Method executed by classical processor and quantum computing system and device thereof

Abstract

The invention discloses a method executed by a classical processor and a quantum computing system and an apparatus thereof. In one aspect, the method includes defining one or more random quantum circuits, where a noisy experimental implementation of each random quantum circuit is approximated by a depolarization channel with respective polarization parameters; for each defined random quantum circuit, generating, by the quantum computing system, a set of experimental data, where data items in the set of experimental data include a string of measurement bits corresponding to an experimental implementation of the random quantum circuit; determining, for each of the one or more random quantum circuits, an estimate of a respective polarization parameter, including using series inversion to maximize a log-likelihood of the polarization parameter conditioned by a set of respective experimental data; and determining an estimate of fidelity of the quantum computing system based on the determined estimates of the respective polarization parameters.

Description

[0001] This application is a divisional application of the patent application filed on October 25, 2019, with application number 201980097975.1 and entitled "Bayesian Quantum Circuit Fidelity Estimation". Technical Field

[0002] This manual relates to quantum computing. Background Technology

[0003] Quantum computing uses quantum mechanical phenomena, such as superposition and entanglement, to perform computations. A quantum circuit is an example model used in quantum computing, where computation is a series of quantum logic gates that are reversible transformations of a quantum mechanical simulation of an n-bit register. Summary of the Invention

[0004] This specification describes techniques for estimating the fidelity of quantum circuits.

[0005] Generally, an innovative aspect of the subject matter described in this specification can be implemented in a method for estimating the fidelity of a quantum computing system, the method comprising: defining one or more random quantum circuits, wherein a noisy experimental implementation of each random quantum circuit is approximated by a corresponding polarization parameter via a depolarization channel; for each defined random quantum circuit, generating a set of experimental data by the quantum computing system, wherein data items in the set of experimental data include a string of measurement bits corresponding to the experimental implementation of the random quantum circuit; for each of the one or more random quantum circuits, determining an estimate of the corresponding polarization parameter, including using series inversion to maximize the log-likelihood of the polarization parameter conditioned on the set of corresponding experimental data; and, based on the determined estimate of the corresponding polarization parameter, determining an estimate of the fidelity of the quantum computing system.

[0006] Other embodiments of this aspect include corresponding classical and quantum computer systems, apparatuses, and computer programs recorded on one or more computer storage devices, each computer program being configured to perform actions of the method. A system of one or more computers may be configured to perform specific operations or actions by means of software, firmware, hardware, or a combination thereof installed on the system, wherein the software, firmware, hardware, or combination thereof causes the system to perform actions during operation. One or more computer programs may be configured to perform specific operations or actions by means of instructions, wherein the instructions, when executed by a data processing device, cause the device to perform actions.

[0007] The foregoing and other embodiments may each optionally include one or more of the following features, individually or in combination. In some embodiments, determining the estimate of the corresponding polarization parameter includes: defining a new variable equal to... ,in, Denotes the dimension of Hilbert space, and Representing random quantum circuits The ideal realization of the probability of generating the eigenstate corresponding to the k-th data item in the set of corresponding experimental data; and, replacing the new variable in the first equation for the first derivative of the log-likelihood of the polarization parameter conditioned on the set of corresponding experimental data, to obtain the infinite series representation of the first equation.

[0008] In some implementations, using series inversion to maximize the log-likelihood of the polarization parameter conditioned on the set of corresponding experimental data includes: using series inversion to compute the solution of the infinite series representation of the first equation for the first derivative of the log-likelihood of the polarization parameter conditioned on the set of corresponding experimental data.

[0009] In some implementations, generating a set of experimental data for a defined random quantum circuit includes repeating the following steps a predetermined number of times: initializing the qubit register of the quantum computing system to an initial state; applying the defined random quantum circuit to the initial state to generate an evolved state; and measuring the evolved state to obtain a bit string.

[0010] In some implementations, the method further includes determining the variance of the estimate of the polarization parameter by calculating the second derivative of the log-likelihood of the polarization parameter conditioned on the set of corresponding experimental data.

[0011] In some implementations, the output of an experimental realization of one or more random quantum circuits is approximated by a Porter-Thomas distribution.

[0012] In some implementations, one or more random quantum circuits comprise random quantum circuits that operate on the same number of qubits and have the same circuit depth.

[0013] In some implementations, determining the fidelity estimate of the quantum computing system based on the determined estimates of the corresponding polarization parameters includes: calculating an average estimate of the polarization parameters; and using the average estimate of the polarization parameters to determine the fidelity estimate of the quantum computing system.

[0014] In some implementations, the fidelity F of the quantum computing system is estimated by... Given, among which, Denotes the dimension of Hilbert space, and This represents the number of qubits operated by one or more defined random quantum circuits.

[0015] In some implementations, the method also includes using an average estimate of the polarization parameters to calculate an estimate of the Pauli error rate of the quantum computing system.

[0016] In some implementations, the Pauli error rate of a quantum computing system The estimate is by Given, among which, Denotes the dimension of Hilbert space, and This represents the number of qubits operated by one or more defined random quantum circuits.

[0017] In some implementations, the method further includes using an estimate of the fidelity of the determined quantum computing system to determine one or more properties of the quantum computing system.

[0018] In some implementations, the method further includes: determining one or more adjustments to quantum hardware control parameters based on an estimate of the determined fidelity; and implementing the determined one or more adjustments using quantum computing hardware to perform quantum computing.

[0019] The subjects described in this specification can be implemented in a particular manner to achieve one or more of the advantages below.

[0020] Systems implementing the techniques described herein can estimate the fidelity of quantum circuits implemented by quantum computing hardware with greater accuracy. Specifically, since the estimation is a maximum likelihood estimation, the fidelity estimated using the techniques described herein has smaller variance compared to estimates generated using other techniques, such as cross entropy benchmarking.

[0021] Furthermore, regarding observational data, the estimates generated using the currently described technique are based on direct and easy-to-use analytical expressions for the mean and variance of the circuit fidelity. These analytical expressions enable the obtaining of maximum likelihood estimates of fidelity with computationally efficient variance, and are comparable in complexity to other techniques, such as cross-entropy benchmarking based on the average of quantum observables. Moreover, unlike other techniques such as cross-entropy benchmarking, the currently described technique is scalable to medium-sized quantum circuits, e.g., to 40 qubits and beyond, and is not limited to a specific set of quantum gates, e.g., not limited to Clifford gates.

[0022] The techniques described herein can be applied to improve the precision of quantum computing hardware and quantum control, key features of high-fidelity quantum computing (e.g., because high-fidelity quantum gates require high-precision control). For example, quantum circuit fidelity can be used to calibrate or verify quantum computing hardware, or to determine adjustments that can improve the accuracy or efficiency of existing quantum computing hardware. Because the circuit fidelity estimated using the techniques described in this specification is accurate, adjustments, calibrations, or verifications determined using the estimated circuit fidelity may be more efficient.

[0023] Details of one or more embodiments of the subject matter of this specification are set forth in the following drawings and description. Other features, aspects, and advantages of this subject matter will become apparent from the specification, drawings, and claims. Attached Figure Description

[0024] Figure 1 An example system for benchmarking quantum computing hardware is described.

[0025] Figure 2 This is a flowchart of an example process for estimating the fidelity of quantum computing hardware. Detailed Implementation

[0026] Overview

[0027] Quantum circuits are models for quantum computing, in which quantum logic gates are applied in a specific sequence to register qubits to encode quantum information. Theoretically, any quantum algorithm can be implemented with high precision by applying the correct sequence of quantum logic gates. However, in practice, quantum logic gates are prone to error, resulting in noisy quantum operations rather than unified quantum operations representing ideal quantum logic gates.

[0028] Benchmarking quantum circuits is a necessary step in building a reliable quantum computer. Benchmarking is also used in the process of quantum computer operation for periodic calibration. The task is to characterize how far the quantum states generated by the quantum machine deviate from the states expected by an ideal quantum operation, thus characterizing the number of errors. Benchmarking is typically performed using randomized quantum circuits and outputs a single number called the fidelity of the quantum operation.

[0029] Quantum logic gate fidelity is a feature of noisy quantum operations. With the ideal unified quantum operation A measure of how close they are. For a given quantum state. , and The quantum logic gate fidelity between them can be given by the following equation:

[0030] .

[0031] Estimating the fidelity of quantum logic gates is an important process for adjusting or correcting quantum hardware that physically implements quantum logic gates, and thus also an important process for successfully performing quantum computing.

[0032] This specification describes a Bayesian method for estimating the fidelity of quantum operations, such as quantum circuit fidelity. The methods and systems described herein use a likelihood probability function incorporating a quantum depolarization channel model to obtain a maximum likelihood estimate of the quantum circuit fidelity. The same likelihood function can also be used to determine a probability distribution based on Bayesian rules for the quantum circuit fidelity.

[0033] Example hardware

[0034] Figure 1 An example system 100 for benchmarking quantum computing hardware is depicted. Example system 100 is an example of a system implemented as classical and quantum computer programs on one or more classical and quantum computers at one or more locations, wherein the systems, components, and techniques described below can be implemented.

[0035] System 100 includes a classical processor 102 that communicates data with quantum computing hardware 104. For convenience, the classical processor 102 and the quantum computing hardware 104 are shown as separate entities. However, in some embodiments, the classical processor 102 may be included within the quantum computing hardware 104; for example, the quantum computing hardware 104 may include one or more components for performing classical computation operations.

[0036] Quantum computing hardware 104 includes components for performing quantum computing using quantum circuits. For example, quantum computing hardware 104 includes a quantum system 120 and a control device 122. Quantum system 120 includes one or more multi-level quantum subsystems, such as qubits, for performing algorithmic operations or quantum computing. The specific implementation of the multi-level quantum subsystems included in quantum computing hardware 104 and how these multi-level quantum subsystems interact with each other depends on various factors, including the type of quantum computing performed by the quantum computing hardware. For example, multi-level quantum subsystems may include qubits implemented via atomic, molecular, or solid-state quantum systems. In other examples, qubits may include, but are not limited to, superconducting qubits or semiconductor qubits.

[0037] Multilevel quantum systems can be frequency-tunable. For example, each qubit can have an associated operating frequency that can be adjusted, for example, using one or more control devices 122, such as by applying voltage pulses via one or more drive lines coupled to the qubit. Example operating frequencies include qubit idle frequencies, qubit interaction frequencies, and qubit readout frequencies. Different frequencies correspond to different operations that the qubit can perform. For example, setting the operating frequency to the corresponding idle frequency can put the qubit into a state in which it does not interact strongly with other qubits and can be used to perform single-qubit gates. As another example, where the qubits interact via couplers with fixed coupling, the qubits can be configured to interact with each other by setting the respective operating frequencies of these qubits to a gate-dependent frequency that is detuned from the common interaction frequency of these qubits. In other cases, such as when qubits interact via tunable couplers, the qubits can be configured to interact with each other by setting the parameters of the respective couplers of these qubits to allow interaction between the qubits, and then setting the respective operating frequencies of the qubits to a gate-dependent frequency that is detuned from the common interaction frequency of these qubits. This interaction can be performed to execute gates for two or more qubits.

[0038] The control device 122 may also include a measurement device, such as a readout resonator. The measurement results obtained via the measurement device may be provided to a classical processor included in the quantum computing hardware 104, or may be provided to a classical processor 102 for processing and analysis.

[0039] Classical processor 102 receives input data 106 representing quantum computing hardware to be benchmarked. Classical processor 102 processes the received input data 106 to generate output data 108 representing the benchmarking result. For example, output data 108 may include data representing the estimated fidelity of the quantum computing hardware.

[0040] The classical processor 102 includes multiple components for processing the received input data. For example, the classical processor 102 may include a quantum circuit generator 110, a fidelity estimation module 112, and a post-processing module 114.

[0041] The quantum circuit generator 110 can be configured to define multiple random quantum circuits. The multiple random quantum circuits defined by the quantum circuit generator 110 are quantum circuits that can be implemented by the quantum computing hardware 104 (i.e., the benchmark quantum computing hardware).

[0042] A random quantum circuit is a quantum circuit that includes one or more quantum gates randomly sampled from a predetermined set of quantum gates. For example, quantum circuit generator 110 can define multiple random quantum circuits, each including one or more corresponding randomly sampled single-qubit gates and the same or multiple multi-qubit quantum gates acting on different qubits. For example, random quantum circuit generator 110 can be configured to randomly sample single-qubit gates from a predefined set of single-qubit gates. A non-limiting set of examples may include... , and Quantum gates, among which, Indicates circling Axis Rotate, Indicates circling Axis Rotate, and Represents a non-Clifford diagonal matrix Other non-limiting examples include Clifford+T gates or Haar random sets. In some implementations, single-qubit gates included in a random quantum circuit defined by the random quantum circuit generator 110 may have approximately equal error rates; for example, the error rate of each single-qubit gate in the set of single-qubit gates sampled by the random quantum circuit generator 110 may be from a predetermined range of error rates.

[0043] The random quantum circuits defined by the quantum circuit generator 110 can have different depths. The quantum circuit generator 110 can define circuits of different depths by applying multiple clock cycles of the gates. That is, the quantum circuit generator 110 can define a random quantum circuit of depth d as equivalent to d cycles of the same sequence of gates. In some embodiments, the quantum circuit generator 110 can define a sequence of gates (e.g., including multiple randomly sampled single-qubit gates, followed by multi-qubit gates), and use the defined sequence of gates to define multiple random quantum circuits, wherein each defined random quantum circuit corresponds to a corresponding number of cycles of the defined sequence of gates.

[0044] Quantum circuit 130 is an example of a random quantum circuit generated by quantum circuit generator 110. Example quantum circuit 130 is shown configured for two qubits. , A quantum circuit for operation. Example quantum circuit 130 includes four cycles, wherein each cycle includes two randomly sampled single-qubit gates; for example, cycle 1 includes gates for each qubit. , Single-qubit gate for random sampling of operations , Period 2 includes separate pairs of qubits. , Single-qubit gate for random sampling of operations , And so on. Each cycle also includes a corresponding instance G of a two-qubit gate.

[0045] The quantum circuit generator 110 can define multiple sets of circuits, each operating on the same number of qubits and comprising circuits of the same depth. Because the circuits in the same set have the same number of gates of each type (randomly sampled single-qubit gates and multi-qubit gates), the fidelity of each circuit in the set is similar, as referenced below. Figure 2 A more detailed description follows. Each defined quantum circuit possesses properties that are approximated by noisy experimental implementations of the quantum circuit through the corresponding depolarization channel, as referenced below. Figure 2 Step 202 is described in more detail.

[0046] The classical processor 102 can be configured to transmit data 116 representing a defined quantum circuit to the quantum computing hardware 104. The quantum computing hardware 104 is configured to apply the defined quantum circuit to the quantum system 120 using the control device 122 as described above, and to provide output data representing the result of the circuit implementation, such as data 124 representing a measured bit string.

[0047] The fidelity estimation module 112 can be configured to estimate the fidelity of a quantum circuit generated by the quantum circuit generator 110 and implemented by the quantum computing hardware 104. For example, the fidelity estimation module 112 can be configured to perform the following reference... Figure 2 The described operations. In some implementations, the fidelity estimation module 112 may also be configured to perform additional operations to obtain additional information about the quantum computing hardware, such as fidelity variance, as referenced below. Figure 2 A more detailed description.

[0048] Post-processing module 114 can be configured to process or analyze the estimated fidelity to determine characteristics of quantum computing hardware 104 (e.g., performance of quantum computing hardware 104) or to calibrate or verify quantum computing hardware 104. In some embodiments, post-processing module 114 may also generate output data 126 representing one or more adjustments that can be used to tune and improve quantum computing hardware 104. For example, post-processing module 114 can use the estimated fidelity to determine how to control the quantum computing hardware when implementing a particular quantum circuit or a particular type of quantum circuit, for example, to determine modifications to the programming of control device 122 to achieve quantum gates with higher fidelity. An outer loop can then be executed to find optimal experimental control to improve the performance of quantum computing hardware 104.

[0049] The classical processor 102 provides output data 108 representing the determined purity of the quantum state. The classical processor 102 can also provide output data 126 representing the determined adjustments to the quantum computing hardware 104. The data 126 representing the determined adjustments can be provided to the quantum computing hardware 104 and can be implemented by the quantum computing hardware 104 when performing future calculations to improve the operation and / or performance of the quantum computing hardware 104.

[0050] Programming the hardware

[0051] Figure 2 This is a flowchart of an example process 200 for estimating the fidelity of a quantum computing system. For convenience, process 200 will be described as being performed by a system located in one or more classical and / or quantum computing systems at one or more locations. For example, a system appropriately programmed according to this specification... Figure 1 System 100 can execute process 200.

[0052] The system defines one or more random quantum circuits for estimating the fidelity of a quantum computing system (step 202). The defined random quantum circuit is a quantum circuit that can be implemented by a benchmarked quantum computing system. The one or more random quantum circuits defined by the system comprise circuits that operate on the same number of qubits and have the same circuit depth. Each defined random quantum circuit U has the properties that a noisy experimental implementation of a quantum circuit can be approximated by a corresponding depolarization channel, as given in equation (1) below.

[0053]

[0054] In equation (1), Represents the dimension of Hilbert space. The parameter representing polarization (which is related to quantum circuits) (Related to fidelity, as described in more detail below), and This indicates that quantum circuits have already been applied. The state of the qubit afterwards.

[0055] The system generates a collection of experimental data. (Step 204). The generated set of experimental data includes data items. This represents a measurement bit string corresponding to a corresponding experimental implementation of one or more random quantum circuits. To generate a set of experimental data, the system repeats the following steps a predetermined number of times: initializing the qubit register to an initial state; applying the correspondingly defined quantum circuit to the initial state to generate an evolved state; and measuring the evolved state to obtain the corresponding bit string.

[0056] The system determines an estimate of the fidelity of the quantum computing system based on maximizing the log-likelihood of the polarization of each of one or more random quantum circuits conditioned on the set of generated experimental data (step 206). The system defines the likelihood of the polarization of one of the one or more random quantum circuits conditioned on the corresponding experimental data as given in equation (2) below.

[0057]

[0058] In equation (2), Representing random quantum circuits Noisy implementations generate bit strings from the generated set of experimental data. The probability, This represents the initial state of the quantum system, and Represents bit strings The eigenstates corresponding to (eigenvalues). According to equation (1), the probability... It can also be given by the following equation (3).

[0059]

[0060] In equation (3), .

[0061] The log-likelihood of the polarization of a random quantum circuit, based on the corresponding experimental data, is given by the following equation (4).

[0062]

[0063] The polarization corresponding to the maximum value of the log-likelihood given by equation (4) above Estimate It is given by the following equation (5).

[0064]

[0065] Therefore, in order to determine polarization Estimate The system solves according to the following equation (6). .

[0066]

[0067] The system solves by performing variable substitution and using series inversion to maximize the log-likelihood of the polarization of a stochastic quantum circuit conditioned on the corresponding experimental data. More specifically, the system defines new variables as shown in equation (7) below. .

[0068]

[0069] In equation (7), Denotes the dimension of Hilbert space, and Representing random quantum circuits The ideal realization of the probability of generating the eigenstate corresponding to the k-th data item in the generated set of experimental data.

[0070] The system will be given by the new variables in equation (7). Replace it in equation (6) to give equation (8) below.

[0071]

[0072] in

[0073]

[0074] The system uses series inversion to solve equations (8) and (9) to obtain the polarization. Estimate As given in equation (10) below.

[0075]

[0076] For example, since higher-order terms can be ignored, the system can determine the polarization by calculating the first two terms in equation (10). Estimate .

[0077] The system can determine the polarization corresponding to each of one or more defined random quantum circuits. Estimate That is, the calculations described above with reference to equations (2) to (10) are performed on each of the defined random quantum circuits. Then, the system can determine the polarization based on an estimate of the polarization for each of the defined random circuits. The average of polarization. The average estimate of polarization can be used to determine the fidelity of a quantum computing system.

[0078] As an alternative to performing the calculations described in reference equations (2) through (10) above on each of the defined random quantum circuits, the system can perform a single calculation, where U represents a different defined random quantum circuit, not just one of the defined random quantum circuits. This can produce accurate polarization. Estimate This is because the following condition applies: one or more random quantum circuits defined by the system consist of circuits that operate on the same number of qubits and have the same circuit depth.

[0079] The system calculates Determining the fidelity of quantum computing systems The estimate, of which, Denotes the dimension of Hilbert space, and This represents the number of qubits that the defined random quantum circuit operates on. The system can also be calculated... To determine the Pauli error rate of a quantum computing system.

[0080] In some implementations, the system can also determine the corresponding variance of the polarization estimate by calculating the second derivative of the log-likelihood of the polarization corresponding to the corresponding quantum circuit conditioned on the corresponding experimental data (e.g., by evaluating the following equation (11) for each random quantum circuit).

[0081]

[0082] Then, the system can determine the average variance of the polarization. In an implementation where the output of one or more experimentally realized random quantum circuits can be approximated by a Bode-Thomas distribution, and if... Then the system uses the following equation (12) to approximate equation (12).

[0083]

[0084] In some implementations, the system may also use the fidelity estimate and / or the variance of the fidelity estimate and the Pauli error rate to determine one or more characteristics of the quantum computing system. For example, the estimated fidelity or Pauli error rate can be used to determine the performance of the quantum computing system. As another example, the estimated fidelity can be used to (i) calibrate, (ii) verify, or (iii) benchmark the quantum computing hardware that implements quantum circuits.

[0085] In some implementations, the system can use an estimate of fidelity and / or the variance of that estimate to determine one or more adjustments to the quantum computing hardware. For example, the system can determine adjustments to the control parameters of a control model used by the quantum computing hardware to implement quantum operations to improve the fidelity of the quantum operations. The system can use the adjusted control model to implement quantum operations with improved fidelity in future quantum computing. The control model can be a model that correlates parameters of a quantum gate (e.g., phase, qubit rotation angle, etc.) with physical parameters (e.g., voltage, pulse shape, frequency, etc.) of the (single) system / (multiple) systems used to implement / control the quantum gate.

[0086] For example, the parameters of a control model can be updated based on optimizing a fidelity-dependent cost function (also called an objective function or loss function) with respect to the parameters of the control model. The cost function may include one or more terms that depend on fidelity. In some embodiments, the cost function is the fidelity itself. Optimization processes (such as gradient descent) can be used to significantly optimize the cost function. The optimization process can be iterative.

[0087] The digital and / or quantum themes, as well as the implementations of digital functional operations and quantum operations described in this specification, can be implemented in digital electronic circuits, suitable quantum circuits, or more generally, in quantum computing systems, in tangibly embodied digital and / or quantum computer software or firmware, in digital and / or quantum 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.

[0088] The embodiments of the digital and / or quantum themes described in this specification can be implemented as one or more digital and / or quantum computer programs, i.e., one or more modules of digital and / or quantum computer program instructions encoded on a tangible, non-transitory storage medium for execution by a data processing device or for controlling the operation of a data processing device. The digital and / or quantum computer storage medium can be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, one or more qubits, or a combination thereof. Alternatively or additionally, the program instructions can be encoded on an artificially generated propagation signal capable of encoding digital and / or quantum information, for example, a machine-generated electrical, optical, or electromagnetic signal that generates the digital and / or quantum information for transmission to a suitable receiver device for execution by a data processing device.

[0089] The terms quantum information and quantum data refer to information or data carried, held, or stored in quantum systems, where the smallest non-trivial system is a qubit, i.e., a system that defines the unit of quantum information. It should be understood that the term "qubit" encompasses all quantum systems that can be appropriately approximated as two-level systems in the corresponding context. Such quantum systems can include, for example, multi-level systems with two or more levels. For example, such systems can include atomic, electron, photon, ion, or superconducting qubits. In many implementations, the computational basis state is identified as the ground state and the first excited state; however, it should be understood that other arrangements identifying the computational state as higher-level excited states are also possible.

[0090] The term "data processing device" refers to digital and / or quantum data processing hardware and encompasses all types of devices, apparatuses, and machines for processing digital and / or quantum data, including programmable digital processors, programmable quantum processors, digital computers, quantum computers, multiple digital and quantum processors or computers, and combinations thereof. The device may also be or include special-purpose logic circuitry, such as FPGAs (Field-Programmable Gate Arrays), ASICs (Application-Specific Integrated Circuits), or quantum simulators—that is, quantum data processing devices designed to simulate or generate information about a particular quantum system. Specifically, a quantum simulator is a special-purpose quantum computer that does not have the capability to perform general-purpose quantum computing. In addition to hardware, the device may optionally include code that creates an execution environment for digital and / or quantum computer programs, such as code constituting processor firmware, protocol stacks, database management systems, operating systems, or combinations thereof.

[0091] Digital computer programs, also referred to or described as programs, software, software applications, modules, software modules, scripts, or code, can be written in any form of programming language (including compiled or interpreted languages, or declarative or procedural languages), and can be deployed in any form (including as standalone programs or as modules, components, subroutines, or other units suitable for use in a digital computing environment). Quantum computer programs, also referred to or described as programs, software, software applications, modules, software modules, scripts, 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 (e.g., QCL or Quipper).

[0092] Digital and / or quantum computer programs may, but do not need to, correspond to files in a file system. Programs may be stored in portions of files that hold other programs or data (e.g., one or more scripts stored in a markup language document), in a single file dedicated to the program in question, or in multiple co-located files (e.g., files storing one or more modules, subroutines, or code portions). Digital and / or quantum computer programs may be deployed to execute on a single digital computer or a single quantum computer, or on multiple digital and / or quantum computers located at one site or distributed across multiple sites and interconnected through digital and / or quantum data communication networks. A quantum data communication network should be understood as a network that can use quantum systems (e.g., qubits) to transmit quantum data. Typically, digital data communication networks cannot transmit quantum data, but quantum data communication networks can transmit both quantum data and digital data.

[0093] The processes and logic flows described in this specification can be executed by one or more programmable digital and / or quantum computers operating with one or more digital and / or quantum processors, wherein the digital and / or quantum processors appropriately execute one or more digital and / or quantum computer programs to perform functions by manipulating input digital and quantum data and generating outputs. The processes and logic flows can also be executed by items such as: dedicated logic circuitry (e.g., FPGA or ASIC, or a quantum simulator), or a combination of dedicated logic circuitry or a quantum simulator and one or more programmable digital and / or quantum computers.

[0094] For a system of one or more digital and / or quantum computers, being "configured" to perform a specific operation or action means that the system has software, firmware, hardware, or a combination thereof installed thereon that causes the system to perform the operation or action in operation. For one or more digital and / or quantum computer programs, being configured to perform a specific operation or action means that one or more programs include instructions that, when executed by a digital and / or quantum data processing device, cause the device to perform an operation or action. A quantum computer can receive instructions from a digital computer that, when executed by a quantum computing device, cause the device to perform an operation or action.

[0095] Digital and / or quantum computers suitable for executing digital and / or quantum computer programs can be based on general-purpose or dedicated, or general-purpose and dedicated digital and / or quantum processors, or can be based on any other type of central digital and / or quantum processing unit. Typically, the central digital and / or quantum processing unit will receive instructions and digital and / or quantum data from read-only memory, random access memory, or a quantum system suitable for transmitting quantum data (e.g., photons), or a combination thereof.

[0096] The fundamental elements of a digital and / or quantum computer are a central processing unit (CPU) for executing or running instructions and one or more memory devices for storing instructions and digital and / or quantum data. The CPU and memory may be supplemented or incorporated into dedicated logic circuitry or a quantum simulator. Typically, a digital and / or quantum computer will also include, and / or be operatively coupled to, receive digital and / or quantum data from or transfer digital and / or quantum data to: one or more high-capacity storage devices for storing digital and / or quantum data, such as magnetic disks, magneto-optical disks, optical disks, or quantum systems suitable for storing quantum information. However, a digital and / or quantum computer does not require such a device.

[0097] Digital and / or quantum computer-readable media suitable for storing digital and / or quantum computer program instructions and digital and / or quantum data include all forms of non-volatile digital and / or quantum memories, media, and memory devices, including, for example: semiconductor memory devices, such as EPROM, EEPROM, and flash memory devices; disks, such as internal hard disks or removable disks; magneto-optical disks; CD-ROMs and DVD-ROMs; and quantum systems, such as trapped atoms or electrons. It should be understood that quantum memory is a device capable of storing quantum data for long periods with high fidelity and efficiency, such as an optical-matter interface, where light is used for transmission and matter is used for storing and maintaining the quantum characteristics of the quantum data, such as superposition or quantum coherence.

[0098] Control of the various systems or portions thereof described in this specification can be implemented in a digital and / or quantum computer program product including instructions stored on one or more non-transitory machine-readable storage media and executable on one or more digital and / or quantum processing devices. The systems or portions thereof described in this specification can each be implemented as an apparatus, method, or system, wherein the apparatus, method, or system may include one or more digital and / or quantum processing devices and a memory for storing executable instructions that perform the operations described in this specification.

[0099] While this specification contains numerous specific details of implementation, these details should not be construed as limiting the scope of what may be claimed, but rather as descriptions of features that may be specific to particular implementations. Specific features described in the context of individual implementations may also be implemented in combination in a single implementation. Conversely, various features described in the context of a single implementation may also be implemented separately in multiple implementations, or may be implemented in any suitable sub-combination. Furthermore, although features may be described above as functioning in a particular combination and even initially claimed as such, in some cases, one or more features from a claimed combination may be removed from that combination, and the claimed combination may involve sub-combinations or variations thereof.

[0100] Similarly, although the operations are depicted in a specific order in the accompanying drawings, this should not be construed as requiring these operations to be performed in the specific order or sequence shown, or as requiring all the shown operations to achieve the desired result. In certain situations, multitasking and parallel processing may be advantageous. Furthermore, the separation of various system modules and components in the embodiments described above should not be construed as requiring such separation in all embodiments, and it should be understood that the described program components and systems can generally be integrated into a single software product or packaged into multiple software products.

[0101] Specific embodiments of this subject matter have been described. Other embodiments fall within the scope of the appended claims. For example, the actions described in the claims can be performed in a different order and still achieve the desired result. As an example, the processes depicted in the drawings do not necessarily require the specific order or sequence shown to achieve the desired result. In some cases, multitasking and parallel processing may be advantageous.

Claims

1. A method executed by one or more classical processors and a quantum computing system, the method comprising: For each of one or more random quantum circuits, the quantum computing system generates an experimental dataset, wherein a noisy experimental implementation of each random quantum circuit is approximated by a depolarization channel having corresponding polarization parameters and data items, wherein the data items in the experimental dataset include a string of measurement bits corresponding to the experimental implementation of the one or more random quantum circuits. For each of the one or more random quantum circuits, an estimate of the corresponding polarization parameter is determined by the one or more classical processors, wherein determining the estimate includes applying a maximization process to the log-likelihood of the polarization parameter conditioned on the corresponding experimental dataset, the maximization process including the use of series inversion; The fidelity of the quantum computing system is estimated by the one or more classical processors based on the determined estimates of the corresponding polarization parameters; and The quantum computing system is calibrated using an estimate of its fidelity.

2. The method according to claim 1, wherein, Determining the estimate of the corresponding polarization parameter includes: Define the new variable as equal to ,in, Represents the dimension of Hilbert space. Representing random quantum circuits The ideal realization of the probability of generating the eigenstate corresponding to the k-th data item in the corresponding experimental dataset. It is the bit string of the k-th data item; Substitute the new variable into the first equation of the first derivative of the log-likelihood of the polarization parameter conditioned on the corresponding experimental dataset to obtain the infinite series representation of the first equation.

3. The method according to claim 2, wherein, Maximizing the log-likelihood of the polarization parameters conditioned on the corresponding experimental dataset using series inversion includes: Series inversion is used to compute the solution of the infinite series representation of the first equation of the first derivative of the log-likelihood of the polarization parameters conditioned on the corresponding experimental dataset.

4. The method according to claim 1, wherein, The experimental dataset for the defined random quantum circuit is generated and repeated a predetermined number of times.

5. The method of claim 1, further comprising determining the variance of the estimate of the corresponding polarization parameter by calculating the second derivative of the log-likelihood of the polarization parameter conditioned on the corresponding experimental dataset: in, It is the log-likelihood of the polarization parameters conditioned on the corresponding experimental dataset. It is the variance of the estimate of the corresponding polarization parameter.

6. The method according to claim 1, wherein, The output of the experimental implementation of the one or more random quantum circuits is approximated by the Porter-Thomas distribution.

7. The method according to claim 1, wherein, The one or more quantum circuits include random quantum circuits that operate on the same number of qubits and have the same circuit depth.

8. The method according to claim 1, wherein, Determining the fidelity of the quantum computing system based on the determined estimates of the corresponding polarization parameters includes: Calculate the average estimate of the polarization parameters; and The average estimate of the polarization parameters is used to determine the fidelity estimate of the quantum computing system.

9. The method according to claim 8, wherein, The fidelity of the quantum computing system The estimate is by Given, among which, Represents the dimension of Hilbert space. Indicates polarization, This represents the number of qubits that are operated on by one or more defined random quantum circuits.

10. The method of claim 8, further comprising using an average estimate of the polarization parameter to calculate an estimate of the Pauli error rate of the quantum computing system, wherein, The Pauli error rate of the quantum computing system The estimate is by Given, among which, Represents the dimension of Hilbert space. Indicates polarization, This represents the number of qubits that are operated on by one or more defined random quantum circuits.

11. The method according to any one of claims 1 to 10, wherein, Calibrate the quantum computing system using an estimate of its fidelity, which includes: Based on the determined fidelity estimate, one or more adjustments to the quantum hardware control parameters are determined by applying an optimization process to a fidelity-dependent cost function to optimize the cost function with respect to the parameters of the control model, which correlates the parameters of the quantum gate with the physical parameters of the system used to implement / control the quantum gate; and Implement one or more determined adjustments to perform quantum computing using quantum computing hardware.

12. The method according to claim 1, wherein, Calibrating the quantum computing system using an estimate of its fidelity includes using the estimate of the quantum computing system's fidelity to determine adjustments to the quantum computing system that improve its accuracy and / or efficiency.

13. An apparatus comprising: One or more classic processors; as well as Quantum computing hardware that communicates data with one or more classical processors; The apparatus is configured to perform the method according to any one of claims 1 to 12.

14. A method executed by one or more classical processors and a quantum computing system, the method comprising: For each of one or more random quantum circuits, the quantum computing system generates an experimental dataset, wherein a noisy experimental implementation of each random quantum circuit is approximated by a depolarization channel having corresponding polarization parameters and data items, wherein the data items in the experimental dataset include a string of measurement bits corresponding to the experimental implementation of the one or more random quantum circuits. For each of the one or more random quantum circuits, an estimate of the corresponding polarization parameter is determined by the one or more classical processors, wherein determining the estimate includes applying a maximization process to the log-likelihood of the polarization parameter conditioned on the corresponding experimental dataset, the maximization process including the use of series inversion; and The Pauli error rate of the quantum computing system is estimated by the one or more classical processors based on the determined estimates of the corresponding polarization parameters.

15. The method according to claim 14, wherein, The Pauli error rate of the quantum computing system The estimate is by Given, among which, Represents the dimension of Hilbert space. This indicates the number of qubits that are operated on by the one or more random quantum circuits.

16. The method of claim 14, wherein, Determining the estimate of the corresponding polarization parameter includes: Define the new variable as equal to ,in, Represents the dimension of Hilbert space. Representing random quantum circuits The ideal realization of the probability of generating the eigenstate corresponding to the k-th data item in the corresponding experimental dataset. It is the bit string of the k-th data item; Substitute the new variable into the first equation of the first derivative of the log-likelihood of the polarization parameter conditioned on the corresponding experimental dataset to obtain the infinite series representation of the first equation.

17. The method according to claim 16, wherein, Maximizing the log-likelihood of the polarization parameters conditioned on the corresponding experimental dataset using series inversion includes: Series inversion is used to compute the solution of the infinite series representation of the first equation of the first derivative of the log-likelihood of the polarization parameters conditioned on the corresponding experimental dataset.

18. The method according to claim 14, wherein, The experimental dataset for the defined random quantum circuit is generated and repeated a predetermined number of times.

19. The method of claim 14, further comprising determining the variance of the estimate of the corresponding polarization parameter by calculating the second derivative of the log-likelihood of the polarization parameter conditioned on the corresponding experimental dataset: in, It is the log-likelihood of the polarization parameters conditioned on the corresponding experimental dataset. It is the variance of the estimate of the corresponding polarization parameter.

20. The method of claim 14, wherein, The output of the experimental implementation of the one or more random quantum circuits is approximated by the Porter-Thomas distribution.

21. The method according to claim 14, wherein, The one or more quantum circuits include random quantum circuits that operate on the same number of qubits and have the same circuit depth.

22. The method according to claim 14, wherein, Determining the Pauli error rate of the quantum computing system based on the determined estimates of the corresponding polarization parameters includes: Calculate the average estimate of the polarization parameters; and The average estimate of the polarization parameters is used to determine the estimate of the Pauli error rate of the quantum computing system.

23. The method according to any one of claims 14 to 22, further comprising using an estimate of the Pauli error rate of the quantum computing system to determine the performance of the quantum computing system.

24. The method of claim 23, further comprising: One or more adjustments to the control parameters of the quantum hardware are determined based on the estimated Pauli error rate. as well as Implement one or more determined adjustments to perform quantum computing using quantum computing hardware.

25. An apparatus comprising: One or more classic processors; as well as Quantum computing hardware that communicates data with one or more classical processors; The apparatus is configured to perform the method of any one of claims 14 to 24.

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