Quantum data processing system

Abstract

Methods, systems, and apparatus, including computer programs, for quantum data processing. In one aspect, a method includes storing a plurality of copies of a quantum state in a quantum memory, including: for each copy of the quantum state, i) probing a target system by an initialized quantum sensor to obtain an evolved quantum state of the quantum sensor, ii) transducing the evolved quantum state of the quantum sensor into a quantum state of a quantum buffer, iii) logically encoding the quantum state of the quantum buffer into a quantum error correction code, and iv) moving the logically encoded quantum state of the quantum buffer into the quantum memory; loading the plurality of copies of the quantum state in the quantum memory into a quantum computer; processing, by the quantum computer, the plurality of copies of the quantum state to obtain a purified quantum state; and measuring the purified quantum state to determine a property of the target system.

Description

TECHNICAL FIELD

[0001] This specification relates to quantum sensing and quantum computing. BACKGROUND

[0002] A quantum sensor is a quantum device that uses the sensitivity of a quantum system to external perturbations to measure a physical quantity or parameter, including magnetic or electric fields, time, frequency, rotation, temperature, or pressure. Quantum devices are characterized by quantized energy levels and can include superconducting or spin qubits, electrons of neutral atoms or trapped ions, magnetic or vibrational states. In a conventional quantum sensing protocol, a quantum sensor is initialized and interacted with a signal of interest. The quantum state of the quantum sensor is then transduced and / or read out. Phase estimation or parameter estimation techniques are applied to the readout data obtained from a series of such readouts to reconstruct the physical quantity of interest. SUMMARY

[0003] This specification describes a quantum data processing system.

[0004] In general, one innovative aspect of the subject matter described in this specification can be implemented in a method that includes storing a plurality of copies of a quantum state in a quantum memory, including: for each copy of the quantum state, i) probing a target system with an initialized quantum sensor to obtain an evolved quantum state of the quantum sensor, ii) transducing the evolved quantum state of the quantum sensor into a quantum state of a quantum buffer, iii) logically encoding the quantum state of the quantum buffer into a quantum error correction code, and iv) moving the logically encoded quantum state of the quantum buffer into the quantum memory; loading the plurality of copies of the quantum state in the quantum memory into a quantum computer; processing the plurality of copies of the quantum state by the quantum computer to obtain a purified quantum state; and measuring the purified quantum state to determine a property of the target system.

[0005] Other implementations of these aspects include corresponding computer systems, apparatus, and computer programs recorded on one or more computer storage devices, each configured to perform the actions of the methods. A system of one or more computer and / or quantum computers can be configured to perform particular operations or actions by virtue of having software, firmware, hardware, or a combination thereof installed on the system that in operation

[0006] The foregoing and other implementations can each alone or in combination optionally include one or more of the following features. In some implementations, the quantum sensor is configured to maintain quantum coherence.

[0007] In some implementations, the evolved quantum state of the quantum sensor encodes a property of the target system at the time of the probing.

[0008] In some implementations, the evolved quantum state of the quantum sensor includes states of a plurality of qubits or states of bosons or photon modes.

[0009] In some implementations, the probing of the target system to obtain the evolved quantum state of the quantum sensor is performed with a limited signal-to-noise ratio.

[0010] In some implementations, the quantum sensor is configured to implement full or partial quantum error correction on the evolved quantum state of the quantum sensor.

[0011] In some implementations, the quantum sensor includes a first computational medium and the quantum buffer includes a second computational medium, where the second computational medium is different from the first computational medium.

[0012] In some implementations, the logically encoding the quantum state of the quantum buffer into the quantum error correction code includes applying a unitary encoding quantum circuit to the quantum state of the quantum buffer or performing a state injection technique.

[0013] In some implementations, the quantum error correction code includes a code distance that depends on at least one of: operations performed by the quantum computer to obtain the purified quantum state or an expected duration required to store multiple copies of the quantum state.

[0014] In some implementations, the quantum error correction code is the quantum buffer.

[0015] In some implementations, the processing the multiple copies of the quantum state to obtain the purified quantum state includes performing a linear distillation technique to purify the multiple copies of the quantum state.

[0016] In some implementations, the linear distillation technique includes a quantum state distillation, a virtual state distillation, or a quantum principal component analysis algorithm.

[0017] In some implementations, the measuring the purified quantum state to determine the property of the target system includes providing measurement results to a quantum machine learning system to learn the property of the target system.

[0018] In some implementations, the target system includes a transient target system.

[0019] The subject matter described in this specification can be implemented in particular implementations so as to realize one or more of the following advantages.

[0020] In conventional quantum data processing, quantum sensors interface with classical systems. This forces premature use of measurements, which destroys quantum information. Thus, subsequent data purification / extraction or processing steps are exponentially costly in terms of number of copies.

[0021] To reduce these costs, the presently described quantum data processing system includes quantum sensors that interface with quantum devices. The quantum devices implement quantum transduction and quantum storage techniques over multiple data collection repetitions to exceed the capabilities of quantum sensors that only couple to classical computers. In particular, the presently described quantum data processing system achieves an exponential advantage in the number of measurements that must be made based on the size of the quantum sensors. This exponential advantage can be achieved even when both the quantum storage and the quantum processor have noise. Thus, the presently described techniques are particularly suitable for implementations using near-term quantum computing devices (e.g., noisy intermediate-scale quantum (NISQ) devices).

[0022] Additionally, the presently described quantum data processing system can achieve increased sensitivity and improved ability to de-noise signals from quantum sensors compared to conventional quantum data processing systems.

[0023] Additionally, unlike conventional quantum data processing systems, the presently described quantum data processing system can collect and process quantum data in transient sensing applications where only limited data collection time is available.

[0024] Additionally, the presently described quantum data processing system is modular and different components can be changed or upgraded as needed to accommodate the needs of a particular application.

[0025] Furthermore, the presently described quantum data processing system can be used in a variety of applications, for example, to enable improved chemical identification, improved quantum material characterization, and more precise sensing for imaging applications, including medical imaging applications such as MRI.

[0026] The details of one or more implementations of the subject matter of this specification are set forth in the accompanying drawings and the description below. Other features, aspects, and advantages of the subject matter will become apparent from the description, the drawings, and the claims. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 is a diagram comparing conventional processes for collecting and processing quantum data with the presently described quantum-enhanced processes for collecting and processing quantum data.

[0028] Figure 2is a block diagram of an example quantum data processing system.

[0029] Figure 3 is a diagram of an example quantum computing device.

[0030] Figure 4 is a flowchart of an example process for processing quantum data.

[0031] Figure 5 and Figure 6 is a flowchart of an example process for storing multiple copies of a quantum state in a quantum memory.

[0032] Figure 7 is a diagram illustrating a quantum advantage realized in learning physical states using the presently described techniques.

[0033] Figure 8 is a diagram illustrating a quantum advantage realized in learning physical dynamics using the presently described techniques.

[0034] Like reference numbers and designations in the various drawings indicate like elements. DETAILED DESCRIPTION

[0035] SUMMARY

[0036] This specification describes quantum data processing methods and systems for collecting and processing quantum data that have an exponential speedup over classical processing of the same data. The data collection step is performed a fixed number of times or continuously. During the data collection step, a quantum sensor probes a target system and collects data from the target system. The data is transferred into a quantum buffer that is compatible with a logical encoding and encoded into a quantum error correcting code. The encoded data is then shuttled into a quantum memory. Once a sufficient number of copies of the data are collected in the quantum memory, the quantum memory is loaded into a quantum computer. The quantum computer performs quantum data processing to purify or further refine the data. The refined data can then be used to measure and extract information about the target system that can be fed to a classical computer or experimenter for further analysis.

[0037] Figure 1 is a diagram 100 comparing a conventional process 102 for collecting and processing quantum data with a quantum-enhanced process 104 for collecting and processing quantum data presently described. In the conventional process 102, a quantum sensor interfaces with a classical machine running a classical algorithm. The classical machine can store and process classical information. In the quantum-enhanced process 104, the quantum sensor interfaces with a quantum machine running a quantum algorithm. The quantum machine can store and process quantum information.

[0038] In stage (a), experiments are performed. Each experiment includes probing a target physical system using a quantum sensor, as described below with reference to Figure 2 In more detail, the target physical system can be a real-world system of interest, such as a molecule, a virus, DNA, a planet, or a black hole.

[0039] In some implementations, each experiment produces a physical quantum state p. In these implementations, the goal of the data processing is to learn something about p, as shown in stage (b). In the classical process 102, multiple copies of p are measured individually to obtain classical measurement data. The classical measurement data is stored in a classical memory. A classical computer processes the classical measurement data to output a prediction for a property of p. In the quantum-enhanced process 104, the quantum state p can coherently alter quantum information stored in a memory of a quantum machine. Copies of p are stored as quantum data in a quantum memory. A quantum memory is a memory that stores quantum states that can generally be superposed; in contrast, a classical memory stores states only as binary states. The quantum machine processes the quantum data and performs a measurement on the quantum memory to output a prediction for a property of the quantum data p. It can be shown that, for some tasks, the number of experiments required to learn the target property of p is exponential in n when using the classical process 102, but is only polynomial in n when using the quantum-enhanced process 104. For appropriately defined tasks, a quantum advantage of order one can be achieved using a protocol as simple as storing two copies of p in a quantum memory and performing an entangling measurement.

[0040] In other implementations, each experiment is a physical process that evolves a quantum state. In these implementations, the goal of the data processing is to learn something about the physical process , as shown in stage (c). In the classical process 102, a classical machine uses classical bit strings to specify an input state and obtain classical measurement data. In the quantum-enhanced process 104, the evolution coherently alters a memory of a quantum machine— the input state is entangled with a quantum memory in the quantum machine, and the output state is coherently retrieved by the quantum machine. In these implementations, the quantum-enhanced process 104 achieves a similar exponential advantage.

[0041] Example operating environment

[0042] Figure 2is a block diagram of an example quantum data processing system 200 for performing the presently described quantum-enhanced data processing techniques. The example quantum data processing system 200 is an example of a system implemented as a classical and quantum computer program on one or more classical computers and quantum computing devices in one or more locations, in which the systems, components, and techniques described herein can be implemented.

[0043] The example quantum data processing system 200 includes one or more quantum sensors, such as quantum sensor 204, quantum buffer 208, quantum memory 214, quantum computer 216, and classical or quantum computer 218. A quantum sensor is a quantum device configured to probe a corresponding target system (e.g., target system 202) and collect data 206 from the target system. The target system 202 is a system of interest, e.g., a system from which a physical quantity or parameter is to be estimated, and can vary based on the quantum data processing task performed by the quantum data processing system 200. The target system 202 and the physical quantity or parameter can be quantum or classical. For example, the data collected by the quantum sensor 204 can result from a classical process. In these cases, by implementing the techniques described in this specification, properties of such classical processes can be determined exponentially faster even though the source data is classical. Reference is made to Figure 4 The example target system is described in more detail.

[0044] To probe the target system 202, the quantum sensor 204 interacts with the target system 202, and the quantum state of the quantum system included in the quantum sensor 204 (hereinafter referred to as the quantum state of the quantum sensor 204) evolves for a predetermined sensing time. During the evolution, the state of the quantum sensor 204 becomes dependent on the physical quantity or parameter of interest and reflects the state of the target system 202. In this way, the quantum sensor 204 collects data 206 from the target system 202, where the data 206 is the evolved quantum state of the quantum sensor 204. In some implementations, the data 206 can be collected with a limited signal-to-noise ratio. In some implementations, the quantum sensor 204 can implement full or partial quantum error correction to improve its sensing or data retention capabilities. In some implementations, the quantum sensor 204 can maintain quantum coherence.

[0045] The type of quantum sensor 204 included in the quantum data processing system 200 depends on the target system 202 and the physical quantity or parameter of interest. For example, in magnetic force measurements, electrical measurements, temperature measurements, and chemical sensing applications, the quantum sensor 204 can be a solid-state quantum sensor that includes nitrogen vacancies (isolated or distributed in a network) in a diamond. Other example quantum sensors include hyperpolarized spins in a gas, nuclear spins of chemical species in a solution, or cavity modes for sensing photonic states or detecting extraneous particles.

[0046] As a specific example, in some implementations, the target system 202 can be an unknown metabolite, and the physical quantity / property can be the structure of the unknown metabolite. In this example, the structure of the unknown metabolite can be determined through features related to spin magnetization, electronic or vibrational excitation, or charge transport, and the quantum sensor can include hyperpolarized gases compatible with spin transport, nitrogen vacancies in diamond with sufficient spatial resolution, or nanomechanical sensors for vibrational measurements.

[0047] As another example, in some implementations, the target system can be some system for which the density distribution of the unknown interior of the system is to be determined, for example, imaging within a cave, a container, or a building. In this example, the physical quantities to be determined can include the amount, distribution, and type of matter, and material properties such as density or rigidity, and the quantum sensor can include quantum sensors sensitive to the effects of gravity, for example, advanced atomic interferometers or atomic fountains, which use quantum effects to sense the gravity between different spatial locations of atoms. The quantum data processing system can increase the sensitivity and capabilities of these sensors.

[0048] In some implementations, the system can include multiple quantum sensors probing the target system 202 in parallel. Probing the target system 202 using multiple quantum sensors in parallel can reduce the amount of time states are held in memory and increase the sampling rate, particularly in cases where sensing is performed on multiple copies of the same target system (e.g., many copies of a molecule). Alternatively or additionally, the multiple quantum sensors can include different types of quantum sensors. For example, collecting complementary data from different types of sensors in parallel can increase the capabilities of the quantum data processing system, for example, enabling the system to extract more accurate and insightful information, and thus improved estimates of physical properties and parameters, and made possible by the structure and workflow of the quantum data processing system.

[0049] In a conventional quantum data processing system (i.e., a system different from the quantum data processing system described in this specification), after the quantum state of the quantum sensor 204 evolves for a predetermined sensing time and collects data 206 from the target system, the evolved quantum state of the quantum sensor 204 is measured. The target system 202 will be probed repeatedly by the quantum sensor 204 during the total available measurement time, and estimates of the physical quantities or parameters of interest will be inferred via classical computation from the accumulated measurement data. Thus, quantum information is destroyed early in the process, making subsequent data purification / extraction or data processing exponentially expensive in terms of the number of probes.

[0050] To avoid these costs, the quantum data processing system 200 transfers the data 206 collected by the quantum sensor 204 to a quantum buffer 208. The quantum buffer 208 is a quantum computing device configured to logically encode quantum information. For example, the quantum buffer 208 can be a superconducting computer including superconducting qubits, an ion trap quantum computer, or a quantum computer including photonic qubits in cluster states.

[0051] Because the quantum sensor 204 and the quantum buffer 208 can be different quantum devices including different quantum media, these devices can operate at different energy scales. For example, in some implementations, the quantum sensor 204 can provide data as a state in a bosonic cavity mode, while the quantum buffer 208 can include superconducting qubits. Thus, to transfer the data 206, the quantum data processing system 200 is configured to perform quantum transduction on the data 206 collected by the quantum sensor 204 to convert the data 206 into a transduced data 210 in a suitable form.

[0052] The particular transduction performed by the quantum data processing system 200 depends on the types of the quantum sensor 204 and the quantum buffer 208 included in the quantum data processing system 200 and can vary. For example, the quantum data processing system 200 can perform a microwave-to-optical transduction to transform data from optical photonic states of the quantum sensor 204 to superconducting quantum states of the quantum buffer 208. As another example, the quantum data processing system 200 can perform optical-to-ion transduction on an ion trap quantum buffer, cavity mode-to-superconducting qubit transduction on a superconducting quantum buffer, or cavity mode-to-photonic qubit transduction on a quantum buffer including photonic qubits in cluster states. In some implementations, the transduction can be performed with limited fidelity.

[0053] In some implementations, the quantum data processing system 200 logically encodes the transduced data 210 in the quantum buffer 208 into a quantum error correction code to generate logically encoded data 212. Logically encoding the transduced data 210 accommodates storage of multiple copies of the probed data and subsequent computation on the probed data. In some implementations, the quantum data processing system 200 can logically encode the transduced data 210 by applying unitary encoding circuits or state injection techniques. In these implementations, the logical encoding can have a fidelity limited by the computational operations performed to apply the unitary encoding circuits or state injection techniques.

[0054] The quantum memory 214 is configured to store the logically encoded data 212 obtained from the quantum buffer 208. In some embodiments, for example, in cases where computational resources are limited, the quantum error correction code can be the quantum buffer itself. Example logical encoding and quantum storage systems that can be implemented by the quantum data processing system 200 include normalizing into surface codes, state injection into surface codes, direct encoding or injection into quantum LDPC codes, injection into surface codes then injection into LDPC or higher rate codes, or direct transfer from a logical sensor into a logically encoded state. The quantum memory can be, for example, an optical quantum memory, such as a cavity-based quantum memory or a dielectric-based quantum memory (e.g., an atomic, ionic, or molecular based memory). It will be appreciated that many examples of quantum memories can alternatively be used.

[0055] In some embodiments, the code distance used by the quantum data processing system can be determined by, for example, the subsequent computation performed on the data by the quantum computer 216 as described below and / or the expected waiting time required to store a sufficient number of copies of the state in the quantum memory 214. For example, in addition to the required computation time, the code distance can be determined by the waiting time to receive a copy of the quantum state for a given protocol, for example, if 10 copies of the quantum state are required and the computation is expected to take a certain amount of time. The physical error rate in the device and the threshold in the encoding can be used to calculate the required code distance from these factors to securely ensure that the information will not decay within the computer on this timescale and under these operations. In some embodiments, the code distance d can scale as d ~ log(expected waiting time + computation time).

[0056] The quantum memory 214 is configured to store the logically encoded data 212 obtained from the quantum buffer 208. For example, as described below with reference to Figure 3 In more detail, the quantum data processing system 200 can repeatedly probe the target system 202 to collect a plurality of copies of the evolved quantum state of the quantum sensor 204 (in this specification, a copy of the evolved quantum state is understood to mean the quantum state obtained after the quantum sensor 204 is reset and / or initialized and interacted with the target system 202 for a predetermined sensing time to obtain the evolved quantum state of the quantum sensor). Each copy can be transduced and logically encoded before being stored in the quantum memory 214.

[0057] Once a predetermined number of copies of the evolved quantum state of the quantum sensor 204 are stored in the quantum memory 214, the stored data 220 can be loaded into the quantum computer 216 for processing. The predetermined number of copies depends on the operations to be performed on the data by the quantum computer 216 and can vary.

[0058] The quantum computer 216 is configured to process data received from the quantum memory 214, for example, by applying a quantum algorithm. In some embodiments, the quantum computer 216 can purify data received from the quantum memory 214. For example, the quantum computer can perform quantum data extraction on the data using a linear distillation technique (e.g., quantum state distillation, virtual state distillation, or quantum principal component analysis method (qPCA)). The data extraction step realizes an exponential advantage over classical methods in terms of the number of copies of the record needed to perform the extraction. Reference is made below to Figure 3 An example quantum computer 314 is described for processing data received from the quantum memory 214.

[0059] The quantum data processing system 200 can perform measurements on the extracted quantum data to obtain measurement data 222 and extract relevant information. The measurement data 222 can be provided to the classical or quantum computer 216 for further analysis, for example, to estimate a physical quantity or parameter of interest. In some embodiments, the extracted information can be provided as input to a quantum machine learning system included in the classical or quantum computer 218 to learn properties about the data. In Figure 2 In some embodiments, the quantum data processing system 200 can include one computing device that is configured to perform the operations described above with reference to the quantum computer 216 and the classical or quantum computer 218.

[0060] In some embodiments, the quantum data processing system 100 can be included in or applied to a communication or quantum internet setting. For example, the quantum data processing system 200 can operate on data received from a quantum internet, quantum network, or quantum repeaters along a quantum network. In these embodiments, a quantum communication protocol can also be included. In these settings, the quantum data processing system 200 can be used to recover from errors with additional effectiveness beyond the code distance of the original message.

[0061] Figure 3 An example classical / quantum computer 300 is depicted for performing some or all of the classical and quantum operations described in this specification, for example, the operations described above with reference to the quantum computer 216 and the classical or quantum computer 218. The example classical / quantum computer 300 includes an example quantum computing device 302. The quantum computing device 302 is intended to represent a variety of forms of quantum computing devices. The components shown here, their connections and relationships, and their functions, are meant to be examples only, and are not meant to limit implementations of the applications described and / or claimed in this document.

[0062] Example quantum computing device 302 includes a qubit assembly 352 and a control and measurement system 304. The qubit assembly includes multiple qubits, such as qubit 306, for performing algorithmic operations or quantum computation. Although Figure 3 The qubits shown are arranged in a rectangular array, but this is a schematic depiction and not intended to be limiting. The qubit assembly 352 also includes adjustable coupling elements, such as coupler 308, which allows interaction between the coupled qubits. Figure 3 In the schematic diagram, each qubit is tunably coupled to each of its four neighboring qubits by means of a corresponding coupling element. However, this is an example arrangement of qubits and couplers, and other arrangements are possible, including non-rectangular arrangements, arrangements that allow coupling between non-adjacent qubits, and arrangements that include tunable coupling between more than two qubits.

[0063] Each qubit can be a physical two-level quantum system or device, having energy levels representing logic values ​​0 and 1. The specific physical implementation of multiple qubits and how they interact with each other depends on various factors, including the type of quantum computing device 302 included in example computer 300 or the type of quantum computing being performed by the quantum computing device. For example, in an atomic quantum computer, qubits can be implemented via atoms, molecules, or solid-state quantum systems (e.g., hyperfine atomic states). As another example, in a superconducting quantum computer, qubits can be implemented via superconducting or semiconducting qubits (e.g., superconducting transmon states). As yet another example, in an NMR quantum computer, qubits can be implemented via nuclear spin states.

[0064] In some implementations, quantum computing can be performed, for example, by loading qubits from a quantum memory and applying a sequence of unitary operators to the qubits. Applying unitary operators to qubits can include applying a corresponding sequence of quantum logic gates to the qubits, for example, to implement quantum algorithms such as quantum principal component algorithms. Example quantum logic gates include single-qubit gates (e.g., Pauli-X, Pauli-Y, Pauli-Z (also known as X, Y, Z)), Hadamard gates, S-gates, rotations, two-qubit gates (e.g., controlled-X, controlled-Y, controlled-Z (also known as CX, CY, CZ)), controlled-NOT gates (also known as CNOT), controlled-swap gates (also known as CSWAP), and gates involving three or more qubits (e.g., Tofoli gates). The quantum logic gates can be implemented by applying control signals 310 generated by the control and measurement system 304 to the qubits and couplers.

[0065] For example, in some implementations, the qubits in the qubit assembly 352 can be frequency tunable. In these examples, each qubit can have an associated operating frequency that can be adjusted by applying a voltage pulse via one or more drive lines coupled to the qubit. Example operating frequencies include a qubit idle frequency, a qubit interaction frequency, and a qubit readout frequency. Different frequencies correspond to different operations that the qubit can perform. For example, setting the operating frequency to the corresponding idle frequency can place the qubit in a state in which it does not strongly interact with other qubits and it can be used to perform single-qubit gates. As another example, in the case that the qubits interact via couplers with fixed couplings, the qubits can be configured to interact with each other by setting their respective operating frequencies at some gate-dependent frequency that is detuned from their common interaction frequency. In other cases, e.g., when the qubits interact via tunable couplers, the qubits can be configured to interact with each other by setting the parameters of their respective couplers to enable interaction between the qubits, and then by setting the respective operating frequencies of the qubits at some gate-dependent frequency that is detuned from their common interaction frequency. Such interactions can be performed in order to perform multi-qubit gates.

[0066] The type of control signals 310 used depends on the physical implementation of the qubits. For example, the control signals can include RF or microwave pulses in NMR or superconducting quantum computer systems, or optical pulses in atomic quantum computer systems.

[0067] The quantum computation can be completed by measuring the state of the qubits using the respective control signals 310, e.g., using a quantum observable such as X or Z. The measurement causes a readout signal 312 representing the measurement result to be transmitted back to the control and measurement system 304. The readout signal 312 can include an RF, microwave, or optical signal, depending on the physical scheme of the quantum computing device and / or the qubits. For convenience, Figure 3 The control signals 310 and readout signals 312 shown in FIG. 3 are depicted as addressing only selected elements of the qubit assembly (i.e., the top and bottom rows), but during operation, the control signals 310 and readout signals 312 can address every element in the qubit assembly 352.

[0068] The control and measurement system 304 is an example of a classical computer system that can be used to perform various operations on the qubit assembly 352 as described above, as well as other classical subroutines or computations. The control and measurement system 304 includes one or more classical processors (e.g., classical processor 314), one or more memory units (e.g., memory 316), and one or more I / O units (e.g., I / O unit 318) connected through one or more data buses. The control and measurement system 304 can be programmed to send control signal sequences 310 to the qubit assembly, e.g., to perform a selected sequence of quantum gate operations, and to receive readout signals 312 from the qubit assembly, e.g., as part of performing a measurement operation.

[0069] The processor 314 is configured to process instructions for execution within the control and measurement system 304. In some embodiments, the processor 314 is a single-threaded processor. In other embodiments, the processor 314 is a multi-threaded processor. The processor 314 is capable of processing instructions stored in the memory 316.

[0070] The memory 316 stores information within the control and measurement system 304. In some embodiments, the memory 316 includes a computer-readable medium, a volatile memory unit and / or a non-volatile memory unit. In some cases, the memory 316 can include a storage device capable of providing mass storage for the control and measurement system 304, such as a hard disk device, an optical disk device, a storage device that is shared over a network (e.g., a cloud storage device) by multiple computing devices, and / or some other mass storage device.

[0071] The I / O unit 318 provides input / output operations for the control and measurement system 304. The I / O unit 318 can include a D / A converter, an A / D converter, and an RF / microwave / optical signal generator, transmitter, and receiver, by which the control signals 310 are sent to the qubit assembly and the readout signals 312 are received from the qubit assembly, as appropriate for the physical scheme of the quantum computer. In some embodiments, the I / O unit 318 can also include one or more network interface devices, such as an Ethernet card, a serial communication device (e.g., an RS-232 port), and / or a wireless interface device (e.g., an 802.11 card). In some embodiments, the I / O unit 318 can include a driver device configured to receive input data and send output data to other external devices, such as a keyboard, a printer, and a display device.

[0072] Although in the example of FIG. 3 the control and measurement system 304 is shown as a single system, in other embodiments the control and measurement system 304 can include multiple systems that are connected together through a network, such as the Internet, an intranet, an extranet, or a local area network (LAN). In some embodiments, the control and measurement system 304 can include multiple systems that are connected together through a network, such as the Internet, an intranet, an extranet, or a local area network (LAN). Figure 3An example control and measurement system 304 has been described in this specification, but implementations of the subject matter and functional operations described herein may be implemented in other types of digital electronic circuits, or in computer software, firmware, or hardware, including the structures disclosed herein and their structural equivalents, or combinations thereof.

[0073] Example system 300 also includes example classical processor 350. According to some embodiments, classical processor 350 can be used to perform classical computational operations described herein, such as the classical machine learning methods described herein.

[0074] Example process for processing quantum data

[0075] Figure 4 This is a flowchart of an example process 400 for processing quantum data. For convenience, process 400 will be described as being executed by a quantum data processing system. For example, a process appropriately programmed according to this specification... Figure 2 The quantum data processing system 200 can execute process 400.

[0076] The system stores multiple copies of the quantum state in a quantum memory (step 402). The quantum state can encode properties of the corresponding target system or process, as described in more detail below. In some implementations, quantum sensors (e.g., sensors that interact coherently with the physical world) can be used to generate copies of the quantum state, as referenced below. Figure 5 In other embodiments, copies of the quantum state can be generated by simulating a quantum simulator or a gate-based quantum computer. In other embodiments, copies of the quantum state can be generated by evolving the initial quantum state under a target process (e.g., an evolution operator).

[0077] The system loads multiple copies of the quantum state from the quantum memory into the quantum computer (step 404). In some embodiments, the system uses the quantum computer to process the multiple copies of the quantum state to obtain a purified quantum state (step 406). The purified quantum state is a quantum state representing multiple copies of the quantum state. To process the multiple copies of the quantum state and obtain a purified quantum state, the system may perform linear distillation techniques to purify the multiple copies of the quantum state, for example, performing quantum state distillation, virtual state distillation, or quantum principal component analysis algorithms.

[0078] The system uses a quantum computer to measure purified quantum states. The measured purified quantum states are used to determine the properties of the target system or target process using classical or quantum computing (step 408). For example, in some implementations, the system may provide the measurement results to a quantum machine learning system to learn the properties of the target system or target process.

[0079] Figure 5 is a flowchart of a first example process 500 for storing multiple copies of a quantum state in a quantum memory. The example process 500 can be used to perform step 402 of the example process 400 described above, e.g., when the example process 400 is used to learn properties of a physical state or system. For convenience, the process 500 will be described as being performed by a quantum data processing system. For example, a quantum data processing system 200, appropriately programmed in accordance with this specification, can perform the process 500. Figure 2 The quantum data processing system 200 of

[0080] To store one copy of the quantum state in the quantum memory, the system probes the target system using the quantum sensor (initialized in the initial quantum state) to obtain an evolved quantum state of the quantum sensor (step 502). The evolved quantum state of the quantum sensor encodes properties of the target system at the time of the probe, and can be a state of multiple qubits or a state of a boson or a photon mode, as described above with reference to step 302. In some embodiments, the system can probe the target system with a limited signal-to-noise ratio. Figure 2

[0081] The system then transfers the information encoded in the evolved quantum state of the quantum sensor to a quantum state of the quantum buffer. In some embodiments, the quantum sensor and the quantum buffer can comprise different computational media. For example, the quantum sensor can comprise a first computational medium, and the quantum buffer can comprise a second computational medium, where the second computational medium is different from the first computational medium. Thus, to transfer the information encoded in the evolved quantum state of the quantum sensor to the quantum state of the quantum buffer, the system transduces the evolved quantum state of the quantum sensor to the quantum state of the quantum buffer (step 504).

[0082] The system then logically encodes the quantum state of the quantum buffer into a quantum error correction code (step 506). For example, the system can apply a unitary encoding quantum circuit to the quantum state of the quantum buffer or perform a state injection technique. In some embodiments, the quantum error correction code distance can depend on at least one of: operations performed by the quantum computer to obtain the extracted quantum state, as described below with reference to step 306, or an expected duration of time required to store multiple copies of the quantum state in the quantum memory.

[0083] ​In some implementations, the system moves the logically encoded quantum state of the quantum buffer into the quantum memory (step 508). In cases where the quantum buffer encoding is different from the quantum memory encoding, the system can move the logically encoded quantum state of the quantum buffer into the quantum memory. For example, in cases where a large number of copies of the quantum state are needed and the qubits are sparse, the higher code rate in the quantum memory and the fast encoding in the buffer can be beneficial. In other implementations, the quantum buffer and the quantum memory can be the same device, and thus the logically encoded quantum state will not need to be moved into the quantum memory.

[0084] Steps 502-508 are repeated until a predetermined number of copies of the quantum state are stored in the quantum memory, or until a predetermined duration expires, e.g., in cases where the target system is a transient system and the time interval in which the target system can be probed is limited. Example transient systems include chemicals that decompose in a short time. For example, in some chemical systems, e.g., when imaging or inspecting a dye, photo bleaching (destruction of the dye through interaction with light) can occur on a short time scale of < 100 ms, and if the process of preparing the dye is unknown, there is a limited opportunity for measurement. Another example transient system includes rare sensing events, e.g., detection of cosmic rays, which do not occur frequently, e.g., once per second.

[0085] Figure 6 is a flowchart of a second example process 600 for storing multiple copies of a quantum state in a quantum memory. Example process 600 can be used to perform step 402 of example process 400 described above, e.g., when example process 400 is used to learn properties of a physical dynamics / process. For convenience, process 600 will be described as being performed by a quantum data processing system. For example, quantum data processing system 200 of FIG. 2, suitably programmed in accordance with this specification, can perform process 600. Figure 2 Quantum data processing system 200 of FIG. 2 can perform process 600.

[0086] To store one copy of the quantum state in the quantum memory, the system prepares an initial quantum state with n system qubits entangled with n memory qubits included in the quantum memory (step 602). The system evolves the system qubits under an evolution operator corresponding to the physical dynamics / process to be learned (step 604). The system swaps the system and memory qubits (e.g., by applying a quantum circuit including a plurality of swap gates, each swap gate configured to swap the states of two qubits on which the swap gate operates) (step 606). The system then evolves the system qubits again under the evolution operator (step 608).

[0087] The process 602-608 causes the evolution operator to coherently change the state of the n memory qubits such that the quantum state of the n memory qubits corresponds to the quantum state that would evolve under the evolution operator. Steps 602-608 are repeated until a predetermined number of copies of the quantum state are stored in the quantum memory.

[0088] As described in more detail below, the above reference to Figures 1-6 The described systems and processes can be applied to different learning tasks and quantum-enhanced experiments.

[0089] Example learning task and associated quantum-enhanced experiment: learning quantum states

[0090] One example learning task that can be performed using the presently described techniques is learning properties of a physical system described by an n-qubit state p. In this example, each experiment (e.g., as described above with reference to Figure 1 and Figure 2 The sensor interaction or other state preparation methods described) generates one copy. In the conventional setting, each copy of p is measured to obtain classical data. In the quantum-enhanced setting presently described, a quantum computer stores each copy of p in a quantum memory and acts collectively on the multiple copies of p. In both cases, all quantum data needs to be measured at the end of the learning phase of the process so that only classical data is retained. After learning is complete, the learner is asked to provide accurate predictions of the expected values of observables (i.e., physical quantities) drawn from the set {01, 02,...}, where the number of observables in the set is exponentially large in n. The observables in the set can be incompatible, e.g., each observable can not commute with many of the other observables in the set.

[0091] When applied to this example, the quantum advantage achieved by the presently described techniques can be summarized as follows. There is a distribution of n-qubit states and a set of observables such that in the conventional scenario, at least 2n order experiments are needed to predict the absolute value of one observable chosen from the set, while in the quantum-enhanced scenario presently described, a constant number of experiments is sufficient.

[0092] Quantum advantage can occur even if the state p is unentangled. For example, in some experiments, p a P, where P is an n-qubit Pauli operator and a e (-1, 1). This state can be realized as a probabilistic collection of product states, each of which is an eigenstate of P with eigenvalue a. Even if the state is known to have this form, but P, a are unknown, the exponential separation between regular and quantum-enhanced experiments still holds. Moreover, quantum advantage can be achieved by performing a simple entangling measurement on copies of p. The quantum advantage applies even when the correlations between the n qubits are classical, indicating that quantum-enhanced strategies are beneficial in a wide class of sensing applications.

[0093] Figure 7 is a plot 700 illustrating quantum advantage achieved using the presently described techniques to learn a physical state. Specifically, the plot shows results for a task corresponding to estimating the amplitude of the expected value of a Pauli observable with respect to a physical state. In this example, the physical state is an unentangled n-qubit state p = 2 -n (I + aP), where a = ±0.95, P is a Pauli operator, and both a, P are unknown. After all measurements are completed and learning is terminated, two different Pauli operators Q1 and Q2 are announced, one of which is P and the other of which is not equal to P. The machine is configured to determine which of |tr(Q1p)| and |tr(Q2p)| is larger.

[0094] Part (a) of the plot 700 shows that quantum-enhanced experiments are performed repeatedly N times, and the corresponding data is fed into a supervised machine learning model (e.g., a gated recurrent neural network (GRU)) to make predictions. In a regular scenario where copies of p are measured one after another, the best known strategy is to use randomized Clifford measurements, which require an exponential number of copies to achieve the task with a reasonable probability of success. In the presently described quantum-enhanced scenario, copies of p can be stored in a quantum memory two at a time, and Bell measurements between the two copies can be performed to extract a snapshot of the state.

[0095] A supervised ML model is trained to determine which of two n-qubit Pauli operators has a larger amplitude of expected value under the unknown state p. In this example, cross-entropy is used as the training loss. In some implementations, the neural network can be trained using noiseless simulation data for small system sizes (n < 8). Then, when experimental data for large system sizes (8 < n < 20) is provided, the neural network can be used to make predictions. The probability of correct prediction is used as the prediction accuracy. Random guessing produces a prediction accuracy of 0.5. The curve shown at part (b) of the process 600 shows the performance of the ML model as the neural network is trained.

[0096] The curve shown in part (c) of illustration 700 shows the quantum advantage in the number of experiments required to achieve >70% prediction accuracy as a function of system size n. Here, (Q) corresponds to the results of running a supervised ML model based on quantum-enhanced experimental runs, and (C) corresponds to the results of running the best known conventional strategy. The dashed line (C, LB) is the proven lower bound for any conventional strategy. It can be seen that the presently described quantum-enhanced experiments far outperform the best conventional results (C, LB) that are theoretically achievable, even when run on a noisy quantum processor.

[0097] Example learning task and associated quantum-enhanced experiment: quantum principal component analysis

[0098] Another example learning task for which a quantum advantage can be achieved when implementing the presently described techniques is quantum principal component analysis (PCA). In this task, each experiment produces a copy of p, and the goal is to predict the properties of the (first) principal component of p, i.e., the eigenvector |y> of p with the largest eigenvalue. For example, it can be desired to predict the expected values of several observables in the state |y>. This task can become valuable in future quantum sensing applications. If an imperfect quantum sensor transduces the quantum state it detects into a quantum memory, then this state can be corrupted by noise. However, it can be reasonably expected that the properties of the principal component are relatively robust with respect to noise, and thus that a large amount of information about the undamaged state is preserved.

[0099] When applied to this example, the quantum advantage achieved by the presently described techniques can be summarized as follows. In the conventional scenario, at least 2n n / 2 experiments are required to learn the fixed properties of the principal component of an unknown n-qubit quantum state, whereas a constant number of experiments is sufficient in the quantum-enhanced scenario.

[0100] Example learning task and associated quantum-enhanced experiment: learning quantum dynamics

[0101] Another example learning task that can be performed using the presently described techniques is learning the properties of a physical process rather than a physical state. In these embodiments, each experiment implements a physical process Physical Process is interfaced with a quantum machine in the quantum-enhanced setting and a classical machine in the conventional setting (as described above with reference to Figure 1 .

[0102] In these examples, the quantum machine can learn an approximate model of any polynomial-time quantum process from only a polynomial number of experiments. Given a distribution of input states, the approximate model can learn accurately predict the output state. In contrast, implementing the same task in a conventional setting would require an exponential number of experiments. That is, when applied to this example, the quantum advantage achieved by the presently described techniques can be summarized as follows. Consider a polynomial-time physical process and a probability distribution over n-qubit input states. In a conventional scenario, at least 2 n experiments are required to learn an approximate model that accurately predicts the output state with average accuracy, whereas a polynomial number of experiments suffices in the quantum-enhanced scenario.

[0103] Figure 8 SUMMARY Figure 1 Figure 2 Figure 7 Example learning task and associated quantum-enhanced experiment: quantum principal component analysis Example learning task and associated quantum-enhanced experiment: learning quantum dynamics Figure 1 Figure 8 SUMMARY Figure 1 Figure 2 Figure 7 Example learning task and associated quantum-enhanced experiment: quantum principal component analysis Example learning task and associated quantum-enhanced experiment: learning quantum dynamics Figure 1 Figure 8 SUMMARY Figure 1 Figure 2 Figure 7 Example learning task and associated quantum-enhanced experiment: quantum principal component analysis Example learning task and associated quantum-enhanced experiment: learning quantum dynamics Figure 1 Figure 8 SUMMARY Figure 1 Figure 2 Figure 7 is a plot 800 illustrating the quantum advantage achieved using the presently described techniques to learn a physical process. Specifically, this plot illustrates results corresponding to the task of learning to identify a symmetry class of unknown evolution operators using unsupervised ML (where the unknown evolution operators are drawn from the class of all unitary transformations or from the class of time-reversal symmetric unitary transformations (i.e., real orthogonal transformations)).

[0104] In a conventional scenario, the unknown evolution operator is repeatedly applied to an initial state and each qubit of the output state is measured in the Y-basis. Under T-symmetric evolution, the output state has purely real amplitudes; thus, the expectation value of any purely imaginary observable such as the Pauli operator is always zero. In contrast, after general unitary evolution, the expectation value is generally non-zero but can be exponentially small, thus difficult to distinguish from zero. In the quantum-enhanced scenario, n additional memory qubits are used. The initial state is prepared with the n system qubits entangled with the n memory qubits. The system qubits are evolved under the unknown evolution operator. The system qubits and memory qubits are swapped, and the system qubits are evolved again. Then n Bell measurements are performed, each acting on one system qubit and one memory qubit.

[0105] As shown in part (a) of plot 800, a quantum-enhanced experiment can be performed for each physical process a number of times (e.g., 500 times) with each access twice. The data is fed into an unsupervised ML model to learn a one-dimensional representation describing the different physical dynamics of the physical processes.... Alternatively, unsupervised ML can be applied to data obtained from the best known conventional experiment (each access once) for each physical process 1000 times.

[0106] Each evolution operator is a one- or two-dimensional n-qubit quantum circuit, as shown in part (d) of the illustration 800. After sampling many different evolution operators from the two symmetry classes (and obtaining data from each sampled evolution multiple times), an unsupervised ML model is used to find a one-dimensional representation of the evolution operators. The representation learned by the unsupervised ML model is shown in parts (b) and (c) of the illustration 800.

[0107] Part (b) of the illustration shows the representation learned by the unsupervised ML for the 1D dynamics. Each point corresponds to a different physical process The vertical lines at the bottom show the exact 1D representation of each of the time-reversal symmetry (diamonds), while the other half does not satisfy the time-reversal symmetry (circles). Part (c) of the illustration shows a similar representation learned by the unsupervised ML for the 2D dynamics. Parts (b) and (c) of the illustration 800 show that using quantum-enhanced data, the ML model found a complete separation between the two symmetry classes (in the case of quantum enhancement, the results from the general symmetry class appear on the left-hand side of the graph, while the results from the T symmetry class are separated and appear only on the right-hand side). When using data from regular experiments, there is no discernible classification separation (the results from the general and T symmetry classes are mixed together, with no visible separation). The signal from the quantum-enhanced experiments is strong enough that the two classes are easily identified without access to any labeled training data. Part (d) of the illustration shows two example classes for the connectivity geometry used to implement the 1D (top) and 2D (bottom) dynamics.

[0108] Implementations of the subject matter and operations described in this specification can be implemented in digital electronic circuitry, analog electronic circuitry, suitable quantum circuitry, or more generally quantum computing systems, in tangibly-embodied software or firmware, in computer hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. The term “quantum computing system” can include, but is not limited to, a quantum computer, a quantum information processing system, a quantum cryptography system, or a quantum simulator.

[0109] Implementations of the subject matter described in this specification can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions encoded on a tangible non-transitory storage medium for execution by, or to control the operation of, data processing apparatus. The computer storage medium can be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory, one or more quantum bits, or a combination of one or more of them. Alternatively or additionally, the program instructions can be encoded on an artificially generated propagated signal, e.g., a machine-generated electrical, optical, or electromagnetic signal that is generated to encode information for transmission to suitable receiver apparatus for execution by a data processing apparatus. The computer programs can be implemented in a high level procedural or object oriented programming language to be executed by a computer or quantum processor using an operating system. Alternatively, the programs can be implemented in assembly or machine language, if desired. The language can be a compiled or interpreted language, and combined on one computer or quantum processor, or distributed between two or more computers or quantum processors.

[0110] The terms quantum information and quantum data refer to information or data carried by, held or stored in a quantum system, where the smallest non-trivial system is a qubit, i.e., a system defining a unit of quantum information. It will be appreciated that the term “qubit” includes all quantum systems that can be appropriately approximated as a two-level system in the respective context. Such quantum systems can include multi-level systems, e.g., having two or more energy levels. As examples, such systems can include atoms, electrons, photons, ions, or superconducting qubits. In many implementations, the computational basis states are identified with a ground state and a first excited state, however it will be appreciated that other arrangements are possible in which the computational states are identified with higher energy level excited states.

[0111] The term “data processing apparatus” refers to digital and / or quantum data processing hardware and encompasses all kinds of apparatus, devices, and machines for processing digital and / or quantum data, including by way of example, a programmable digital processor, a programmable quantum processor, a digital computer, a quantum computer, multiple digital and quantum processors or computers, and combinations thereof. The apparatus can also be, or further include, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit) or a quantum simulator, i.e., a quantum data processing apparatus designed to simulate or produce information about a particular quantum system. In particular, a quantum simulator is a special purpose quantum computer that does not have the ability to perform general quantum computation. The apparatus can optionally include, in addition to the hardware, code that creates an execution environment for digital and / or quantum computer programs, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them.

[0112] A digital computer program, which can also be referred to or described as a program, software, software application, module, software module, script, or code, can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a digital computing environment. A quantum computer program, which can also be referred to or described as a program, software, software application, module, software module, script, or code, can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and translated into a suitable quantum programming language, or can be written in a quantum programming language, such as QCL or Quipper.

[0113] A computer program can, but need not, correspond to a file in a file system. A program can be stored in a portion of a file that is used to store other programs or data, for example, in a single file dedicated to the program in question, or in multiple coordinated files, for example, files that store one or more modules, sub programs, or portions of code. A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a digital and / or quantum data communication network. A quantum data communication network is understood to be a network that can transmit quantum data using quantum systems, such as qubits. Typically, a digital data communication network cannot transmit quantum data, however a quantum data communication network can transmit both quantum data and digital data.

[0114] The processes and logic flows described in this specification can be performed by one or more programmable computers operating with one or more processors, as appropriate, to execute one or more computer programs to perform functions by operating on input data and generating output. The processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, for example, an FPGA or an ASIC, or a quantum simulator, or by a combination of special purpose logic circuitry and one or more programmed digital and / or quantum computers.

[0115] For a system of one or more computers to be configured to perform particular operations or actions means that the system has installed on it software, firmware, hardware, or a combination of them that in operation causes the system to perform the operations or actions. For one or more computer programs to be configured to perform particular operations or actions means that the one or more programs include instructions that, when executed by data processing apparatus, cause the apparatus to perform the operations or actions. For example, a quantum computer can receive instructions from a digital computer that, when executed by the quantum computing apparatus, cause the apparatus to perform operations or actions.

[0116] The computer used to execute a computer program can be based on a general or special purpose processor or any other type of central processing unit. Generally, a central processing unit will receive instructions and data from a read-only memory, a random access memory, or a quantum system suitable for transmitting quantum data (e.g., photons), or a combination thereof.

[0117] The elements of a computer include a central processing unit for executing or running instructions and one or more memory devices for storing instructions and digital, analog, and / or quantum data. The central processing unit and memory can be supplemented or incorporated into by special purpose logic circuitry or quantum simulators. Generally, a computer will also include one or more mass storage devices (e.g., a magnetic disk, magneto-optical disk, optical disk, or quantum system suitable for storing quantum information) for storing data, or be operatively coupled to receive data from or transfer data to the mass storage device(s), or both. However, a computer need not have such devices.

[0118] Quantum circuit elements (also referred to as quantum computing circuit elements) include circuit elements for performing quantum processing operations. That is, quantum circuit elements are configured to perform operations on data in a non-deterministic manner utilizing quantum mechanical phenomena such as superposition and entanglement. Certain quantum circuit elements, such as qubits, can be configured to represent and operate on more than one state of information at the same time. Examples of superconducting quantum circuit elements include circuit elements such as quantum LC oscillators, qubits (e.g., flux qubits, phase qubits, or charge qubits), and superconducting quantum interference devices (SQUIDs) (e.g., RF-SQUIDs or DC-SQUIDs).

[0119] In contrast, classical circuit elements generally process data in a deterministic manner. Classical circuit elements can be configured to collectively execute instructions of a computer program by performing basic arithmetic, logical, and / or input / output operations on data, where the data is represented in analog or digital form. In some embodiments, classical circuit elements can be used to transmit data to and / or receive data from quantum circuit elements through electrical or electromagnetic connections. Examples of classical circuit elements include CMOS circuit-based circuit elements, rapid single flux quantum (RSFQ) devices, reciprocal quantum logic (RQL) devices, and ERSFQ devices, which are energy-reduced versions of RSFQ that do not use bias resistors.

[0120] In certain instances, some or all of the quantum and / or classical circuit elements can be implemented using, for example, superconducting quantum and / or classical circuit elements. Fabrication of superconducting circuit elements can require deposition of one or more materials, such as superconductors, dielectrics, and / or metals. Depending on the materials selected, these materials can be deposited using deposition processes such as chemical vapor deposition, physical vapor deposition (e.g., evaporation or sputtering), or epitaxy techniques, among other deposition processes. Processes for fabricating the circuit elements described herein can require removal of one or more materials from the device during fabrication. Depending on the material to be removed, the removal process can include, for example, wet etching techniques, dry etching techniques, or lift-off processes. Materials forming the circuit elements described herein can be patterned using known photolithography techniques (e.g., photolithography or e-beam lithography).

[0121] During operation of a quantum computing system using superconducting quantum circuit elements and / or superconducting classical circuit elements, such as the circuit elements described herein, the superconducting circuit elements are cooled within a cryostat to a temperature that allows the superconductor material to exhibit superconducting properties. A superconductor (alternatively, superconducting) material can be understood as a material that exhibits superconducting properties at or below a superconducting critical temperature. Examples of superconductor materials include aluminum (with a superconducting critical temperature of 1.2 Kelvin) and niobium (with a superconducting critical temperature of 9.3 Kelvin). Accordingly, superconducting structures, such as superconducting traces and superconducting ground planes, are formed from materials that exhibit superconducting properties at or below a superconducting critical temperature.

[0122] In certain embodiments, control signals for quantum circuit elements (e.g., qubits and qubit couplers) can be provided using classical circuit elements that are electrically and / or electromagnetically coupled to the quantum circuit elements. The control signals can be provided in digital and / or analog form.

[0123] Computer-readable media suitable for storing computer program instructions and data include all forms of non-volatile digital and / or quantum memory, media and memory devices, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto-optical disks; CD-ROM and DVD-ROM disks; and quantum systems, e.g., trapped atoms or electrons. It is understood that quantum memory is a device that can store quantum data for long periods of time with high fidelity and high efficiency, e.g., an optical-matter interface in which light is used for transmission and matter is used to store and preserve quantum features of the quantum data, such as superposition or quantum coherence.

[0124] Control of the various systems described in this specification, or portions of it, can be implemented in a computer program product that includes instructions stored on one or more non-transitory machine-readable storage media, and that can be executed on one or more processing devices. The systems described in this specification, or portions of it, can each be implemented as a device, method, or system that can include one or more processing devices and memory to store executable instructions to perform the operations described in this specification.

[0125] While this specification contains many specific implementation details, these should not be construed as limitations on the scope of what can be claimed, but as descriptions of features that can be specific to particular implementations. Certain features described in this specification in the context of separate implementations can also be implemented in combinations. Conversely, various features described in the context of a single implementation can also be implemented separately or in any suitable subcombination. Moreover, although features can be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination and the claimed combination can be directed to a subcombination or variation of a subcombination.

[0126] Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring such order, nor that all illustrated operations be performed, to implement desirable results. In certain circumstances, multitasking and parallel processing can be advantageous. Moreover, the separation of various system modules and components in the implementations described above should not be understood as requiring such separation in all implementations, and it should be understood that the described program components and systems can generally be integrated in a single software product or packaged into multiple software products.

[0127] Particular implementations of the subject matter have been described. Other implementations are within the scope of the following claims. For example, the acts recited in the claims can be performed in a different order and still achieve desirable results. As one example, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve the desired results. In some instances, multitasking and parallel processing can be advantageous.

Claims

1. A computer-implemented method comprising: storing a plurality of copies of a quantum state in a quantum memory, including, for each copy of the quantum state, i) probing a target system by an initialized quantum sensor to obtain an evolved quantum state of the quantum sensor, ii) transducing the evolved quantum state of the quantum sensor into a quantum state of a quantum buffer, iii) logically encoding the quantum state of the quantum buffer into a quantum error correction code, and iv) moving the logically encoded quantum state of the quantum buffer into the quantum memory; loading the plurality of copies of the quantum state in the quantum memory into a quantum computer; processing the plurality of copies of the quantum state by the quantum computer to obtain a purified quantum state; and measuring the purified quantum state to determine a property of the target system.

2. The method of claim 1, wherein, the quantum sensor is configured to maintain quantum coherence.

3. The method of claim 1 or 2, wherein, the evolved quantum state of the quantum sensor encodes a property of the target system at the time of probing.

4. The method of claim 1 or 2, wherein, the evolved quantum state of the quantum sensor includes states of a plurality of qubits or states of bosons or photon modes.

5. The method of claim 1 or 2, wherein, probing the target system to obtain the evolved quantum state of the quantum sensor is performed with a finite signal-to-noise ratio.

6. The method of claim 1 or 2, wherein, the quantum sensor is configured to implement full or partial quantum error correction on the evolved quantum state of the quantum sensor.

7. The method of claim 1 or 2, wherein, the quantum sensor includes a first computational medium and the quantum buffer includes a second computational medium, wherein the second computational medium is different from the first computational medium.

8. The method of claim 1 or 2, wherein logically encoding quantum states of the quantum buffer as a quantum error correcting code comprises: applying a unitary encoding quantum circuit to the quantum state of the quantum buffer or performing a state injection technique.

9. The method of claim 1 or 2, wherein, the quantum error correction code includes a code distance that depends on at least one of: operations performed by the quantum computer to obtain the purified quantum state or an expected duration required to store the plurality of copies of the quantum state.

10. The method of claim 1 or 2, wherein, the quantum error correction code is the quantum buffer.

11. The method of claim 1 or 2, wherein processing a plurality of copies of the quantum state to obtain a purified quantum state comprises: performing a linear distillation technique to purify the plurality of copies of the quantum state.

12. The method of claim 11, wherein, the linear distillation technique includes a quantum state distillation, a virtual state distillation, or a quantum principal component analysis algorithm.

13. The method of claim 1 or 2, wherein measuring the purified quantum state to determine a property of the target system comprises: providing measurement results to a quantum machine learning system to learn a property of the target system.

14. The method of claim 1 or 2, wherein the target system includes a transient target system.

15. A quantum data processing system comprising a quantum sensor, a quantum buffer, a quantum memory, and a quantum computer, wherein the quantum data processing system is configured to perform operations comprising: storing a plurality of copies of a quantum state in a quantum memory, including, for each copy of the quantum state, i) probing a target system by a quantum sensor to obtain an evolved quantum state of the quantum sensor, ii) transducing the evolved quantum state of the quantum sensor into a quantum state of a quantum buffer, iii) logically encoding the quantum state of the quantum buffer into a quantum error correction code, and iv) moving the logically encoded quantum state of the quantum buffer into the quantum memory; loading the plurality of copies of the quantum state in the quantum memory into the quantum computer; processing the plurality of copies of the quantum state by the quantum computer to obtain a purified quantum state; and measuring the purified quantum state to determine a property of the target system. processing, by the quantum computer, the multiple copies of the quantum state to obtain a purified quantum state; and measuring, by the quantum computer, the purified quantum state to determine a property of the target system.

16. The quantum data processing system of claim 15, wherein, The quantum sensor is configured to maintain quantum coherence.

17. The quantum data processing system of claim 15 or 16, wherein, The evolved quantum state of the quantum sensor encodes a property of the target system upon measurement.

18. The quantum data processing system of claim 15 or 16, wherein, The evolved quantum state of the quantum sensor comprises states of multiple qubits or states of bosons or photon modes.

19. The quantum data processing system of claim 15 or 16, wherein, The quantum sensor is configured to probe the target system so as to evolve the quantum state of the quantum sensor with a limited signal-to-noise ratio.

20. The quantum data processing system of claim 15 or 16, wherein, The quantum sensor is configured to implement full or partial quantum error correction on the evolved quantum state of the quantum sensor.

21. The quantum data processing system of claim 15 or 16, wherein, The quantum sensor comprises a first computational medium and the quantum buffer comprises a second computational medium, wherein the second computational medium is different from the first computational medium.

22. The quantum data processing system of claim 15 or 16, wherein, The quantum data processing system is configured to logically encode the quantum state of the quantum buffer into a quantum error correcting code by applying a unitary encoding quantum circuit to the quantum state of the quantum buffer or by performing a state injection technique.

23. The quantum data processing system of claim 15 or 16, wherein, The quantum error correcting code comprises a code distance that depends on at least one of: operations performed by the quantum computer to obtain the purified quantum state or an expected duration required to store the multiple copies of the quantum state.

24. The quantum data processing system of claim 15 or 16, wherein, The quantum error correcting code is the quantum buffer.

25. The quantum data processing system of claim 15 or 16, wherein, The quantum computer is configured to process the multiple copies of the quantum state to obtain a purified quantum state by performing a linear distillation technique to purify the multiple copies of the quantum state.

26. The quantum data processing system of claim 25, wherein, The linear distillation technique comprises a quantum state distillation, a virtual state distillation or a quantum principal component analysis algorithm.

27. The quantum data processing system of claim 15 or 16, wherein, The quantum computer is configured to provide measurement results obtained by measuring the purified quantum state to a quantum machine learning system to learn a property of the target system.

28. The quantum data processing system of claim 15 or 16, wherein, The target system comprises a transient target system.

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