubit couplers, in accordance with another exemplary embodiment of the present disclosure.

[0028] [Figure 11] 10A-B schematically illustrate quantum devices comprising an array of superconducting qubits having superconducting data qubits coupled to superconducting ancillary qubits using superconducting qubit couplers, in accordance with another exemplary embodiment of the present disclosure.

[0029] [Figure 12] 1 is a flow diagram of a method for performing a quantum error correction process, according to an exemplary embodiment of the present disclosure.

[0030] [Figure 13] 1 illustrates a schematic diagram of a quantum computing system according to an exemplary embodiment of the present disclosure.

[0031] [Figure 14] 1 illustrates a schematic diagram of an exemplary architecture of a computing environment for hosting a quantum computing platform and performing quantum information processing, according to an exemplary embodiment of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0032] Exemplary embodiments of the present disclosure are described in further detail below with respect to quantum devices that implement superconducting qubit couplers for coupling superconducting data qubits (data qubits) to superconducting auxiliary qubits (auxiliary qubits) in a manner that facilitates quantum operations such as parity checks for quantum error correction while suppressing crosstalk between the data qubits. It should be understood that the various features illustrated in the accompanying drawings are schematic diagrams and not drawn to scale. Also, the same or similar reference numerals are used throughout the drawings to indicate the same or similar features, elements, or structures, and thus, detailed descriptions of the same or similar features, elements, or structures will not be repeated with respect to each of the drawings. Furthermore, as used herein, the term "exemplary" means "serving as an example, instance, or illustration." Any embodiment or design described herein as "exemplary" is not to be construed as preferred or advantageous over other embodiments or designs.

[0033] Furthermore, the phrase "configured to" when used in conjunction with a circuit, structure, element, component, etc. that performs one or more functions or otherwise provides certain functions is intended to encompass embodiments in which the circuit, structure, element, component, etc. is implemented in hardware, software, and / or combinations thereof, and in implementations that include hardware, where it is understood that hardware may include quantum circuit elements (e.g., qubits, coupler circuits, etc.), discrete circuit elements (e.g., transistors, inverters, etc.), programmable elements (e.g., application specific integrated circuit (ASIC) chips, field programmable gate array (FPGA) chips, etc.), processing devices (e.g., central processing units (CPUs), graphics processing units (GPUs), etc.), one or more integrated circuits, and / or combinations thereof. Thus, by way of example only, when a circuit, structure, element, component, etc. is defined as being configured to provide a particular function, it is intended to encompass, but not be limited to, embodiments in which the circuit, structure, element, component, etc. is comprised of an element, processing device, and / or integrated circuit that enables it to perform the particular function when in an operational state (e.g., connected or otherwise deployed in a system, powered on, receiving input, and / or generating output), and to encompass embodiments in which the circuit, structure, element, component, etc. is in a non-operational state (e.g., not connected or otherwise deployed in a system, not powered on, not receiving input, and / or not generating output) or in a partially operational state.

[0034] As known in the art, quantum computing provides a computational paradigm that utilizes the fundamental principles of quantum mechanics to perform calculations. Quantum computing algorithms and applications are defined using quantum circuits. Quantum circuits are computational routines that define coherent quantum operations to be performed on quantum data stored on qubits in conjunction with operations performed using classical computation. Quantum circuits are utilized to define complex algorithms and applications in abstract ways that can be executed on a quantum computer. In a quantum computer, atomic operations include gate operations applied to qubits (e.g., single-qubit gate operations, two-qubit gate operations, multi-qubit gate operations (e.g., three or more qubits)) to perform quantum computing operations for a given application. Quantum circuits enable a quantum computer to receive classical data, perform quantum operations based on the received data, and output a classical solution.

[0035] A single qubit can have a |0> or |1> basis state, or a linear combination of such basis states known as a superposition state. As is known in the art, the states of a qubit can be represented graphically as points on a unit sphere (radius=1) called the Bloch sphere, as shown in FIG. 1. In particular, FIG. 1 shows an exemplary Bloch sphere 100, where the basis state |0> or |1> of the qubit is represented along the Z axis of the Bloch sphere 100, with point 101 on the positive Z axis representing the ground state |0> and point 102 on the negative Z axis representing the first excited state |1> of the qubit.

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[0036] The state of a given qubit can be altered by applying a single-qubit gate operation to the given qubit, which rotates the qubit's current state, for example, about the X-axis, Y-axis, and / or Z-axis, depending on the given gate operation. Rotation about the Z-axis results in a change in the angle φ. Additionally, qubits can be controlled using entanglement gate operations to entangle the states of two or more qubits, thereby generating a combined state of two or more qubits that contains more information than the individual states of the qubits. In this regard, qubit-based quantum computing operates on two key principles of quantum physics: superposition and entanglement, where superposition essentially allows a given qubit to represent both 1 and 0 simultaneously, and entanglement allows multiple qubits in superposition states to be correlated with each other such that the state of one qubit can depend on the state of another qubit, such that more information can be encoded in multiple entangled qubits compared to encoding the qubits individually. Thus, quantum information processing, based on the principles of qubit superposition and entanglement steps, enables quantum computers to solve difficult problems that are difficult to solve using classical computers.

[0037] A key challenge in the development of quantum computers is the sensitivity of the quantum states of qubits to noise and errors. For example, quantum systems can interact with the environment in a way that causes decoherence of the qubit states. As is known in the art, quantum error correction (QEC) techniques are utilized to protect quantum information from errors caused by qubit state decoherence and other quantum noise. Generally, QEC techniques are based on error-correcting codes that store quantum information and protect the quantum state against a set of errors. To perform reliable quantum computation, it is necessary to use qubits that are encoded with error-correcting codes.

[0038] Quantum error correcting codes are utilized to encode a quantum system into a subspace (referred to as the code space) of the overall qubit space so that errors caused by decoherence in the quantum system can be detected and corrected based on the error correcting code. In general, quantum error correcting codes provide a way to store (or transmit) M bits of quantum information using N qubits (where N>M) such that the quantum information can be recovered if any subset of the N qubits experiences any error. For a quantum error code to adequately protect a quantum state against a set of errors, the code space is selected such that each error transforms the state in a way that allows the quantum error correction system to perform a suitable measurement to determine which error occurred without actually obtaining any information about the state of the qubits stored in the code, which would necessarily disturb the state of the qubits.

[0039] In the context of quantum computing, superconducting auxiliary qubits can be utilized for a variety of purposes, such as quantum error correction. The terms "superconducting auxiliary qubit" or "anchor qubit" generally refer to a superconducting qubit that is utilized to facilitate one or more quantum operations associated with one or more other superconducting qubits. For example, when used in conjunction with one or more exemplary embodiments, a superconducting auxiliary qubit is utilized to facilitate one or more error detection / correction operations associated with one or more superconducting data qubits.

[0040] As described in more detail below, the superconducting auxiliary qubit is coupled to one or more superconducting data qubits using a superconducting multimode qubit coupler. As used herein, the term "superconducting data qubit" or "data qubit" refers to a superconducting qubit utilized to store the computational state of a quantum system. Furthermore, the data qubit is utilized to encode a logical qubit in an error correction code. In the context of quantum error correction, the auxiliary qubit is entangled with the states of multiple data qubits that encode the logical qubit state for quantum error correction, and in quantum error codes, the states of the auxiliary qubits are directly measured and used to detect errors in the data qubits. In other words, in the context of quantum error correction, logical qubits are constructed from physical data qubits, and each logical qubit is encoded in multiple physical data qubits having entangled states.

[0041] Quantum error correction systems utilize ancillary qubits to determine error syndromes. For example, the error syndromes can be determined by a process that includes performing a series of operations in which the ancillary qubits are entangled with multiple data qubits, and then measuring the ancillary qubits to determine whether an error is present in the encoded state of the data qubits. This process allows information to be inferred about the data qubits without directly reading out the data qubits, which would result in a collapse of the data qubit's state. While the syndrome measurement provides information about the error that occurred, it does not provide the quantum information stored in the logical qubits, as the measurement may collapse any quantum superposition of the logical qubit with other qubits in the quantum system.

[0042] As noted above, superconducting quantum computing systems can be implemented using superconducting qubits. For example, a superconducting transmon (transmission line shunted plasma oscillation) qubit is a type of superconducting qubit that includes a superconducting tunnel junction device (e.g., a Josephson junction) connected in parallel with a capacitor. Figures 2A and 2B schematically illustrate a superconducting transmon qubit that can be utilized to implement data qubits and ancillary qubits, according to exemplary embodiments of the present disclosure. More specifically, Figure 2A is a schematic lumped-element circuit representation of a superconducting transmon qubit 200, and Figure 2B schematically illustrates a planar circuit configuration 201 of the superconducting transmon qubit 200 of Figure 2A, according to exemplary embodiments of the present disclosure.

[0043] 2A, superconducting transmon qubit 200 comprises a superconducting tunnel junction device 210 and a capacitor 220 connected in parallel. In some embodiments, superconducting tunnel junction device 210 has a Josephson energy E J and critical current I C 2A is a Josephson tunnel junction device 210 having a capacitance C. The capacitor 220 has a capacitance C. The Josephson tunnel junction device 210 has a small junction capacitance that is omitted from FIG. 2A for ease of illustration. The capacitance C of the capacitor 220 is large relative to the junction capacitance of the Josephson tunnel junction device 210. The Josephson tunnel junction 210, when shunted with the capacitor 220, functions as a nonlinear inductor that forms an anharmonic LC oscillator with individually addressable energy levels (e.g., two lowest energy levels corresponding to a ground state |0> and a first excited state |1>).

[0044] 2B, the planar circuit configuration 201 of the superconducting transmon qubit 200 comprises a first superconducting pad 220-1, a second superconducting pad 220-2, and a Josephson tunnel junction device 210 coupled to and disposed between the first and second superconducting pads 220-1 and 220-2. The first and second superconducting pads 220-1 and 220-2 comprise electrodes of a coplanar parallel-plate capacitor structure corresponding to the capacitor 220 (having capacitance C) of the superconducting transmon qubit 200.

[0045] In general, superconducting transmon qubits are commonly utilized in superconducting quantum computing systems because they offer good coherence times and have relatively simple structures that facilitate coupling with other superconducting circuit elements, qubit readout resonators, and the like. Such structures can be designed to capacitively or inductively couple the transmon qubit to other circuit elements, including microwave and magnetic flux drive lines, readout resonators, and couplers, to control and readout the state of the transmon qubit. Furthermore, transmon qubits can be designed to have a relatively high anharmonic spectrum, where the frequency separation between the computational and non-computational states is relatively high, enabling efficient use of the superconducting transmon qubit as a two-level quantum system.

[0046] Specifically, as known in the art, the operating frequency (alternatively, the transition frequency) of a superconducting qubit is the frequency corresponding to the energy difference between the ground state |0> and the first excited state |1> of the qubit. With superconducting qubits, while higher energy levels (e.g., |2>, |3>, etc.) are available for a given qubit, quantum systems are designed to isolate the two lowest energy levels of the superconducting qubit (i.e., the ground state |0> and the first excited state |1>), thereby ignoring the higher energy states and utilizing each superconducting qubit as a fundamental two-level system for quantum computation. As used herein, the term "anharmonicity" refers to the frequency (f 01 ) and (ii) the frequency (f 12 )

[0047] The Josephson tunnel junction device 210 of the superconducting transmon qubit 200 must achieve a target critical current I to achieve a given anharmonicity for the qubit potential. c and Josephson energy E J For a Josephson tunnel junction, the resulting superconducting current I flowing through the tunnel junction and the junction voltage V across the tunnel junction are determined by the superconducting phase difference

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[0048] Another type of superconducting qubit that can be utilized to implement a quantum system includes a superconducting multimode qubit that includes a multimode two-junction qubit architecture, as shown schematically in Figures 3A and 3B. More specifically, Figure 3A is a schematic lumped-element circuit representation of a superconducting multimode qubit 300, alternatively referred to as a superconducting tunable coupler qubit (TCQ). The superconducting multimode qubit 300 comprises a shunt capacitor 321 and two capacitive shunt superconducting Josephson tunnel junctions connected in series between a first node N1 and a second node N2 of the superconducting multimode qubit 300. The first capacitive shunt Josephson tunnel junction has a first Josephson tunnel junction device 322 connected in parallel with a first capacitor 323. The second capacitive shunt Josephson tunnel junction has a second Josephson tunnel junction device 324 connected in parallel with a second capacitor 325. The shunt capacitor 321 has a capacitance C S and the first Josephson tunnel junction device 322 has a Josephson energy E J1 and the second Josephson tunnel junction device 324 has a Josephson energy E J2 The first capacitor 323 has a capacitance C1 and the second capacitor 325 has a capacitance C2. The first and second capacitive shunt superconducting Josephson tunnel junctions are coupled to an intermediate node N3.

[0049] 3B, in accordance with an exemplary embodiment of the present disclosure, shows a planar circuit configuration of the superconducting multimode qubit 300 of FIG. 3A. More specifically, FIG. 3B shows a planar superconducting multimode qubit 301 comprising a first superconducting pad 301-1, a second superconducting pad 301-2, and a third (middle) superconducting pad 301-3, where a first Josephson tunnel junction device 322 is coupled to and between the first and third superconducting pads 301-1 and 301-3, and a second Josephson tunnel junction device 324 is coupled to and between the second and third superconducting pads 301-2 and 301-3. In this configuration, the superconducting pads 301-1, 301-2, and 301-3 comprise planar capacitor electrodes that form a coplanar parallel plate capacitor structure. For example, in the exemplary configuration of Figure 3B, first and second superconducting pads 301-1 and 301-2 comprise planar capacitor electrodes of shunt capacitor 321 of Figure 3A. Furthermore, first and third superconducting pads 301-1 and 301-3 comprise planar capacitor electrodes of first capacitor 323 of Figure 3A, and second and third superconducting pads 301-2 and 301-3 comprise planar capacitor electrodes of second capacitor 325 of Figure 3A. The first, second, and third superconducting pads 301-1, 301-2, and 301-3 correspond to first, second, and third nodes N1, N2, and N3, respectively, in Figure 3A.

[0050] The planar superconducting multimode qubit 301 has two excitation modes with distinct frequencies and distinct spatial symmetries. More specifically, the planar superconducting multimode qubit 301 has two distinct excitation modes corresponding to the symmetric and antisymmetric coupling of excitations associated with the two junctions, where the two distinct, normal modes include: (i) a low-frequency “bright” mode (referred to herein as the A-mode) that has a non-zero dipole moment, and (ii) a high-frequency “dark” mode (referred to herein as the B-mode) that lacks a dipole moment and does not couple to external fields. Figure 3C schematically illustrates the two distinct excitation modes of the planar superconducting multimode qubit 301 of Figure 3B, where the “bright” mode is shown as the A-mode 302 and the “dark” mode is shown as the B-mode 304.

[0051] 3C, A-mode 302 has a charge pattern in which, at any given time, first and second superconducting pads 301-1 and 301-2 have opposite charges, and third (middle) superconducting pad 301-3 has a net zero charge. On the other hand, B-mode 304 has a charge pattern in which, at any given time, first and second superconducting pads 301-1 and 301-2 have the same charge, and third (middle) superconducting pad 301-3 has a charge that is opposite to the charge of first and second superconducting pads 301-1 and 301-2. A-mode and B-mode have different frequencies, e.g., mode frequency f of B-mode 304. B is the mode frequency f of A mode 302 A , which allows for the separate excitation of one mode relative to the other.

[0052] To implement scalable quantum computing systems (e.g., quantum processors) using superconducting qubits, for example, to enable independent qubit control for high-fidelity single-qubit gate operations and to implement high-fidelity entanglement gates (e.g., two-qubit gates) between superconducting qubits, it is important to minimize or eliminate crosstalk and undesired ZZ interactions between coupled or nearby qubits. As noted above, an entanglement gate is an operation in which an external field (e.g., a microwave signal) is applied to a quantum processor to generate an entangled state between two or more separate qubits. For example, a controlled phase gate between two qubits (referred to herein as a CPHASE gate) is a type of entanglement gate in which one qubit (e.g., a target qubit) gains a phase shift if and only if both qubits are in their first excited states.

[0053] A ZZ interaction is a type of longitudinal interaction between two qubits or modes in which excitation of one qubit or mode causes a shift in the transition frequency of the other qubit or mode. In some cases, a ZZ interaction can produce a state-dependent shift in qubit frequency equivalent to a state-dependent phase shift, thereby providing a means to entangle two different qubits and generate, for example, a CPHASE gate. A ZZ interaction is sometimes referred to as longitudinal coupling or denoted as chi or 2-chi coupling. On the other hand, in some cases, unwanted ZZ interaction between two superconducting qubits is a source of crosstalk that can reduce the fidelity of gate operation.

[0054] For example, static ZZ interaction is a type of ZZ interaction that exists between two qubits or modes in the absence of any external RF drive. This “always-on” interaction involves unwanted crosstalk, which can be detrimental to a quantum system of qubits by inhibiting independent control of each qubit and by generating undesired entanglement. In particular, static ZZ coupling can arise between nearby qubits, where the state of one qubit affects the qubit frequency of a neighboring qubit, and where static ZZ coupling can result in gate errors. In this regard, static ZZ interaction is a type of undesired crosstalk between nearby qubits that can adversely affect the fidelity of single-qubit gate operations that are calibrated under the assumption that the qubit frequency is fixed.

[0055] Another source of crosstalk between nearby qubits includes exchange interactions that occur when a microwave pulse is applied to one qubit (such as for a single-qubit gate operation), which can potentially affect another nearby qubit if an exchange interaction exists between such nearby qubits. For example, if an exchange interaction exists between two qubits, applying a microwave pulse to one qubit can potentially excite the other qubit, which is a form of crosstalk that can be detrimental.

[0056] In the context of quantum error correction, where multiple data qubits are coupled to the same ancillary qubit, when successive entanglement gate operations are performed to entangle the ancillary qubit with each data qubit, it is desirable to selectively control the interaction between the data qubit and the ancillary bit while suppressing crosstalk (e.g., ZZ interaction) between the data qubits. Furthermore, when non-destructive measurements of the ancillary qubits are performed to determine error syndromes without changing the state of the data qubits coupled to them, it is desirable to suppress crosstalk between the ancillary qubit and the data qubit. In this regard, exemplary embodiments of the present disclosure are described in further detail below with respect to techniques for controlling the interaction between a superconducting data qubit and a superconducting ancillary qubit to facilitate quantum error correction (e.g., parity check) while suppressing crosstalk between the data qubits.

[0057] In some embodiments, a superconducting multimode qubit coupler is utilized to couple a superconducting data qubit with a superconducting auxiliary qubit in a manner that suppresses crosstalk between the superconducting data qubits while controlling the exchange interaction for entangling the data qubit with the auxiliary qubit. For example, in some embodiments, a flux-tunable superconducting multimode qubit coupler is implemented to couple the superconducting data qubit with the superconducting auxiliary qubit. In some embodiments, the flux-tunable superconducting multimode qubit coupler is based on a multimode two-junction superconducting qubit architecture, as described above in conjunction with Figures 3A-3C.

[0058] For example, Figures 4A and 4B schematically illustrate a tunable superconducting multimode qubit coupler utilized to couple a superconducting data qubit with a superconducting annular qubit, according to exemplary embodiments of the present disclosure. More specifically, Figure 4A is a schematic lumped-element circuit representation of a flux-tunable superconducting multimode qubit coupler 400, and Figure 4B schematically illustrates a planar circuit configuration 401 of the tunable superconducting multimode qubit coupler 400 of Figure 4A, according to exemplary embodiments of the present disclosure. Tunable superconducting multimode qubit coupler 400 has a multimode two-junction superconducting qubit architecture similar to superconducting multimode qubit 300 (Figure 3A), except that the superconducting multimode qubit is configured to be flux-tunable by replacing Josephson tunnel junction devices with superconducting quantum interference devices (SQUIDs). As described in more detail below, the SQUID forms a superconducting loop (referred to as a SQUID loop) through which an external magnetic flux can be passed to control the interaction (e.g., smooth the exchange interaction or suppress crosstalk) between superconducting qubits that are coupled to each other through the tunable superconducting multimode qubit coupler 400.

[0059] More specifically, as shown in FIG. 4A, tunable superconducting multimode qubit coupler 400 includes a shunt capacitor 421 (capacitance C S , and two capacitively shunt superconducting Josephson tunnel junctions connected in series between a first node N1 and a second node N2 of the tunable superconducting multimode qubit coupler 400. The first capacitively shunt Josephson tunnel junction has a first Josephson tunnel junction device 422 connected in parallel with a first capacitor 423 (having a capacitance C1). The first Josephson tunnel junction device 422 has a capacitance I C1 Critical current and Josephson energy E J1The second capacitively shunted Josephson tunnel junction includes a SQUID 424 connected in parallel with a second capacitor 425 (having a capacitance C2). The SQUID 424 includes a first Josephson tunnel junction device 424-1 and a second Josephson tunnel junction device 424-2, which are connected in parallel between a first node N1 and a third node N3 of the tunable superconducting multimode qubit coupler 400 to form a superconducting loop.

[0060] The SQUID424 has an effective critical current I CS , and an external magnetic field Φ ext The Josephson energy E is tunable by applying JS In this regard, the SQUID 424 effectively operates as a single Josephson tunnel junction device having a target external magnetic field Φ through the superconducting loop, which is applied by the SQUID 424 via a flux bias control line disposed in the vicinity of the SQUID 424. ext , the tunable superconducting multimode qubit coupler 400 can be tuned. The flux bias control lines supply a current (e.g., a DC current) to an inductor element disposed adjacent to the superconducting loop of the SQUID 424, thereby applying an external magnetic field Φ ext is applied. ext is a very special method to calculate the critical current I CS and thus the Josephson energy E of SQUID424. JS Adjust.

[0061] The flux tuning of tunable superconducting multimode qubit coupler 400 serves to control the exchange interaction (e.g., smooth the exchange interaction or suppress crosstalk) between first and second superconducting qubits that are capacitively coupled to the A-mode and B-mode, respectively, of tunable superconducting multimode qubit coupler 400. In particular, as shown schematically in FIG. 4A , coupling capacitors 430 and 432 (connected to respective nodes N1 and N2) enable capacitive coupling of the superconducting qubit to the A-mode of tunable superconducting multimode qubit coupler 400. Additionally, coupling capacitor 434 (connected to node N3) enables capacitive coupling of the superconducting qubit to the B-mode of tunable superconducting multimode qubit coupler 400. Coupling capacitors 430, 432, and 434 may be implemented by direct capacitive coupling (via gap capacitance) or by superconducting planar transmission lines such as coplanar waveguides.

[0062] The tunable superconducting multimode qubit coupler 400 varies the amount of external magnetic flux applied to the superconducting loop of the SQUID 424 to control the critical current I CS and therefore the Josephson energy E of SQUID424. JS For example, tunable superconducting multi-mode qubit coupler 400 can be tuned to operate in a first state (e.g., an "off" state or a "deactivated" state) or a second state (e.g., an "on" state or an "activated" state) by adjusting the critical current I of SQUID 424. CS The critical current I of the Josephson tunnel junction device 422 C1 and the Josephson energy E of each of the Josephson tunnel junction device 422 and the SQUID 424 is equal to or substantially equal to J1 and E JS The SQUID 424 can be tuned to operate in the "off" state by applying an amount of external magnetic flux to the superconducting loop of the SQUID 424 to bring about a balance in .

[0063] In the “off” state, tunable superconducting multimode qubit coupler 400 enforces mode-selective coupling, creating a condition of essentially zero interaction between superconducting qubits capacitively coupled to their respective A and B modes. More specifically, in the “off” state of tunable superconducting multimode qubit coupler 400, the superconducting qubits capacitively coupled to nodes N1 and N2 of tunable superconducting multimode qubit coupler 400 are exchange coupled only to the A mode of tunable superconducting multimode qubit coupler 400, and the superconducting qubit capacitively coupled to node N3 of tunable superconducting multimode qubit coupler 400 is exchange coupled only to the B mode of tunable superconducting multimode qubit coupler 400. In the "off" state of tunable superconducting multimode qubit coupler 400, the A-mode and B-mode have distinct and separate charge patterns as shown in FIG. 3C, resulting in suppression of crosstalk (e.g., static ZZ interaction) between superconducting qubits coupled by tunable superconducting multimode qubit coupler 400.

[0064] On the other hand, the tunable superconducting multimode qubit coupler 400 can reduce the critical current I of the SQUID 424. CS The critical current I of the Josephson tunnel junction device 422 C1 and the Josephson energy E of each of the Josephson tunnel junction device 422 and the SQUID 424 is not equal to (e.g., greater than) J1 and E JS The SQUID 424 can be tuned to operate in the "on" state by applying an amount of external magnetic flux to the superconducting loop of the SQUID 424 to create an imbalance in the Josephson energy E J1 and E JS3C , which disrupts the mode-selective coupling of tunable superconducting multimode qubit coupler 400 and causes the superconducting qubit to exchange couple to both the A-mode and B-mode of tunable superconducting multimode qubit coupler 400. In the “on” state of tunable superconducting multimode qubit coupler 400, the exchange coupling of both superconducting qubits to both the A-mode and B-mode results in exchange coupling (e.g., ZZ interaction) between superconducting qubits that are capacitively coupled to the A-mode and B-mode of tunable superconducting multimode qubit coupler 400.

[0065] 4B, the exemplary planar circuit configuration 401 of the tunable superconducting multimode qubit coupler 400 of FIG. 4A includes a first superconducting pad 401-1, a second superconducting pad 401-2, and a third superconducting pad 401-3. The first and second superconducting pads 401-1 and 401-2 have a shunt capacitance C S 4A )。 Josephson tunnel junction device 422 is coupled to and between first superconducting pad 401-1 and third superconducting pad 401-3. First and third superconducting pads 401-1 and 401-3 include electrodes of a coplanar parallel plate capacitor structure corresponding to first capacitor 423 (FIG. 4A). SQUID 424 is coupled to and between second superconducting pad 401-2 and third superconducting pad 401-3. Second and third superconducting pads 401-2 and 401-3 include electrodes of a coplanar parallel plate capacitor structure corresponding to second capacitor 425 (FIG. 4A).

[0066] For illustrative purposes, exemplary embodiments of quantum systems and devices as described herein implement a flux-tunable superconducting multimode qubit coupler based on the tunable multimode qubit framework of Figures 4A and 4B to control the interaction between a superconducting data qubit and a superconducting ancillary qubit. It should be noted, however, that other suitable tunable multimode qubit architectures may be utilized as the coupler for controlling the interaction between a superconducting data qubit and a superconducting ancillary qubit. Such a tunable multimode qubit implements the combination of two strongly interacting, anharmonic oscillators with a composite quantum system characterized by multiple excitation modes that exhibit strong longitudinal coupling between them; i.e., excitation of one mode can strongly shift the transition frequency of another mode.

[0067] 5 illustrates a quantum device 500 including a superconducting data qubit 510 coupled to a superconducting auxiliary qubit using a tunable superconducting multimode qubit coupler, in accordance with an exemplary embodiment of the present disclosure. In particular, FIG. 5 illustrates a quantum device 500 including a superconducting data qubit 510, a first superconducting multimode qubit coupler 520, a second superconducting multimode qubit coupler 530, and a superconducting auxiliary qubit 540. Quantum device 500 further includes a plurality of control lines, including, but not limited to, qubit drive lines 512 and 542, qubit readout lines 514 and 544, and flux bias control lines 522 and 532.

[0068] 2A and 2B, respectively. In other embodiments, superconducting data qubit 510 and superconducting auxiliary qubit 540 may be implemented using other types of superconducting qubits, such as superconducting fluxonium qubits. In some embodiments, superconducting data qubit 510 and superconducting auxiliary qubit 540 comprise fixed frequency qubits (not tunable), while in other embodiments, superconducting data qubit 510 and / or superconducting auxiliary qubit 540 may be tunable qubits, e.g., tunable transition frequencies.

[0069] In some embodiments, qubit drive lines 512 and 542 are coupled (e.g., capacitively coupled) to superconducting data qubit 510 and superconducting auxiliary qubit 540, respectively. In some embodiments, qubit drive lines 512 and 542 are configured to apply control signals (e.g., microwave control pulse signals) to independently alter the state of each superconducting data qubit 510 and superconducting auxiliary qubit 540. For example, microwave control pulses may be applied to qubit drive line 512 to perform single-qubit gate operations on superconducting data qubit 510 or otherwise alter the computational state of superconducting data qubit 510 as needed to execute a quantum algorithm. Furthermore, during an initial phase of a quantum error correction cycle, a microwave control pulse may be applied to qubit drive line 542 to initialize superconducting auxiliary qubit 540 to the ground state |0>. As is known in the art, the state of a qubit can be determined by applying a control signal (f 01 can be varied by applying a microwave control signal (e.g., controlling pulses) having a center frequency equal to the transition frequency f 01corresponds to the energy difference between the ground state |0> and the excited state |1> of the qubit. Furthermore, the axis of rotation about a given axis of the Bloch sphere 100 (e.g., the X-axis, the Y-axis, or any axis in the XY plane) and the amount (angle) of such rotation are based on the phase of the microwave control signal and the amplitude and duration of the microwave control signal, respectively.

[0070] Additionally, in some embodiments, qubit readout lines 514 and 544 are coupled to superconducting data qubit 510 and superconducting auxiliary qubit 540, respectively, using known techniques to perform distributed readout. In some embodiments, qubit readout lines 514 and 544 comprise transmission line readout resonators (e.g., coplanar waveguide resonators) configured to have resonant frequencies detuned from the respective transition frequencies of superconducting data qubit 510 and superconducting auxiliary qubit 540. Due to the coupling of qubit readout lines 514 and 544 to the respective superconducting data and superconducting auxiliary qubits 510 and 540, there is a shift in the resonant frequency of the transmission line readout resonator depending on the state of the respective superconducting data and superconducting auxiliary qubits 510 and 540. Changes in the resonant frequency of a transmission line readout resonator coupled to a given qubit are utilized to determine the readout state of the given qubit, e.g., the ground state |0> or the first excited state |1>, where, for readout, the superposition state of the given qubit is projected onto the ground state or the first excited state, as known in the art.

[0071] In some embodiments, the first and second superconducting multimode qubit couplers 520 and 530 each comprise a flux-tunable superconducting multimode qubit coupler such as those described above in conjunction with Figures 4A and 4B. As noted above, the tunable superconducting multimode qubit coupler 400 (Figure 4A) has two distinct normal excitation modes (e.g., distinct A- and B-modes of excitation with distinct frequencies and spatial symmetries, as shown in Figure 3C). Flux bias control lines 522 and 532 are used to apply flux bias control signals to the respective first and second superconducting multimode qubit couplers 520 and 530, as needed for a given operation, to control (enable or disable) mode-selective exchange coupling between superconducting data qubit 510 and first superconducting multimode qubit coupler 520, between first and second superconducting multimode qubit couplers 520 and 530, and between superconducting auxiliary qubit 540 and second superconducting multimode qubit coupler 530.

[0072] More specifically, in some embodiments, the superconducting data qubit 510 is capacitively coupled to a first mode (e.g., A mode) of the first superconducting multimode qubit coupler 520, and the superconducting ancillary qubit 540 is capacitively coupled to a first mode (e.g., A mode) of the second superconducting multimode qubit coupler 530. Furthermore, the second mode (e.g., B mode) of the first superconducting multimode qubit coupler 520 is capacitively coupled to a second mode (e.g., B mode) of the second superconducting multimode qubit coupler 530. The first and second superconducting multimode qubit couplers 520 and 530 are configured to mediate interactions (e.g., ZZ interactions) with and between the superconducting data qubit 510 and the superconducting ancillary qubit 540, respectively, for different operation modes.

[0073] Advantageously, mediating the coupling between superconducting data qubit 510 and superconducting auxiliary qubit 540 through superconducting multimode qubit couplers 520 and 530, each having two distinct excitation modes, enables simultaneous suppression of both the static ZZ interaction and the exchange interaction between superconducting data qubit 510 and superconducting auxiliary qubit 540 when at least one of superconducting multimode qubit couplers 520 and 530 is in an off state. Superconducting multimode qubit couplers 520 and 530 can be flux tuned to be in an off state to enforce a mode-selective exchange coupling in which superconducting data qubit 510 is exchange coupled only to the first mode (A-mode) of first superconducting multimode qubit coupler 520 and superconducting auxiliary qubit 540 is exchange coupled only to the first mode (A-mode) of second superconducting multimode qubit coupler 530. In this configuration, despite the second-mode (B-mode) capacitive coupling of the first and second superconducting multi-mode qubit couplers 520 and 530, there is substantially zero interaction between the superconducting data qubit 510 and the superconducting ancillary qubit 540.

[0074] Figure 6 shows a schematic diagram of a quantum device comprising a superconducting data qubit coupled to a superconducting auxiliary qubit using a tunable superconducting multi-mode qubit coupler and a superconducting transmission line resonator, in accordance with an exemplary embodiment of the present disclosure. In particular, Figure 6 shows a schematic diagram of quantum device 600, which is similar to quantum device 500 of Figure 5, except that a first superconducting multi-mode qubit coupler 520 is coupled to a superconducting auxiliary qubit 540 by a superconducting transmission line resonator 630 (instead of a second superconducting multi-mode qubit coupler 530 as in Figure 5). This configuration can be utilized for long-range coupling in cases where the superconducting auxiliary qubit 540 is disposed relatively far away from the superconducting data qubit 510. Advantageously, superconducting transmission line resonator 630 eliminates the need to utilize a dedicated superconducting multimode qubit coupler for superconducting auxiliary qubit 540 (e.g., second superconducting multimode qubit coupler 530) because superconducting transmission line resonator 630 serves to reduce crosstalk between superconducting data qubit 510 and other superconducting data qubits that are coupled to the same superconducting auxiliary qubit 540. In particular, superconducting transmission line resonator 630 has a relatively large capacitance to ground that acts as a divider that reduces ZZ coupling between superconducting data qubits that are coupled to the same superconducting auxiliary qubit.

[0075] In some embodiments, superconducting transmission line resonator 630 comprises a coplanar waveguide resonator having a given resonant frequency selected (e.g., detuned) based on the transition frequencies of superconducting data qubit 510 and superconducting auxiliary qubit 540. In some embodiments, a first end of superconducting transmission line resonator 630 is capacitively coupled to the B-mode of superconducting multimode qubit coupler 520, and a second end of superconducting transmission line resonator 630 is capacitively coupled to and directed toward superconducting auxiliary qubit 540.

[0076] 7A schematically illustrates a method of utilizing a tunable superconducting multimode qubit coupler to control the interaction between a superconducting data qubit and a superconducting ancillary qubit, according to an exemplary embodiment of the present disclosure. In particular, FIG. 7A schematically illustrates a process 700 for controlling the interaction between a data qubit 701 and an ancillary qubit 702 by utilizing first and second tunable superconducting multimode qubit couplers 703 and 704 (similar to the coupling configuration of quantum device 500 of FIG. 5). As illustrated schematically in FIG. 7A, when both the first and second tunable superconducting multimode qubit couplers 703 and 704 are flux-tuned to their off states 700-1, the superconducting data qubit 701 has exchange coupling with only the A-mode of the first tunable superconducting multimode qubit coupler 703, and the superconducting ancillary qubit 702 has exchange coupling with only the A-mode of the second tunable superconducting multimode qubit coupler 704. Furthermore, the B modes of the first and second tunable superconducting multi-mode qubit couplers 703 and 704 are exchange coupled to each other. In the off state 700-1, there is substantially no interaction (static ZZ or exchange interaction) between the superconducting data qubit 701 and the superconducting ancillary qubit 702.

[0077] 7A , when both the first and second tunable superconducting multimode qubit couplers 703 and 704 are flux-tuned to the “on” state 700-2, the superconducting data qubit 701 has exchange coupling with both the A-mode and B-mode of the first tunable superconducting multimode qubit coupler 703, and the superconducting ancillary qubit 702 has exchange coupling with both the A-mode and B-mode of the second tunable superconducting multimode qubit coupler 704. Furthermore, the B-mode of the first tunable superconducting multimode qubit coupler 703 has exchange coupling with both the A-mode and B-mode of the second tunable superconducting multimode qubit coupler 704, and similarly, the B-mode of the second tunable superconducting multimode qubit coupler 704 has exchange coupling with both the B-mode and A-mode of the first tunable superconducting multimode qubit coupler 703. Furthermore, the A-mode of the first tunable superconducting multimode coupler 703 has exchange coupling with the A-mode and B-mode of the second tunable superconducting multimode qubit coupler 704, and vice versa. In the on state 700-2, there is no substantial exchange interaction between the superconducting data qubit 701 and the superconducting ancillary qubit 702.

[0078] 7A schematically illustrates the different energy levels (e.g., frequencies) of the A-mode and B-mode of superconducting data qubit 701, superconducting ancillary qubit 702, and first and second tunable superconducting multimode qubit couplers 703 and 704. In an exemplary, non-limiting embodiment, superconducting data qubit 701 has a transition frequency f Q1 and the superconducting annular qubit 702 is configured to have a transition frequency f Q1 Detuned from the transition frequency f Q2 Furthermore, in some embodiments, in the off state, the first and second tunable superconducting multimode qubit couplers 703 and 704 are configured to have a standard A-mode frequency (f A ) and standard B-mode frequency (f B) of the first and second tunable superconducting multimode qubit couplers 703 and 704, respectively. A ) and standard B-mode frequency (f B ) is lower than the transition frequency of the superconducting data qubit 701 and the superconducting ancillary qubit 702. Furthermore, the standard A-mode frequency (f A ) is the standard B-mode frequency (f B ) lower than

[0079] 7A, when the first and second tunable superconducting multi-mode qubit couplers 703 and 704 are both flux-tuned to the “on” state 700-2, the energies (frequencies) of the A-mode and B-mode of the first and second tunable superconducting multi-mode qubit couplers 703 and 704 increase to be closer to the transition frequencies of the superconducting data qubit 701 and the superconducting ancillary qubit 702. This results in a disruption of the mode-selective coupling due to a transformation of the A-mode and B-mode charge patterns such that the B-mode produces a net dipole moment (it is no longer a purely “dark” mode). This conversion between the A and B modes (e.g., an increase in mode frequency, a change in charge pattern, etc.) results in the superconducting data qubit 701 and the superconducting auxiliary qubit 702 having exchange coupling with both the A and B modes of the respective first and second tunable superconducting multi-mode qubit couplers 703 and 704, which enables and mediates a ZZ interaction between the superconducting data qubit 701 and the superconducting auxiliary qubit 702, causing the state of the superconducting data qubit 701 to become entangled with the state of the superconducting auxiliary qubit 702.

[0080] Note that in other embodiments, the mode coupling of superconducting data qubit 701 and superconducting auxiliary qubit 702 to the respective first and second tunable superconducting multimode qubit couplers 703 and 704 can be implemented differently, where superconducting data qubit 701 and superconducting auxiliary qubit 702 are capacitively coupled to the B-mode of the respective first and second tunable superconducting multimode qubit couplers 703 and 704 and capacitively coupled to the A-mode of the first and second tunable superconducting multimode qubit couplers 703 and 704. In such a configuration, in the off state of the first and second tunable superconducting multimode qubit couplers 703 and 704, the mode-selective coupling is implemented such that superconducting data qubit 701 has exchange coupling only to the B-mode of the first superconducting multimode qubit coupler 703, and superconducting auxiliary qubit 702 has exchange coupling only to the B-mode of the second superconducting multimode qubit coupler 704. Depending on a given mode-coupling configuration, the coupling capacitances of the superconducting data qubit 701 and the superconducting ancillary qubit 702 to the respective first and second tunable superconducting multi-mode qubit couplers 703 and 704 can be fine-tuned to achieve sufficient exchange coupling for the given mode-coupling configuration.

[0081] Figures 7B and 7C diagrammatically illustrate methods for utilizing a tunable superconducting multi-mode qubit coupler to control the interaction between a superconducting data qubit and a superconducting annular qubit, according to exemplary embodiments of the present disclosure. The diagrammatic illustrations in Figures 7B and 7C are based on computer simulations illustrating exchange interaction (e.g., ZZ interaction) characteristics for quantum systems such as those shown in Figure 5 and Figure 6, respectively.

[0082] In particular, FIG. 7B shows the Josephson energy E of the SQUIDs of the first and second superconducting multimode qubit couplers. JS7B shows a graph 710 illustrating the amount of static ZZ interaction (Y-axis) between a superconducting transmon data qubit and a superconducting transmon auxiliary qubit coupled through first and second superconducting multimode qubit couplers (configured as shown in FIG. 5 ) as a function of SQUID Josephson energy E from about 10 GHz to about 30 GHz. More particularly, FIG. 7B shows a curve 712 illustrating the amount of static ZZ interaction between a superconducting transmon data qubit and a superconducting transmon auxiliary qubit coupled through first and second superconducting multimode qubit couplers (configured as shown in FIG. 5 ), where the first and second superconducting multimode qubit couplers are coupled through a SQUID Josephson energy E from about 10 GHz to about 30 GHz. JS In the simulation of FIG. 7B, the first and second superconducting multimode qubit couplers are modeled with the same or similar operating parameters, and the Josephson energy E of the SQUIDs of the first and second superconducting multimode qubit couplers is JS were varied simultaneously and remained the same or nearly the same as each other over the energy range shown in FIG. 7B.

[0083] Curve 712 shows the amount of ZZ interaction between the superconducting transmon data qubit and the superconducting transmon ancillary qubit when the flux-tuned superconducting multimode qubit coupler is tuned to different states, e.g., the on and off states. As shown in FIG. 7B, in the off state, there is essentially no ZZ coupling between the superconducting transmon data qubit and the superconducting transmon ancillary qubit (e.g., the ZZ interaction is 1×10 -5 kHz). Furthermore, in the on state, there is a relatively large amount of ZZ interaction between the superconducting transmon data qubit and the superconducting transmon ancillary qubit (e.g., 1 × 10 4 (close to kHz).

[0084] Next, Figure 7C shows the Josephson energy E of the SQUID of the superconducting multimode qubit coupler. JS7C shows a graph 720 illustrating the amount of ZZ interaction (Y-axis) between a superconducting transmon data qubit and a superconducting transmon auxiliary qubit coupled through a single superconducting multimode qubit coupler and a superconducting transmission line resonator (configuration as shown in FIG. 6) as a function of frequency (X-axis). More particularly, FIG. 7C shows a curve 722 illustrating the amount of ZZ interaction between a superconducting transmon data qubit and a superconducting transmon auxiliary qubit, where the superconducting multimode qubit coupler achieves a SQUID Josephson energy E from about 7.5 GHz to about 25 GHz. JS , and the superconducting transmon data qubit and the superconducting transmon ancillary qubit are flux-tuned over a range of 1×10. Curve 722 shows the amount of ZZ interaction between the superconducting transmon data qubit and the superconducting transmon ancillary qubit with the flux-tuned superconducting multi-mode qubit coupler tuned to different states, e.g., the on and off states. As shown in FIG. 7C, in the off state, there is a relatively small amount of ZZ coupling between the superconducting transmon data qubit and the superconducting transmon ancillary qubit (e.g., 1×10 -1 kHz). Furthermore, in the on state, there is a relatively large amount of ZZ coupling between the superconducting transmon data qubit and the superconducting transmon ancillary qubit (e.g., 1 × 10 3 (close to kHz).

[0085] 5 and 6 schematically illustrate quantum devices 500 and 600 with one superconducting data qubit coupled to one superconducting auxiliary qubit, it should be understood that, depending on the application, a superconducting quantum device such as a quantum processor may be implemented using a superconducting qubit array having tens, hundreds, thousands, or more superconducting qubits, including data qubits and auxiliary qubits, that are coupled together using techniques such as those described herein to facilitate error correction and suppress crosstalk. For example, Figure 8 schematically illustrates a quantum device comprising an array of superconducting qubits with a superconducting data qubit coupled to a superconducting auxiliary qubit using a superconducting qubit coupler, according to an exemplary embodiment of the present disclosure.

[0086] 8 schematically illustrates a quantum device comprising a superconducting qubit array 800 having superconducting data qubits 810-1, 810-2, and 810-3 and tunable superconducting multimode qubit couplers 820-1, 820-2, and 820-3 capacitively coupled to superconducting data qubits 810-1, 810-2, and 810-3, respectively. Superconducting qubit array 800 further comprises tunable superconducting multimode qubit coupler 830 and superconducting auxiliary qubit 840 capacitively coupled to tunable superconducting multimode qubit coupler 830. In some embodiments, as schematically illustrated in FIG. 8, superconducting data qubits 810-1, 810-2, and 810-3 and superconducting auxiliary qubit 840 each comprise a superconducting transmon qubit having a circuit configuration and layout similar to the exemplary embodiments shown and described above in conjunction with FIGS. 2A and 2B, the details of which will not be repeated. Furthermore, tunable superconducting multimode qubit couplers 820-1, 820-2, 820-3, and 830 each have similar circuit configurations and layouts as the exemplary embodiment shown and described above in conjunction with Figures 4A and 4B, the details of which will not be repeated.

[0087] As further shown in Figure 8, each superconducting data qubit 810-1, 810-2, and 810-3 is capacitively coupled to the A-mode of a respective tunable superconducting multimode qubit coupler 820-1, 820-2, and 820-3. More specifically, in the illustration of Figure 8, the A-mode coupling is achieved through direct capacitive coupling (gap capacitance) of first and second superconducting pads 220-1 and 220-2 of superconducting data qubit 810-1 to respective first and second superconducting pads 401-1 and 401-2 of tunable superconducting multimode qubit coupler 820-1. Similarly, superconducting ancillary qubit 840 is capacitively coupled (via direct capacitive coupling) to the A-mode of tunable superconducting multimode qubit coupler 830.

[0088] Superconducting qubit array 800 further includes capacitive bus 850 configured to capacitively couple tunable superconducting multimode qubit couplers 820-1, 820-2, and 820-3 to tunable superconducting multimode qubit coupler 830. Capacitive bus 850 includes (i) a first capacitor pad 851 connected to first tunable superconducting multimode qubit coupler 820-1 by a first superconducting transmission line 851-1, (ii) a second capacitor pad 852 connected to second tunable superconducting multimode qubit coupler 820-2 by a second superconducting transmission line 852-1, (iii) a third capacitor pad 853 connected to third tunable superconducting multimode qubit coupler 820-3 by a third superconducting transmission line 853-1, and (iv) a fourth capacitor pad 854 connected to tunable superconducting multimode qubit coupler 830 by a fourth superconducting transmission line 854-1. First, second, and third capacitor pads 851, 852, and 853 are disposed adjacent different edges of fourth capacitor pad 854. The fourth capacitor pad 854 has a size larger than the respective sizes of the first, second, and third capacitor pads 851, 852, and 853. In some embodiments, the superconducting transmission lines 851-1, 852-1, 853-1, and 854-1 are implemented as superconducting coplanar waveguides.

[0089] 8, capacitive bus 850 is coupled to the B-modes of each of tunable superconducting multimode qubit couplers 820-1, 820-2, 820-3, and 830. In this configuration, the B-modes of tunable superconducting multimode qubit couplers 820-1, 820-2, 820-3, and 830 are commonly coupled together through capacitive bus 850. Capacitive bus 850 is structured to ensure that the amount of capacitive coupling of tunable superconducting multimode qubit coupler 830 (of superconducting annular qubit 840) to each of tunable superconducting multimode qubit couplers 820-1, 820-2, and 820-3 (of superconducting data qubits 810-1, 810-2, and 810-3) is greater than the amount of capacitive coupling between tunable superconducting multimode qubit couplers 820-1, 820-2, and 820-3. This is achieved, for example, by making the size of the fourth capacitor pad 854 larger than the sizes of the first, second, and third capacitor pads 851, 852, and 853, respectively.

[0090] As described above, suppression of crosstalk (e.g., exchange interactions or static ZZ interactions) between superconducting data qubits 810-1, 810-2, and 810-3 and between superconducting ancillary qubit 840 and superconducting data qubits 810-1, 810-2, and 810-3 is achieved by deactivating tunable superconducting multimode qubit couplers 820-1, 820-2, 820-3, and 830, whereby respective flux control signals are applied to the SQUIDs 424 of each of tunable superconducting multimode qubit couplers 820-1, 820-2, 820-3, and 830 to tune the SQUIDs 424 to have the same Josephson energy as the respective single Josephson tunnel junction devices 422 of tunable superconducting multimode qubit couplers 820-1, 820-2, 820-3, and 830. When tunable superconducting multimode qubit couplers 820-1, 820-2, 820-3, and 830 are in a deactivated state, superconducting data qubits 810-1, 810-2, and 810-3 and superconducting ancillary qubit 840 are coupled only to the A mode of their respective tunable superconducting multimode qubit couplers 820-1, 820-2, 820-3, and 830, thereby suppressing or otherwise turning off interactions between superconducting data qubits 810-1, 810-2, and 810-3 and superconducting ancillary qubit 840.

[0091] On the other hand, to turn on ZZ coupling between superconducting auxiliary qubit 840 and a given one of superconducting data qubits 810-1, 810-2, and 810-3, respective flux control signals are applied to the SQUIDs of tunable superconducting multimode qubit coupler 830 and associated tunable superconducting multimode qubit couplers 820-1, 820-2, 820-3 for the given superconducting data qubit to tune the SQUIDs to have different Josephson energies as each single Josephson tunnel junction device in the superconducting multimode qubit coupler, thereby disrupting the mode-selective coupling and coupling superconducting auxiliary qubit 840 and the given superconducting data qubit to the B mode of the superconducting multimode qubit coupler, and therefore to each other.

[0092] 8 shows three superconducting data qubits 810-1, 810-2, and 810-3 selectively coupled to a single superconducting auxiliary qubit 840 through respective superconducting multi-mode qubit couplers, in other embodiments, more than three superconducting data qubits can be coupled to superconducting auxiliary qubit 840. For example, fourth capacitor pad 854 of capacitive bus 850 shown in Figure 8 is rectangular, which provides three edges for coupling to three capacitor pads 851, 852, and 853. In other embodiments, fourth capacitor pad 854 can have other shapes to provide additional edges for coupling additional pairs of data qubits and associated multi-mode qubit couplers. For example, the fourth capacitor pad 854 may be hexagonal to provide five edges for coupling to five capacitor pads (e.g., allowing five superconducting data qubits to be coupled to a single auxiliary qubit), or octagonal to provide seven edges for coupling to seven capacitor pads (e.g., allowing seven superconducting data qubits to be coupled to a single auxiliary qubit), etc.

[0093] In some embodiments, superconducting data qubits 810-1, 810-2, and 810-3 and superconducting auxiliary qubit 840 have transition frequencies that are detuned from one another. For example, in an exemplary non-limiting embodiment, superconducting data qubits 810-1, 810-2, and 810-3 and superconducting auxiliary qubit 840 have transition frequencies of approximately 5.5 GHz, detuned by plus / minus 100 MHz. For example, the superconducting data qubits may have transition frequencies of 5.45 GHz, and superconducting auxiliary qubit 840 has a transition frequency of 5.55 GHz. Furthermore, in some embodiments, each tunable superconducting multimode qubit coupler 820-1, 820-2, 820-3, and 830 is substantially the same, e.g., at the same standard A-mode and B-mode frequencies. For example, in an exemplary non-limiting embodiment, in the off state, each tunable superconducting multimode qubit coupler 820-1, 820-2, 820-3, and 830 has a standard A-mode frequency of about 2.5 GHz and a standard B-mode frequency of about 4.0 GHz. Furthermore, in some embodiments, the coupling capacitance between the superconducting transmon qubit and each superconducting multimode qubit coupler is on the order of about 10 femtofarads (fF) to about 20 fF.

[0094] 8 shows a schematic diagram of an array of superconducting qubits having superconducting data qubits coupled to the auxiliary qubits using superconducting multimode qubit couplers that are effective to control interactions in the case of relatively short-range coupling between straddling or stacked qubit chips, where the auxiliary qubits are disposed relatively close to the superconducting data qubits. In other embodiments, for long-range coupling between superconducting data qubits and superconducting auxiliary qubits, a long coplanar waveguide resonator can be utilized to couple the superconducting multimode qubit coupler (associated with the superconducting data qubits) to the superconducting auxiliary qubits, eliminating the need to couple the superconducting auxiliary qubits to the associated superconducting multimode qubit coupler.

[0095] 9 schematically illustrates a quantum device comprising an array of superconducting qubits, with superconducting data qubits coupled to superconducting ancillary qubits using superconducting qubit couplers and transmission line resonators, in accordance with an exemplary embodiment of the present disclosure. In particular, FIG. 9 schematically illustrates a quantum device comprising a superconducting qubit array 900 having superconducting data qubits 910-1, 910-2, and 910-3, and tunable superconducting multimode qubit couplers 920-1, 920-2, and 920-3 capacitively coupled to superconducting data qubits 910-1, 910-2, and 910-3, respectively. Superconducting qubit array 900 further includes a superconducting ancillary qubit 940 coupled to tunable superconducting multimode qubit couplers 920-1, 920-2, and 920-3 by a superconducting transmission line resonator 950.

[0096] 9, superconducting data qubits 910-1, 910-2, and 910-3 and superconducting ancillary qubit 940 each include a superconducting transmon qubit having a circuit configuration and layout similar to the exemplary embodiment shown and described above in conjunction with Figures 2A and 2B, the details of which will not be repeated. Furthermore, tunable superconducting multimode qubit couplers 920-1, 920-2, and 920-3 each have a circuit configuration and layout similar to the exemplary embodiment shown and described above in conjunction with Figures 4A and 4B, the details of which will not be repeated.

[0097] In some embodiments, superconducting transmission line resonator 950 comprises a coplanar waveguide resonator bus having a given resonant frequency (e.g., near 5 GHz). Superconducting transmission line resonator 950 can be several millimeters in length spanning the same qubit chip, or can extend from a first qubit chip to a second qubit chip that are vertically stacked and coupled together via indium bump bonds using known structures and fabrication techniques. In some embodiments, superconducting data qubits 910-1, 910-2, and 910-3 and associated tunable superconducting multimode qubit couplers 920-1, 920-2, and 920-3 are disposed on the first qubit chip, while superconducting auxiliary qubit 940 (and other auxiliary qubits) are disposed on the second qubit chip.

[0098] 9, a first end of superconducting transmission line resonator 950 is capacitively coupled to the B-modes of each of tunable superconducting multimode qubit couplers 920-1, 920-2, and 920-3 via respective coupling capacitors 951, 952, and 953, and a second end of superconducting transmission line resonator 950 is capacitively coupled to superconducting ancillary qubit 940 via coupling capacitor 954. Coupling capacitors 951, 952, 953, and 954 may be implemented using suitable capacitive coupling structures and techniques known to those skilled in the art.

[0099] Depending on the length of superconducting transmission line resonator 950, tunable superconducting multimode qubit couplers 920-1, 920-2, and 920-3 can couple to superconducting transmission line resonator 950 at the fundamental mode of superconducting transmission line resonator 950 (e.g., near 5 GHz) or at a higher mode where the length of superconducting transmission line resonator 950 is longer, where the length of the transmission line resonator is adjusted so that the higher mode is also near 5 GHz and where the lower frequency modes do not play a role. For example, in some embodiments, superconducting transmission line resonator 950 has an open-circuit half-wavelength (λ / 2) transmission line behaving as a parallel resonant circuit with length 1=(n×λ) / 2, where n denotes the number of resonant modes (n=1, 2, 3, ...). Thus, for a target resonance of approximately 5 GHz, the superconducting transmission line resonator 950 must have either (i) a length l=λ / 2(n=1) corresponding to a fundamental mode frequency of f≈5 GHz, or (ii) a length l=λ / 2(n=1) corresponding to a fundamental mode frequency of f≈5 GHz. n The length l=(n×λ) / 2 corresponds to a higher mode frequency of =n×f≈5 GHz.

[0100] 9 , coupling superconducting auxiliary qubit 940 directly to superconducting transmission line resonator 950 ensures that superconducting data qubits 910-1, 910-2, and 910-3 couple more strongly to superconducting auxiliary qubit 940 than they couple to each other. Indeed, as noted above, superconducting transmission line resonator 950 has a relatively large capacitance to ground that serves to reduce crosstalk between superconducting data qubits 910-1, 910-2, and 910-3 that are coupled to superconducting auxiliary qubit 940, and thus superconducting transmission line resonator 950 eliminates the need to couple a dedicated superconducting multi-mode qubit coupler to superconducting auxiliary qubit 940.

[0101] In some embodiments, superconducting data qubits 910-1, 910-2, and 910-3 and superconducting auxiliary qubit 940 have transition frequencies that are detuned from one another and depend in part on the resonance of superconducting transmission line resonator 950. For example, in an exemplary non-limiting embodiment, superconducting auxiliary qubit 940 has a transition frequency that is about 200 MHz to about 300 MHz below the resonance of superconducting transmission line resonator 950. For example, superconducting transmission line resonator 950 can be designed to have a resonance of about 5 GHz, with superconducting auxiliary qubit 940 having a transition frequency of approximately 4.7 GHz to 4.8 GHz. Furthermore, in an exemplary non-limiting embodiment, superconducting data qubits 910-1, 910-2, and 910-3 and superconducting auxiliary qubit 940 have transition frequencies of about 4.7 to 4.8 GHz, but are detuned by plus / minus 100 MHz.

[0102] Also, in some embodiments, each tunable superconducting multimode qubit coupler 920-1, 920-2, and 920-3 is substantially identical, e.g., has the same standard A-mode and B-mode frequencies. For example, in an exemplary non-limiting embodiment, in the off state, each tunable superconducting multimode qubit coupler 920-1, 920-2, and 920-3 has a standard A-mode frequency of about 2.0 GHz and a standard B-mode frequency of about 3.5 GHz. The exemplary operating frequencies can all be adjusted up or down in unison to accommodate other design considerations. Furthermore, in some embodiments, the coupling capacitance between the superconducting transmon data qubit and each superconducting multimode qubit coupler is on the order of about 10 fF to about 20 fF.

[0103] 10 schematically illustrates a quantum device comprising an array of superconducting qubits, each having a superconducting data qubit coupled to a superconducting auxiliary qubit using a superconducting qubit coupler, in accordance with another exemplary embodiment of the present disclosure. In particular, FIG. 10 schematically illustrates a quantum device comprising a superconducting qubit array 1000 having superconducting data qubits 1010-1 and 1010-2 and associated tunable superconducting multimode qubit couplers 1020-1 and 1020-2 capacitively coupled to the superconducting data qubits 1010-1 and 1010-2, respectively. Superconducting qubit array 1000 further comprises a superconducting auxiliary qubit 1040 coupled to a plurality of tunable superconducting multimode qubit couplers 1030-1, 1030-2, and 1030-3. Superconducting qubit array 1000 further comprises a plurality of capacitive buses 1050-1, 1050-2, and 1050-3.

[0104] Superconducting qubit array 1000 is similar in configuration to superconducting qubit array 800 of Figure 8, except that superconducting auxiliary qubit 1040 includes a superconducting quadrupole transmon qubit, which enables dipole-dipole interaction and coupling with at least three tunable superconducting multimode qubit couplers 1030-1, 1030-2, and 1030-3 as shown. Superconducting quadrupole transmon qubit 1040 operates in a similar manner to superconducting transmon qubits as shown in Figures 2A and 2B, except that superconducting quadrupole transmon qubit 1040 has a different configuration of shunt capacitor pads that have a quadrupole charge pattern when excited.

[0105] 10 , a superconducting quadrupole transmon qubit 1040 includes a single Josephson tunnel junction device 1045 having a Manhattan Josephson junction framework and first, second, third, and fourth superconducting pads 1041, 1042, 1043, and 1044 that collectively comprise capacitor electrode pads that form a shunt capacitor of the superconducting quadrupole transmon qubit 1040. The first, second, third, and fourth superconducting pads 1041, 1042, 1043, and 1044 of the superconducting quadrupole transmon qubit 1040 are arranged in a rectangular array. The first and second superconducting pads 1041 and 1042 are configured to implement a first capacitor electrode of the shunt capacitor and are commonly connected to a first electrode of the single Josephson tunnel junction device 1045. The third and fourth superconducting pads 1043 and 1044 are configured to implement second capacitor electrodes of a shunt capacitor and are commonly connected to the second electrode of a single Josephson tunnel junction device 1045. In an exemplary quadrupole configuration, as shown in Figure 10, the superconducting quadrupole transmon qubit 1040 is configured to capacitively couple directly to the A-mode of each of three tunable superconducting multimode qubit couplers 1030-1, 1030-2, and 1030-3.

[0106] Similar to the exemplary array layout of Figure 8, each capacitive bus 1050-1, 1050-2, and 1050-3 in Figure 10 is configured to couple to three pairs of superconducting data qubits and associated superconducting multimode qubit couplers. For ease of illustration, Figure 10 shows two superconducting data qubits and associated superconducting multimode qubit couplers coupled to capacitive bus 1050-1. Capacitive bus 1050-1 includes (i) a first capacitor pad 1051 connected to a first superconducting multimode qubit coupler 1020-1 by a first superconducting transmission line 1051-1, (ii) a second capacitor pad 1052 connected to a second superconducting multimode qubit coupler 1020-2 by a second superconducting transmission line 1052-1, (iii) a third capacitor pad 1053 connected to a third superconducting multimode qubit coupler (not shown) by a third superconducting transmission line 1053-1, and (iv) a fourth capacitor pad 1054 connected to a tunable superconducting multimode qubit coupler 1030-1 by a fourth superconducting transmission line 1054-1. The exemplary array layout shown in Figure 10 allows for selective coupling of nine superconducting data qubits to superconducting ancilla qubits 1040 by selective activation / deactivation of the appropriate superconducting multimode qubit couplers.

[0107] 11 illustrates a schematic representation of a quantum device comprising an array of superconducting qubits, each having a superconducting data qubit coupled to a superconducting auxiliary qubit using a superconducting qubit coupler, in accordance with another exemplary embodiment of the present disclosure. In particular, FIG. 11 illustrates a schematic representation of a superconducting qubit array 1100 utilizing a tunable transmon qubit coupler that selectively couples the superconducting data qubit with the superconducting auxiliary qubit. For example, superconducting qubit array 1100 includes superconducting data qubits 1110-1 and 1110-2 and tunable superconducting transmon qubit couplers 1120-1 and 1120-2, which are capacitively coupled to superconducting data qubits 1110-1 and 1110-2, respectively. Superconducting qubit array 1100 further includes a tunable superconducting transmon qubit coupler 1130 and a superconducting auxiliary qubit 1140 that is capacitively coupled to tunable superconducting transmon qubit coupler 1130.

[0108] Superconducting data qubits 1110-1 and 1110-2 each comprise a respective planar capacitor including a first superconducting pad 1112-1 and a second superconducting pad 1112-2, and a Josephson tunnel junction device 1114 coupled to and disposed between the first and second superconducting pads 1112-1 and 1112-2. Similarly, superconducting auxiliary qubit 1140 comprises a planar capacitor including a first superconducting pad 1142-1 and a second superconducting pad 1142-2, and a Josephson tunnel junction device 1144 coupled to and disposed between the first and second superconducting pads 1142-1 and 1142-2.

[0109] Tunable superconducting transmon qubit couplers 1120-1 and 1120-2 have respective planar capacitors including first and second superconducting pads 1122-1 and 1122-2, and respective SQUIDs 1124-1 and 1124-2, where each SQUID 1124-1 and 1124-2 each comprises two Josephson tunnel junction devices coupled to and connected in parallel between the first and second superconducting pads 1122-1 and 1122-2. Similarly, tunable superconducting transmon qubit coupler 1130 comprises a planar capacitor including first and second superconducting pads 1132-1 and 1132-2, and SQUID 1134 comprising two Josephson tunnel junction devices coupled to and connected in parallel between the first and second superconducting pads 1132-1 and 1132-2.

[0110] 11, a first superconducting pad 1132-1 of tunable superconducting transmon qubit coupler 1130 is directly capacitively coupled (via gap capacitance) to a second superconducting pad 1122-2 of each of tunable superconducting transmon qubit couplers 1120-1 and 1120-2, and a second superconducting pad 1132-2 of tunable superconducting transmon qubit coupler 1130 is directly capacitively coupled to a first superconducting pad 1142-1 of superconducting auxiliary qubit 1140. Furthermore, a second superconducting pad 1112-2 of each of superconducting data qubits 1110-1 and 1110-2 is directly capacitively coupled (via gap capacitance) to a first superconducting pad 1122-1 of each of tunable superconducting transmon qubit couplers 1120-1 and 1120-2.

[0111] The SQUIDs 1124-1, 1124-2, and 1134 of each tunable superconducting transmon qubit coupler 1120-1, 1120-2, and 1130 provide a flux tunable control mechanism that tunes the transition frequency of each of the tunable superconducting transmon qubit couplers 1120-1, 1120-2, and 1130 using respective flux bias control signals applied to the SQUIDs 1124-1, 1124-2, and 1134 to selectively control the coupling (e.g., exchange interaction) between the superconducting data qubits 1110-1 and 1110-2 and the superconducting ancillary qubit 1140. Each tunable superconducting transmon qubit coupler 1120-1, 1120-2, and 1130 comprises a superconducting qubit coupler configured to operate in a first state (e.g., an off state or a deactivated state) and a second state (e.g., an on state or an activated state) in response to a respective control signal applied thereto.

[0112] More specifically, in some embodiments, a given superconducting transmon qubit coupler is considered to be in the off state when its respective SQUID and transition frequency are tuned to cancel any ZZ coupling between two superconducting transmon qubits (e.g., data qubits and ancillary qubits) that are coupled (either directly or indirectly) to the given superconducting transmon qubit coupler. In particular, a given superconducting transmon qubit coupler is considered to be in the off state when the transition frequency of the given superconducting transmon qubit coupler is tuned (via its respective SQUIDs) to be far from the transition frequency of superconducting data qubits 1110-1 and 1110-2 and the transition frequency of superconducting auxiliary qubit 1140. On the other hand, a given superconducting transmon qubit coupler is considered to be in the on state when its respective SQUID and transition frequencies are tuned to be close to the transition frequencies of two superconducting transmon qubits (e.g., a data qubit and an auxiliary qubit) that are coupled (either directly or indirectly) to the given superconducting transmon qubit coupler.

[0113] For example, in a non-limiting embodiment, if superconducting data qubits 1110-1 and 1110-2 and superconducting auxiliary qubit 1140 have respective transition frequencies in the range of about 5.0 GHz to about 5.5 GHz, a given superconducting transmon qubit coupler is considered to be in the on state when it is tuned (via the flux bias control signal applied to the associated SQUID) to have a transition frequency near 5.0 GHz, whereas a given superconducting transmon qubit coupler is considered to be in the off state when it is tuned (via the flux bias control signal applied to the associated SQUID) to have a transition frequency near 3.5 GHz.

[0114] Because the superconducting data and auxiliary qubits interact not only through a given superconducting transmon qubit coupler but also through direct capacitive coupling, e.g., stray capacitance, capacitance through the transmon coupler itself, or a separate bypass capacitor, cancellation of ZZ coupling occurs between the superconducting data qubit and the superconducting auxiliary qubit that are coupled (either directly or indirectly) to a given superconducting transmon qubit coupler. In this regard, when a given superconducting transmon qubit coupler is tuned to its off-state transition frequency, these two types of capacitive coupling are essentially equal in magnitude but opposite in sign, resulting in a net ZZ coupling of zero.

[0115] It should be noted that the exemplary superconducting quantum devices shown in Figures 2B, 3B, 4B, 8, 9, 10, and 11 can be implemented using planar microwave circuit elements formed on a substrate (e.g., a silicon substrate) using state-of-the-art semiconductor fabrication techniques and materials. For example, the various components of the superconducting qubit (e.g., Josephson tunnel junction devices, inductors, capacitors), interconnects, coupling circuits, flux bias control lines, qubit drive lines, state readout lines, etc., comprise lithographically defined patterns of superconducting material formed on the semiconductor substrate. The circuit elements can be formed using various types of superconducting materials suitable for a given application, including, but not limited to, primary metals such as niobium (Nb), aluminum (Al), tantalum (Ta), and compounds such as titanium nitride (TiN), niobium nitride (NbN), niobium titanium nitride (NbTiN), etc. The Josephson tunnel junction device includes two superconducting electrodes separated by a thin insulating barrier. For example, Josephson tunnel junction devices for superconducting qubits may be fabricated using Al-AlO fabricated using dual angle deposition techniques, or other suitable fabrication techniques. x -Al trilayer tunnel junction.

[0116] 12 is a flow diagram of a method for performing a quantum error correction process according to an exemplary embodiment of the present disclosure. For illustrative purposes, the process flow of FIG. 12 is described in the context of the exemplary quantum system shown in FIG. 8. The quantum computing system begins the quantum error correction process (block 1200). As an initial step, the state of the ancillary qubit is initialized to a ground state (block 1201). For example, in FIG. 8, a microwave control pulse is applied to the superconducting ancillary qubit 840 to initialize the superconducting ancillary qubit 840 to its ground state. The quantum error correction process proceeds by activating a superconducting qubit coupler coupled to the ancillary qubit (block 1202). For example, in FIG. 8 , a flux control signal is applied to the SQUID of tunable superconducting multimode qubit coupler 830 to disrupt the mode-selective coupling of tunable superconducting multimode qubit coupler 830 and exchange couple superconducting ancillary qubit 840 to the A-mode and B-mode of tunable superconducting multimode qubit coupler 830.

[0117] A quantum error correction process proceeds by selectively activating and deactivating, in sequence, the superconducting qubit couplers coupled to the superconducting data qubits to sequentially entangle the state of each data qubit with the state of the superconducting ancillary qubit (block 1203). For example, in Figure 8, a flux control signal is applied to the SQUID 424 of tunable superconducting multimode qubit coupler 820-1 to disrupt the mode-selective coupling of tunable superconducting multimode qubit coupler 820-1, thereby exchange coupling superconducting data qubit 810-1 to the A-mode and B-mode of tunable superconducting multimode qubit coupler 820-1. In this case, superconducting data qubit 810-1 is exchange coupled to superconducting ancillary qubit 840, and the state of superconducting data qubit 810-1 is entangled with the state of superconducting ancillary qubit 840. A flux control signal is then applied to the SQUID 424 of tunable superconducting multimode qubit coupler 820-1 to enforce mode-selective coupling of tunable superconducting multimode qubit coupler 820-1, thereby decoupling superconducting data qubit 810-1 from the B-mode and coupling only to the A-mode of tunable superconducting multimode qubit coupler 820-1. This process is repeated in turn for the remaining superconducting data qubits 810-2 and 810-3.

[0118] Once the state of each superconducting data qubit is entangled with the superconducting auxiliary qubit, the quantum error correction process proceeds by deactivating the superconducting qubit coupler coupled to the auxiliary qubit (block 1204) and then performing a read operation to read out the resulting state of the auxiliary qubit (block 1205). The quantum error correction process proceeds by determining whether an error exists in the quantum state of the superconducting data qubit based on the readout of the superconducting auxiliary qubit (block 1206), and, if present, correcting the determined error (block 1207).

[0119] It should be noted that, although exemplary embodiments are described in the context of utilizing auxiliary qubits in the context of quantum error correction, those skilled in the art will understand that auxiliary qubits can be utilized in quantum circuits for other purposes. For example, the exemplary coupled configurations of quantum systems and devices shown in Figures 5, 6, 8, 9, 10, and 11 can be implemented to facilitate interactions between large sets of data qubits, some of which may be disposed relatively far from one another on the same qubit chip, where multi-mode qubit couplers, transmission line resonators, and auxiliary qubits are essentially utilized as a "superconducting bus" that allows for control and facilitating interactions between the data qubits. In a conventional square or bihexagonal lattice, to perform a gate operation between first and second data qubits spaced relatively far from one another, multiple two-qubit gate operations must be performed to swap the quantum state of the first data qubit with an intermediate data qubit that is immediately adjacent to the second qubit. On the other hand, by utilizing the exemplary coupling configurations shown in Figures 5, 6, 8, 9, 10, and 11, in which first and second data qubits are coupled to the same ancillary qubit, it is possible to perform an entanglement gate operation (e.g., a desired two-qubit gate operation) between a first and second data qubit by (i) performing a "swap" gate operation between the first data qubit and the ancillary qubit, (ii) performing the desired two-qubit gate between the ancillary qubit and the second qubit, and (iii) performing a "swap" gate operation between the ancillary qubit and the first data qubit. A "swap" gate is a two-qubit operation performed to swap the states of the two qubits.

[0120] Figure 13 schematically illustrates a quantum computing system according to an exemplary embodiment of the present disclosure. In particular, Figure 13 schematically illustrates a quantum computing system 1300 comprising a quantum computing platform 1310, a control system 1320, and a quantum processor 1330. In some embodiments, the quantum computing platform 1310 implements a software control program, such as a software-based quantum error correction system 1312, to perform quantum error correction processes, such as those described above in conjunction with Figure 12, and other software-controlled processes, such as qubit calibration operations. Furthermore, in some embodiments, the control system 1320 comprises a multi-channel arbitrary waveform generator 1322 and a qubit readout control system 1324. The quantum processor 1330 comprises a solid-state semiconductor chip having a superconducting qubit array 1332 and a network of qubit drive lines, coupler flux bias control lines, and qubit state readout lines 1334, as well as other circuit QED components that may be required for a given application or quantum system configuration.

[0121] In some embodiments, control system 1320 and quantum processor 1330 are disposed in a dilution refrigeration system 1340 capable of generating cryogenic temperatures sufficient to operate the components of control system 1320 for quantum computing applications. For example, quantum processor 1330 may need to be cooled to near absolute zero, e.g., 10-15 millikelvin (mK), to enable the superconducting qubits to exhibit quantum behavior. In some embodiments, dilution refrigeration system 1340 comprises a multi-stage dilution refrigerator capable of maintaining the components of control system 1320 at different cryogenic temperatures as needed. For example, quantum processor 1330 may need to be cooled to, e.g., 10-15 mK, while the circuit components of control system 1320 may operate at cryogenic temperatures higher than 10-15 mK (e.g., cryogenic temperatures in the range of 3 K to 4 K), depending on the configuration of the quantum computing system.

[0122] In some embodiments, superconducting qubit array 1332 comprises a quantum system of superconducting data qubits, superconducting auxiliary qubits, and superconducting qubit couplers, such as those shown in Figures 8, 9, 10, or 11. The number of superconducting qubits in qubit array 1332 can be on the order of tens, hundreds, thousands, or more. A network 1334 of qubit drive lines, coupler flux bias control lines, and qubit state readout lines, etc., is configured to apply microwave control signals to superconducting qubit and coupler circuits in superconducting qubit array 1332 to perform various types of gating operations, e.g., single gating operations, entanglement gating operations (e.g., CPHASE gating operations), error correction operations, etc., and to read out the quantum states of the superconducting qubits. For example, as described above, when executing quantum information processing algorithms, microwave control pulses are applied to the qubit drive lines of each superconducting qubit to change the quantum state of the superconducting qubit (e.g., changing the quantum state of a given qubit between a ground state and an excited state, or into a superposition state).

[0123] Additionally, as noted above, the state readout line includes a readout resonator coupled to each superconducting qubit. The state of a given superconducting qubit can be determined through microwave transmission measurements made between readout ports of the readout resonators. The state of the superconducting qubit is readout after executing a quantum algorithm. In some embodiments, a distributed readout operation is performed that utilizes changes in the resonant frequency of a given readout resonator coupled to a given superconducting qubit to read out the state (e.g., ground or excited state) of the given superconducting qubit.

[0124] A network 1334 of qubit drive lines, coupler flux bias control lines, and qubit state readout lines, etc., is coupled to control system 1320 through a suitable hardware input / output (I / O) interface that couples I / O signals between control system 1320 and quantum processor 1330. For example, the hardware I / O interface may include various types of hardware and components, such as RF cables, wiring, RF elements, optical fibers, heat exchangers, filters, amplifiers, isolators, etc.

[0125] In some embodiments, multi-channel arbitrary waveform generator (AWG) 1322 or other suitable microwave pulse signal generator is configured to generate microwave control pulses that are applied to qubit drive lines and coupler drive lines to control the operation of superconducting qubits and associated qubit coupler circuits as they perform various gate operations to implement a given specific quantum information processing algorithm. In some embodiments, multi-channel AWG 1322 has multiple AWG channels that control respective superconducting qubits in superconducting qubit array 1332 of quantum processor 1330. In some embodiments, each AWG channel comprises a baseband signal generator, a digital-to-analog converter (DAC) stage, a filter stage, a modulation stage, an impedance matching network, and a phase-locked loop system to generate local oscillator (LO) signals (e.g., quadrature LO signals LO_I and LO_Q) for respective modulation stages of the respective AWG channel.

[0126] In some embodiments, the multi-channel AWG 1322 includes a quadrature AWG system configured to process quadrature signals, where the quadrature signals have an in-phase (I) signal component and a quadrature-phase (Q) signal component. In each AWG channel, a baseband signal generator is configured to receive baseband data as input (e.g., from a quantum computing platform) and generate digital quadrature signals I and Q representing the input baseband data. In this process, the baseband data input to the baseband signal generator for a given AWG channel is separated into two quadrature digital components, including an in-phase (I) baseband component and a quadrature-phase (Q) baseband component. The baseband signal generator for a given AWG channel generates the requisite digital quadrature baseband IQ signals needed to generate an analog waveform (e.g., a sinusoidal voltage waveform) having a target center frequency that is configured to manipulate or otherwise control a given quantum bit coupled to the output of the given AWG channel.

[0127] The DAC stage for a given AWG channel is configured to convert digital baseband signals (e.g., digital IQ signals output from a baseband signal generator) into analog baseband signals (e.g., analog baseband signals I(t) and Q(t)) having baseband frequencies. The filter stage for a given AWG channel is configured to filter the IQ analog signal components output from the DAC stage, thereby generating filtered analog IQ signals. The modulation stage for a given AWG channel is configured to perform analog IQ signal modulation (e.g., single-sideband (SSB) modulation) by mixing the filtered analog signals I(t) and Q(t) output from the filter stage with quadrature LO signals (e.g., an in-phase LO signal (LO_I) and a quadrature-phase LO signal (LO_Q)) to generate and output an analog RF signal (e.g., a single-sideband regulated RF output signal).

[0128] In some embodiments, qubit readout control system 1324 comprises a microwave pulse signal generator configured to apply a microwave tone to a given readout resonator line of a given superconducting qubit to perform a readout operation to read out the state of the given superconducting qubit, as well as circuitry configured to process the readout signal generated by the readout resonator line to determine the state of the given superconducting qubit using techniques known to those skilled in the art.

[0129] Quantum computing platform 1310 includes a software and hardware platform with various software layers configured to perform various functions, including, but not limited to, creating and implementing various quantum applications using a suitable quantum programming language, configuring and implementing various quantum gate operations, compiling quantum programs into a quantum assembly language, implementing and utilizing a suitable quantum instruction set architecture (ISA), performing calibration operations to calibrate quantum circuit elements and gate operations, etc. Quantum computing platform 1310 further includes a hardware architecture, such as a processor, memory, etc., configured to control the execution of quantum applications and to interface with control system 1320 to (i) generate digital control signals that are converted by control system 1320 to analog microwave control signals to control the operation of quantum processor 1330 when executing a given quantum application, and (ii) acquire and process digital signals received from control system 1320 that represent processing results generated by quantum processor 1330 when performing the various gate operations for a given quantum application.

[0130] In some exemplary embodiments, quantum computing platform 1310 of quantum computing system 1300 may be implemented using any suitable computing system architecture (e.g., as shown in FIG. 14 ) configured to perform methods supporting quantum computing operations by executing computer-readable program instructions embodied in a computer program product including computer-readable storage medium(s) having computer-readable program instructions for causing a processor to perform control methods as described herein.

[0131] Quantum computing platform 1310 includes a software and hardware platform with various software layers configured to perform various functions, including, but not limited to, creating and implementing various quantum applications using a suitable quantum programming language, configuring and implementing various quantum gate operations, compiling quantum programs into a quantum assembly language, implementing and utilizing a suitable quantum instruction set architecture (ISA), performing calibration operations to calibrate quantum circuit elements and gate operations, etc. Quantum computing platform 1310 further includes a hardware architecture, such as a processor, memory, etc., configured to control the execution of quantum applications and to interface with control system 1320 to (i) generate digital control signals that are converted by control system 1320 to analog microwave control signals to control the operation of quantum processor 1330 when executing a given quantum application, and (ii) acquire and process digital signals received from control system 1320 that represent processing results generated by quantum processor 1330 when performing the various gate operations for a given quantum application. In some exemplary embodiments, quantum computing platform 1310 of quantum computing system 1300 may be implemented using any suitable computing system architecture (e.g., as shown in FIG. 14 ) configured to perform methods to support quantum computing operations by executing computer-readable program instructions embodied on a computer program product comprising computer-readable storage medium(s) having computer-readable program instructions for causing a processor to perform control methods as described herein.

[0132] Various aspects of the present disclosure are described through narrative text, flowcharts, block diagrams of computer systems, and / or block diagrams of machine logic included in computer program product (CPP) embodiments. For any flowchart, depending on the technology involved, operations may be performed in an order different from that shown in a given flowchart. For example, again depending on the technology involved, two operations shown in successive flowchart blocks may be performed in reverse order, as a single integrated step, simultaneously, or in an at least partially overlapping manner.

[0133] A computer program product embodiment ("CPP embodiment" or "CPP") is a term used in this disclosure to describe any set of one or more storage media (also referred to as "media"), collectively contained in one or more storage devices, that collectively contain machine-readable code corresponding to instructions and / or data for performing the computer operations specified in a given CPP claim. A "storage device" is any tangible device that can hold and store instructions for use by a computer processor. The computer-readable storage medium may be, but is not limited to, an electronic storage medium, a magnetic storage medium, an optical storage medium, an electromagnetic storage medium, a semiconductor storage medium, a mechanical storage medium, or any suitable combination of the foregoing. Some known types of storage devices that include these media include diskettes, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), compact disc read-only memory (CD-ROM), digital versatile disk (DVD), memory stick, floppy disk, mechanically encoded devices (such as punch cards or pits / lands formed on a major surface of a disk), or any suitable combination of the foregoing. Computer-readable storage media, as the term is used in this disclosure, is not to be construed as storage in the form of a transitory signal per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide, light pulses passing through fiber optic cables, electrical signals communicated through wires, and / or other transmission media. As those skilled in the art will appreciate, data is typically moved at some infrequent time during the normal operation of a storage device, such as during access, defragmentation, or garbage collection, but this does not make the storage device transient because the data is not transient while it is stored.

[0134] Computing environment 1400 of Figure 14 includes an example of an environment for the execution of at least some of the computer code involved in performing the methods of the invention, such as the quantum error correction control code in block 1426 for controlling the quantum error correction functionality of quantum error correction system 1312 of Figure 13. In addition to block 1426, computing environment 1400 includes, for example, a computer 1401, a wide area network (WAN) 1402, an end user device (EUD) 1403, a remote server 1404, a public cloud 1405, and a private cloud 1406. In this embodiment, computer 1401 includes a set of processors 1410 (including processing circuitry 1420 and cache 1421), a communications fabric 1411, volatile memory 1412, persistent storage 1413 (including operating system 1422 and block 1426, as identified above), a set of peripheral devices 1414 (including a user interface (UI), a set of devices 1423, storage 1424, and a set of Internet of Things (IoT) sensors 1425), and a network module 1415. Remote server 1404 includes a remote database 1430. Public cloud 1405 includes a gateway 1440, a cloud orchestration module 1441, a set of host physical machines 1442, a set of virtual machines 1443, and a set of containers 1444.

[0135] Computer 1401 may take the form of a desktop computer, laptop computer, tablet computer, smartphone, smartwatch or other wearable computer, mainframe computer, quantum computer, or any other form of computer or mobile device now known or later developed that is capable of executing programs, accessing a network, or querying a database, such as remote database 1430. As is well understood in the art of computer technology, and depending on the technology, execution of a computer-implemented method may be distributed among multiple computers and / or among multiple locations. While in this presentation of computing environment 1400, to keep the presentation as concise as possible, the detailed discussion focuses on a single computer, specifically computer 1401. Although computer 1401 is not shown in FIG. 14 , it may be located within a cloud. However, computer 1401 is not required to reside within a cloud except to any extent that may be expressly indicated.

[0136] Processor set 1410 includes one or more computer processors of any type now known or later developed. Processing circuitry 1420 may be distributed across multiple packages, e.g., multiple tailored integrated circuit chips. Processing circuitry 1420 may implement multiple processor threads and / or multiple processor cores. Cache 1421 is memory located within the processor chip package and is typically used for data or code that should be available for fast access by threads or cores executing on processor set 1410. Cache memory is typically organized into multiple levels depending on relative proximity to the processing circuitry. Alternatively, some or all caches for a processor set may be located “off-chip.” In some computing environments, processor set 1410 may be designed to operate with qubits and perform quantum computations.

[0137] Computer-readable program instructions are typically loaded onto computer 1401 and cause a series of operational steps to be performed by processor set 1410 of computer 1401, thereby performing a computer-implemented method; thus, the executed instructions embody the method specified in the flowcharts and / or narrative descriptions of the computer-implemented methods contained herein (collectively referred to as "invention methods"). These computer-readable program instructions are stored in various types of computer-readable storage media, such as cache 1421 and other storage media discussed below. The program instructions and associated data are accessed by processor set 1410 to control and direct the execution of the inventive methods. In computing environment 1400, at least some of the instructions for performing the inventive methods may be stored in block 1426 in persistent storage 1413.

[0138] Communications fabric 1411 is the signal transmission path that allows various components of computer 1401 to communicate with one another. Typically, this fabric is made up of switches and conductive paths, such as buses, bridges, switches and conductive paths that form physical input / output ports, etc. Other types of signal communication paths may be used, such as fiber optic and / or wireless communication paths.

[0139] Volatile memory 1412 may be any type of volatile memory, now known or later developed. Examples include dynamic type random access memory (RAM) or static type RAM. Typically, volatile memory is characterized by random access, although this is not required unless expressly indicated. In computer 1401, volatile memory 1412 is located in a single package and is internal to computer 1401; however, alternatively or additionally, volatile memory may be distributed across multiple packages and / or located external to computer 1401.

[0140] Persistent storage 1413 is any form of non-volatile storage for a computer, now known or later developed. The non-volatility of this storage means that stored data remains regardless of whether power is supplied to computer 1401 and / or to persistent storage 1413 directly. Persistent storage 1413 can be read-only memory (ROM), but typically at least a portion of persistent storage allows data to be written, data to be deleted, and data to be rewritten. Some well-known forms of persistent storage include magnetic disks and solid-state storage devices. Operating system 1422 may take several forms, such as various known proprietary operating systems or open-source Portable Operating System Interface-type operating systems that utilize a kernel. The code contained in block 1426 typically includes at least some of the computer code involved in performing the methods of the present invention.

[0141] Peripheral device set 1414 includes the set of peripheral devices of computer 1401. Data communication connections between peripheral devices and other components of computer 1401 may be implemented in various ways, such as Bluetooth® connections, near field communication (NFC) connections, connections formed by cables (such as universal serial bus (USB)-type cables), insertion-type connections (e.g., Secure Digital (SD) cards), connections formed through local area communication networks, and even connections formed through wide area networks such as the Internet. In various embodiments, UI device set 1423 may include components such as display screens, speakers, microphones, wearable devices (such as goggles and smartwatches), keyboards, mice, printers, touchpads, game controllers, and haptic devices. Storage 1424 may be external storage, such as an external hard drive, or insertable storage, such as an SD card. Storage 1424 may be persistent and / or volatile. In some embodiments, storage 1424 may take the form of a quantum computing storage device for storing data in the form of qubits. In embodiments where computer 1401 is required to have a large amount of storage (e.g., where computer 1401 stores and manages a large database locally), then this storage may be provided by a peripheral storage device designed to store very large amounts of data, such as a storage area network (SAN) shared by multiple, geographically distributed computers. IoT sensor set 1425 consists of sensors that can be used in Internet of Things applications. For example, one sensor may be a thermometer and another sensor may be a motion detector.

[0142] Network module 1415 is a collection of computer software, hardware, and firmware that enables computer 1401 to communicate with other computers over WAN 1402. Network module 1415 may include hardware such as a modem or Wi-Fi signal transceiver, software for packetizing and / or depacketizing data for communication network transmission, and / or web browser software for communicating data over the Internet. In some embodiments, the network control and network forwarding functions of network module 1415 are performed on the same physical hardware device. In other embodiments (e.g., embodiments utilizing software-defined networking (SDN)), the control and forwarding functions of network module 1415 are performed on physically separate devices, such that the control function manages several different network hardware devices. Computer-readable program instructions for implementing the methods of the present invention may be downloaded to computer 1401 from an external computer or external storage device, typically through a network adapter card or network interface included in network module 1415.

[0143] WAN 1402 is any wide area network (e.g., the Internet) capable of communicating computer data over non-local distances by any technology for communicating computer data now known or later developed. In some embodiments, a WAN may be replaced and / or supplemented by a local area network (LAN) designed to communicate data between devices located in a local area, such as a Wi-Fi network. WANs and / or LANs typically include copper transmission cables, optical fiber transmissions, wireless transmissions, and computer hardware such as routers, firewalls, switches, gateway computers, and edge servers.

[0144] End-user device (EUD) 1403 is any computer system used and controlled by an end user (e.g., a customer of the enterprise operating computer 1401) and may take any of the forms discussed above in connection with computer 1401. EUD 1403 typically receives useful and useful data from the operation of computer 1401. For example, in a hypothetical case where computer 1401 is designed to provide recommendations to the end user, the recommendations would typically be communicated from network module 1415 of computer 1401 over WAN 1402 to EUD 1403. In this manner, EUD 1403 can display or otherwise present the recommendations to the end user. In some embodiments, EUD 1403 may be a client device such as a thin client, a heavy client, a mainframe computer, a desktop computer, etc.

[0145] Remote server 1404 is any computer system that provides at least some data and / or functionality to computer 1401. Remote server 1404 may be controlled and used by the same entity that operates computer 1401. Remote server 1404 represents a machine that collects and stores useful and useful data for use by other computers, such as computer 1401. For example, in the hypothetical case where computer 1401 is designed and programmed to provide recommendations based on historical data, this historical data may now be provided to computer 1401 from remote database 1430 of remote server 1404.

[0146] A public cloud 1405 is any computer system available for use by multiple organizations that provides on-demand availability of computer system resources and / or other computer capabilities, particularly data storage (cloud storage) and computing power, without direct, active management by users. Cloud computing typically leverages resource sharing to achieve coherence and economies of scale. Direct, active management of the computing resources of the public cloud 1405 is performed by the computer hardware and / or software of a cloud orchestration module 1441. The computing resources provided by the public cloud 1405 are typically implemented by virtual computing environments running on various computers comprising a host physical machine set 1442, which is the universe of physical computers within and / or available in the public cloud 1405. The virtual computing environments (VCEs) typically take the form of virtual machines from a virtual machine set 1443 and / or containers from a container set 1444. It is understood that these VCEs may be stored as images and transferred among and between various hosts of physical machines either as images or after instantiation of the VCE. Cloud orchestration module 1441 manages the transfer and storage of images, deploys new instantiations of VCEs, and manages active instantiations of VCE deployments. Gateway 1440 is a collection of computer software, hardware, and firmware that enables public cloud 1405 to communicate over WAN 1402.

[0147] Some further description of virtualized computing environments (VCEs) is provided here. A VCE can be stored as an "image." A new active instance of a VCE can be instantiated from the image. Two well-known types of VCEs are virtual machines and containers. A container is a VCE that uses operating system-level virtualization. This refers to a feature of an operating system in which the kernel allows the existence of multiple isolated user space instances called containers. These isolated user space instances typically behave as real computers from the perspective of programs running within them. A computer program running on a typical operating system can utilize all of the computer's resources, such as connected devices, files and folders, network shares, CPU power, and quantifiable hardware capabilities. However, a program running inside a container can only use the contents of the container and of the devices assigned to the container; this feature is known as containerization.

[0148] Private cloud 1406 is similar to public cloud 1405, except that the computing resources are available only for use by a single enterprise. While private cloud 1406 is shown in communication with WAN 1402, in other embodiments, the private cloud may be completely disconnected from the Internet and accessible only through a local / private network. A hybrid cloud is a composite of multiple clouds of different types (e.g., private, community, or public cloud types), often each implemented by a different vendor. While each of the multiple clouds remains a separate, discrete entity, the larger hybrid cloud architecture is tied together by standardized or proprietary technologies that enable orchestration, management, and / or data / application portability between the constituent clouds. In this embodiment, both public cloud 1405 and private cloud 1406 are part of a larger hybrid cloud.

[0149] The description of various embodiments of the present disclosure has been presented for purposes of illustration, but it is not intended to be exhaustive or limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein has been selected to best explain the principles, practical applications, or technical improvements to commercially available technologies of the embodiments, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. a first data qubit; a first qubit coupler coupled to the first data qubit; a second qubit coupler coupled to the first qubit coupler; and an ancillary qubit coupled to the second qubit coupler; Equipped with the first qubit coupler is configured to operate in a state to suppress interaction between the first data qubit and the ancillary qubit; The first qubit coupler and the second qubit coupler are each configured to operate in a respective state to enable an interaction between the first data qubit and the ancillary qubit, entangling the state of the first data qubit with the state of the ancillary qubit. device.

2. The device of claim 1 , wherein the first data qubit and the ancillary qubit each comprise a transmon qubit.

3. a second data qubit; and a third qubit coupler coupled to the second data qubit and to the second qubit coupler; Furthermore, the third qubit coupler is configured to operate in a state to suppress interactions between the second data qubit and the first data qubit and to suppress interactions between the second data qubit and the ancillary qubit; The third qubit coupler and the second qubit coupler are each configured to operate in a respective state to enable an interaction between the second data qubit and the ancillary qubit, entangling the state of the second data qubit with the state of the ancillary qubit. A device according to any of the preceding claims.

4. further comprising a capacitive bus configured to capacitively couple the first qubit coupler and the third qubit coupler to the second qubit coupler, the capacitive bus comprising: a first capacitor pad connected to the first qubit coupler by a first transmission line; a second capacitor pad connected to the second qubit coupler by a second transmission line; and a third capacitor pad connected to the third qubit coupler by a third transmission line; and the first capacitor pad and the third capacitor pad are disposed adjacent to a first edge and a second edge, respectively, of the second capacitor pad; The second capacitor pad has a size larger than the size of the first capacitor pad and the size of the third capacitor pad. The device of claim 3.

5. 10. The device of claim 1, wherein the first qubit coupler and the second qubit coupler each comprise a flux-tunable transmon qubit.

6. 10. A device according to any preceding claim, wherein the ancillary qubit comprises a quadrupole transmon qubit.

7. the first qubit coupler has a first multi-mode qubit having a first mode and a second mode; The second qubit coupler includes a second multi-mode qubit having a first mode and a second mode. A device according to any of the preceding claims.

8. the first data qubit is capacitively coupled to the first mode of the first multi-mode qubit; the ancillary qubit is capacitively coupled to the first mode of the second multi-mode qubit; the second mode of the first multi-mode qubit is capacitively coupled to the second mode of the second multi-mode qubit; the first qubit coupler is configured to operate with the first data qubit exchange coupled to only the first mode of the first multi-mode qubit; the first qubit coupler is configured to operate with the first data qubit exchange coupled to both the first mode and the second mode of the first multi-mode qubit; the second qubit coupler is configured to operate with the ancillary qubit exchange coupled to only the first mode of the second multi-mode qubit; The second qubit coupler is configured to operate with the ancillary qubit exchange-coupled to both the first mode and the second mode of the second multi-mode qubit. The device of claim 7.

9. a quantum processor having an array of qubits; and a control system configured to generate control signals to control the quantum processor; Provided with: the array of qubits a first data qubit; a first qubit coupler coupled to the first data qubit; a second qubit coupler coupled to the first qubit coupler; and an ancillary qubit coupled to the second qubit coupler; Equipped with the first qubit coupler is configured to operate in a state to suppress interaction between the first data qubit and the ancillary qubit; The first qubit coupler and the second qubit coupler are each configured to operate in a respective state to enable an interaction between the first data qubit and the ancillary qubit, entangling the state of the first data qubit with the state of the ancillary qubit. system.

10. 10. The system of claim 9, wherein the first data qubit and the ancillary qubit each comprise a transmon qubit.

11. the array of qubits a second data qubit; and a third qubit coupler coupled to the second data qubit and to the second qubit coupler; further comprising the third qubit coupler is configured to operate in a state to suppress interactions between the second data qubit and the first data qubit and to suppress interactions between the second data qubit and the ancillary qubit; The third qubit coupler and the second qubit coupler are each configured to operate in a respective state to enable an interaction between the second data qubit and the ancillary qubit, entangling the state of the second data qubit with the state of the ancillary qubit. A system according to any one of claims 9 to 10.

12. a capacitive bus configured to capacitively couple the first qubit coupler and the third qubit coupler to the second qubit coupler, the capacitive bus comprising: a first capacitor pad connected to the first qubit coupler by a first transmission line; a second capacitor pad connected to the second qubit coupler by a second transmission line; and a third capacitor pad connected to the third qubit coupler by a third transmission line; and the first capacitor pad and the third capacitor pad are disposed adjacent to a first edge and a second edge, respectively, of the second capacitor pad; The second capacitor pad has a size larger than the size of the first capacitor pad and the size of the third capacitor pad. The system of claim 11.

13. 13. The system of claim 9, wherein the first qubit coupler and the second qubit coupler each comprise a flux-tunable transmon qubit.

14. 14. The system of claim 9, wherein the ancillary qubit comprises a quadrupole transmon qubit.

15. the first qubit coupler has a first multi-mode qubit having a first mode and a second mode; The second qubit coupler includes a second multi-mode qubit having a first mode and a second mode.

15. A system according to any one of claims 9 to 14.

16. the first data qubit is capacitively coupled to the first mode of the first multi-mode qubit; the ancillary qubit is capacitively coupled to the first mode of the second multi-mode qubit; the second mode of the first multi-mode qubit is capacitively coupled to the second mode of the second multi-mode qubit; the first qubit coupler is configured to operate with the first data qubit exchange coupled to only the first mode of the first multi-mode qubit; the first qubit coupler is configured to operate with the first data qubit exchange coupled to both the first mode and the second mode of the first multi-mode qubit; the second qubit coupler is configured to operate with the ancillary qubit exchange coupled to only the first mode of the second multi-mode qubit; The second qubit coupler is configured to operate with the ancillary qubit exchange-coupled to both the first mode and the second mode of the second multi-mode qubit. The system of claim 15.

17. Data qubits; a qubit coupler coupled to the data qubit; a transmission line resonator coupled to the qubit coupler; and an ancillary qubit coupled to the transmission line resonator; Equipped with the qubit coupler is configured to operate in a state to suppress interaction between the data qubit and the ancillary qubit; The qubit coupler is configured to operate in a state to enable interaction between the data qubit and the ancillary qubit through the qubit coupler and the transmission line resonator, entangling the state of the data qubit with the state of the ancillary qubit. device.

18. 20. The device of claim 17, wherein the data qubit and the ancillary qubit each comprise a transmon qubit.

19. the qubit coupler has a multi-mode qubit having a first mode and a second mode; the data qubit is capacitively coupled to the first mode of the multi-mode qubit; the transmission line resonator is capacitively coupled to the second mode of the multi-mode qubit; the qubit coupler is configured to operate with the data qubit exchange coupled to only the first mode of the multi-mode qubit; The qubit coupler is configured to operate with the data qubit exchange coupled to both the first mode and the second mode of the multi-mode qubit.

19. A device according to any one of claims 17 to 18.

20. a quantum processor having an array of qubits; and a control system configured to generate control signals to control the quantum processor; Equipped with the array of qubits Data qubits; a qubit coupler coupled to the data qubit; a transmission line resonator coupled to the qubit coupler; and an ancillary qubit coupled to the transmission line resonator; Equipped with the qubit coupler is configured to operate in a state to suppress interaction between the data qubit and the ancillary qubit; The qubit coupler is configured to operate in a state to enable interaction between the data qubit and the ancillary qubit through the qubit coupler and the transmission line resonator, entangling the state of the data qubit with the state of the ancillary qubit. system.

21. 21. The system of claim 20, wherein the data qubit and the ancillary qubit each comprise a transmon qubit.

22. the qubit coupler has a multi-mode qubit having a first mode and a second mode; the data qubit is capacitively coupled to the first mode of the multi-mode qubit; the transmission line resonator is capacitively coupled to the second mode of the multi-mode qubit; the qubit coupler is configured to operate with the data qubit exchange coupled to only the first mode of the multi-mode qubit; The qubit coupler is configured to operate with the data qubit exchange coupled to both the first mode and the second mode of the multi-mode qubit.

22. A system according to any one of claims 20 to 21.

23. initializing the state of the ancillary qubit; placing a first qubit coupler coupled to the ancillary qubit in an activated state; placing a second qubit coupler coupled to a data qubit in an activated state to enable interaction between the data qubit and the ancillary qubit through the first and second qubit couplers in the activated state, and entangling the state of the first data qubit with the state of the ancillary qubit; placing each of the first qubit coupler and the second qubit coupler in a deactivated state; reading out the state of the ancillary qubit after each of the first qubit coupler and the second qubit coupler is placed in the deactivated state; and determining the presence of a quantum error based on said readout of said ancillary qubits; A method for providing the above.

24. placing the first qubit coupler in the activated state comprises applying a first flux control signal to a first superconducting loop of a first superconducting quantum interference device of the first qubit coupler to configure the first qubit coupler from the deactivated state to the activated state; Placing the second qubit coupler in the activated state includes applying a second flux control signal to a second superconducting loop of a second superconducting quantum interference device of the second qubit coupler to configure the second qubit coupler from the deactivated state to the activated state.

24. The method of claim 23.

25. the first qubit coupler has a first multi-mode qubit having a first mode and a second mode; the second qubit coupler has a second multi-mode qubit having a first mode and a second mode; the ancillary qubit is capacitively coupled to the first mode of the first multi-mode qubit; the data qubit is capacitively coupled to the first mode of the second multi-mode qubit; the second mode of the first multi-mode qubit is capacitively coupled to the second mode of the second multi-mode qubit; placing the first qubit coupler in the activated state comprises applying a first flux control signal to a first superconducting loop of a first superconducting quantum interference device of the first multi-mode qubit to exchange couple the ancillary qubit to both the first mode and the second mode of the first multi-mode qubit; Placing the second qubit coupler in the activated state includes applying a second flux control signal to a second superconducting loop of a second superconducting quantum interference device of the second multi-mode qubit to exchange couple the data qubit to both the first mode and the second mode of the second multi-mode qubit.

25. The method of any of claims 23 to 24.

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