Optimal quantum computer error mitigation method under average meaning

Abstract

The invention provides an optimal quantum computer error mitigation method in average meaning, K processing schemes in a given program processing scheme set are used for processing a target quantum program to obtain K processed programs, the K processing schemes define different quantum gate insertion positions and quantum gate types, and the K processing schemes are used for processing the target quantum program to obtain the K processed programs. Or different noise channel amplification rates are respectively defined; respectively inputting the K processed programs into a quantum computer for execution to obtain K actual measurement results; and processing the K actual measurement results by using a given combination scheme to obtain an estimated value of an ideal measurement result of the target quantum program. The method inherits the advantage that the white box method can effectively suppress errors theoretically, and the black box method of machine learning is introduced, so that a better error mitigation effect can be realized under low overhead, the influence of noise in the scale quantum calculation era in noisy is relieved, and the quantum advantage is possibly obtained.

Description

Technical Field

[0001] This application relates to the field of quantum computing technology, and in particular to an average-optimal method for mitigating errors in quantum computers. Background Technology

[0002] Recent advancements in quantum computing have led to the noisy medium-scale quantum era. In this era, error correction in quantum computers is costly, and noise in the hardware directly impacts the execution of quantum programs, generating numerous quantum errors and significantly reducing program fidelity. In particular, these errors are diverse, interconnected, and difficult to characterize precisely, necessitating the development of universal error mitigation techniques to reduce their impact on computation.

[0003] Universal error mitigation techniques refer to those that are not sensitive to specific error types or can be applied to any type of error. These techniques can be broadly categorized into two types: white-box methods and black-box methods. White-box methods establish an error analysis model and then mitigate errors based on that model; black-box methods establish a statistical model of errors and implicitly acquire error-related information through a learning process to alleviate the error.

[0004] White-box and black-box methods each have their advantages and disadvantages. Generally speaking, white-box methods can indicate the degree of error mitigation (e.g., the size of residual error) and, under certain conditions, can completely eliminate errors. However, the cost of building the analytical model for a high-performing white-box method is extremely high. Black-box methods typically cannot completely eliminate errors and are also difficult to indicate the degree of error mitigation, but these methods excel in error suppression with lower overhead and have significant practical value. Designing methods that combine the advantages of both white-box and black-box approaches holds promise for achieving sufficiently good error mitigation at a low cost; however, currently, there is no effective method for combining white-box and black-box approaches. Summary of the Invention

[0005] In view of this, this application provides an average-optimal error mitigation method for quantum computers to solve the above-mentioned technical problems.

[0006] In a first aspect of this application, an average-optimal error mitigation method for quantum computers is provided, the method comprising: Using K processing schemes from a given set of program processing schemes, the target quantum program is processed to obtain K processed programs. The K processing schemes define different quantum gate insertion positions and quantum gate types, or define different noise channel amplification factors. K processed programs were input into a quantum computer for execution, resulting in K actual measurement results; By processing the K actual measurement results using a given combination scheme, an estimate of the ideal measurement result of the target quantum program is obtained. The combination scheme defines the transformation relationship from the K actual measurement results to a single estimate. The combination scheme is obtained by solving for the minimum of the mean squared error on a reference program set, which contains multiple reference programs with the same structure as the target quantum program.

[0007] According to one embodiment of this application, the method further includes: Determine candidate gate positions in the target quantum program, wherein the candidate gate positions include positions before and after each quantum gate in the target quantum program; Based on the candidate insertion gate positions and the predefined set of insertable quantum gate types, a set of candidate insertion gate schemes is generated; K insertion schemes are selected from the candidate insertion scheme set to obtain the program processing scheme set.

[0008] According to one embodiment of this application, generating a set of candidate insertion schemes based on the candidate insertion positions and a predefined set of insertable quantum gate types includes: From the candidate door positions, enumerate all unique combinations of door positions; For each candidate insertion position in each combination of insertion positions, quantum gate types are selected by traversing the set of insertable quantum gate types to generate all candidate insertion schemes corresponding to the combination of insertion positions. All candidate door insertion schemes corresponding to the combinations of all door insertion positions are merged to generate the candidate door insertion scheme set.

[0009] According to one embodiment of this application, when the K processing schemes define different noise channel amplification factors, the step of processing the target quantum program using the K processing schemes from the given set of program processing schemes to obtain K processed programs includes: For each processing scheme in the set of program processing schemes, the noise channels after all quantum gates constituting the target quantum program are uniformly amplified according to the noise channel amplification factor defined in the processing scheme to obtain the corresponding processed program.

[0010] According to one embodiment of this application, the calculation of the mean squared error depends on the ideal measurement result of each reference program and the actual measurement result of the program obtained by applying each processing scheme in the set of program processing schemes to each reference program.

[0011] According to one embodiment of this application, the method further includes: For each rotating gate in the target quantum program, it is randomly replaced with one of a plurality of pre-set Clifford gates with equal probability to obtain the plurality of reference programs with the same structure as the target quantum program; For each reference program, the ideal measurement result corresponding to the reference program is obtained through classical computational simulation. The reference program is then processed using the K processing schemes to obtain K processed reference programs. The K processed reference programs are then input into the quantum computer for execution to obtain K actual measurement results corresponding to the reference program. By using a combination scheme containing K undetermined parameters, the K actual measurement results corresponding to each reference program are processed to obtain the estimated value of the ideal measurement result corresponding to the reference program. The average of the sums of the squares of the differences between the ideal measurement result and the estimated value of the ideal measurement result for each reference program is obtained by averaging the sums of the squares of the differences. Under the premise that the K undetermined parameters meet the preset constraints, the values ​​of the K undetermined parameters are solved with the goal of minimizing the mean squared error, and the combined scheme is obtained.

[0012] In a second aspect of this application, an average-optimal quantum computer error mitigation device is provided, the device comprising: The first processing unit is used to process the target quantum program using K processing schemes from a given set of program processing schemes to obtain K processed programs. The K processing schemes define different quantum gate insertion positions and quantum gate types, or define different noise channel amplification factors. The second processing unit is used to input the K processed programs into the quantum computer for execution, and obtain K actual measurement results; An estimation unit is used to process the K actual measurement results using a given combination scheme to obtain an estimate of the ideal measurement result of the target quantum program. The combination scheme defines the transformation relationship from the K actual measurement results to a single estimate. The combination scheme is obtained by solving for the minimum of the mean squared error on a reference program set, which contains multiple reference programs with the same structure as the target quantum program.

[0013] In a third aspect of this application, an electronic device is provided, including a processor and a memory, the memory storing machine-executable instructions executable by the processor, the processor executing the machine-executable instructions to implement the steps of the method proposed in the above embodiments.

[0014] In a fourth aspect of this application, a machine-readable storage medium is provided, wherein machine-executable instructions are stored therein, and when executed by a processor, the machine-executable instructions implement the steps of the method proposed in the above embodiments.

[0015] In a fifth aspect of this application, a computer program product is provided, including a computer program / instructions that, when executed by a processor, implement the steps of the method proposed in the above embodiments.

[0016] As can be seen from the above technical solution, by using K processing schemes from a given set of program processing schemes, the target quantum program is processed to obtain K processed programs. Each of the K processing schemes defines a different quantum gate insertion position and quantum gate type, or defines a different noise channel amplification factor. The K processed programs are then input into a quantum computer for execution, yielding K actual measurement results. Finally, a given combination scheme is used to process these K actual measurement results to obtain an estimate of the ideal measurement result of the target quantum program. This application, based on white-box methods such as probabilistic errors and zero-noise extrapolation, inherits the theoretical advantage of effectively suppressing errors. Furthermore, it introduces machine learning, a black-box method, to achieve better error mitigation with low overhead, mitigating the impact of noise in the era of noisy medium-scale quantum computing and making the attainment of quantum advantage possible.

[0017] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and do not limit this application. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating an average-valued optimal error mitigation method for quantum computers provided in an embodiment of this application. Figure 2 This is a flowchart illustrating an average-valued optimal quantum computer error mitigation method provided in another embodiment of this application; Figure 3 This is a schematic diagram illustrating a candidate door position according to an embodiment of this application; Figure 4 This is a schematic diagram of a quantum program structure provided in an embodiment of this application; Figure 5 This is a circuit diagram of a variable quantum circuit program defined on a one-dimensional chain, provided in an embodiment of this application; Figure 6 This is a comparison diagram of the error mitigation effect between the method proposed in this application and the Clifford training method provided in the embodiments of this application; Figure 7This is a comparison diagram of the error mitigation effects of the door insertion method and the noise extrapolation method provided in the embodiments of this application; Figure 8 This is a schematic diagram of the structure of an average-valued optimal quantum computer error mitigation device provided in an embodiment of this application; Figure 9 This is a schematic diagram of the hardware structure of an electronic device illustrated in an exemplary embodiment of this application. Detailed Implementation

[0019] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0020] The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The singular forms “a,” “the,” and “the” used in this application and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise.

[0021] To enable those skilled in the art to better understand the technical solutions provided in the embodiments of this application, and to make the above-mentioned objectives, features and advantages of the embodiments of this application more apparent and understandable, the technical solutions in the embodiments of this application will be further described in detail below with reference to the accompanying drawings.

[0022] First, the abbreviations and key terms involved in this application will be explained.

[0023] 1. Quantum Computation: A computing method that utilizes the properties of quantum states, such as superposition and entanglement, to quickly complete computational tasks.

[0024] 2. Qubit: A form of carrier of quantum information.

[0025] 3. Quantum Operation: The way to manipulate qubits to process the quantum information carried by qubits, including quantum gates, qubit state preparation, quantum measurement, etc.

[0026] 4. Quantum Gate: A class of quantum operations that can be represented as unitary transformations between the states of a qubit. Common quantum gates include Pauli I, X, Y, and Z gates, Hadamard (H) gates, Controlled Pauli X gates (CNOT), and rotation gates. (P is the axis of rotation, and θ is the angle of rotation).

[0027] 5. Clifford gates: A special class of quantum gates that, under conjugation, still map the tensor products of Pauli I, X, Y, and Z gates to the tensor products of Pauli gates, i.e., denoted as... It is the Pauli gate tensor product. If it's the Clifford Gate, then... It is still the tensor product of Pauli gate.

[0028] 6. Quantum State Preparation: This is used to set the state of a qubit to a specific state, usually the initial state. This state is called a qubit reset operation.

[0029] 7. Quantum Measurement: A classical description of the state of a qubit.

[0030] 8. Quantum Program: A sequence of quantum operations used to represent a quantum computing process. It consists of qubit states, a series of quantum gates, and quantum measurements. In some embodiments, it is assumed that the quantum gates used in the target quantum program are Clifford gates and rotation gates. This type of quantum program can implement arbitrary quantum operations and is hardware efficient.

[0031] 9. Quantum Error: An unexpected change in the state of a quantum bit, usually caused by noise in the hardware.

[0032] 10. Fidelity: Measures the difference between the actual process and the expected process. The higher the fidelity, the smaller the difference. Fidelity can be used in quantum operations and quantum programming scenarios. In quantum operations, fidelity measures the difference between the actual operation and the expected operation. In quantum programming, fidelity measures the difference between the actual computational result and the correct result (ideal value).

[0033] 11. Noisy Intermediate-Scale Quantum (NISQ): This refers to the period in quantum computing development where quantum computers have tens to hundreds of qubits, and these qubits are subject to noise interference.

[0034] 12. Error mitigation techniques: Techniques used to reduce the impact of quantum errors on the execution of quantum programs.

[0035] 13. Universal error mitigation techniques: Error mitigation techniques that are not sensitive to specific error types or can be applied to any error type are called universal error mitigation techniques.

[0036] 14. Error Mitigation Scheme: The error mitigation scheme in this application includes a set of program processing schemes and a combination scheme. The set of program processing schemes may contain K gate insertion schemes or K noise channel amplification factors, wherein each gate insertion scheme specifies the position information and type of quantum operation inserted into the target quantum program. The combination scheme defines the mapping relationship from the K input measurement results to a single output estimate to obtain the result (estimate) after the original program error is mitigated.

[0037] Recent advancements in quantum computing have led to the noisy medium-scale quantum era. In this era, error correction in quantum computers is costly, and noise in the hardware directly impacts the execution of quantum programs, generating numerous quantum errors and significantly reducing program fidelity. In particular, these errors are diverse, interconnected, and difficult to characterize precisely, necessitating the development of universal error mitigation techniques to reduce their impact on computation.

[0038] Universal error mitigation techniques refer to those that are not sensitive to specific error types or can be applied to any type of error. These techniques can be broadly categorized into two types: white-box methods and black-box methods. White-box methods establish an error analysis model and then mitigate errors based on that model; black-box methods establish a statistical model of errors and implicitly acquire error-related information through a learning process to alleviate the error.

[0039] White-box and black-box methods each have their advantages and disadvantages. Generally speaking, white-box methods can indicate the degree of error mitigation (e.g., the size of residual error) and, under certain conditions, can completely eliminate errors. However, the cost of building the analytical model for a high-performing white-box method is extremely high. Black-box methods typically cannot completely eliminate errors and are also difficult to indicate the degree of error mitigation, but these methods excel in error suppression with lower overhead and have significant practical value. Designing methods that combine the advantages of both white-box and black-box approaches holds promise for achieving sufficiently good error mitigation at a low cost; however, currently, there is no effective method for combining white-box and black-box approaches.

[0040] In view of this, embodiments of this application disclose an average-optimal quantum computer error mitigation method to solve the above-mentioned technical problems.

[0041] like Figure 1 As shown, Figure 1 This application provides an embodiment of an average-means optimal error mitigation method for quantum computers.

[0042] The application of the aforementioned error mitigation method comprises two stages: "processing" and "combination." Given a target program (i.e., the target quantum program, denoted as P) and an error mitigation scheme, the error mitigation scheme includes a set of program processing schemes and a combination scheme. The set of program processing schemes includes K processing schemes, which can be K gate-insertion schemes or K noise channel amplification factors. Each gate-insertion scheme specifies the insertion position and type of the quantum operation inserted into the target quantum program. The combination scheme defines the transformation relationship from the K actual input measurements to a single output estimate.

[0043] Figure 1 Let's take an example where the set of program processing schemes includes K gate insertion schemes. First, a new program is constructed based on the gate insertion schemes in the set. Since the set includes K gate insertion schemes, and each scheme corresponds to a new program, K new programs are constructed. Then, each new program is input into the quantum computer for execution, yielding K corresponding actual measurement results, denoted as... ,…, Finally, by processing the K actual measurement results using the given combination scheme, an estimate of the ideal measurement result of the target quantum program is obtained, denoted as . ,in .

[0044] Constructing a new program based on a gate insertion scheme refers to, based on a given target quantum program, inserting a quantum gate of the corresponding type at the corresponding position according to the insertion position and type of the quantum gate in the gate insertion scheme, thereby constructing a new program.

[0045] The combination scheme is a K-input, 1-output function that takes K actual measurement results of new programs as inputs and outputs an estimate of the ideal measurement result of a given target quantum program.

[0046] like Figure 2 As shown, Figure 2 This application provides an embodiment of an average-meaning optimal quantum computer error mitigation method. This average-meaning optimal quantum computer error mitigation method may include the following steps: S101: Using K processing schemes from the given set of program processing schemes, process the target quantum program respectively to obtain K processed programs, wherein the K processing schemes define different quantum gate insertion positions and quantum gate types, or define different noise channel amplification factors respectively.

[0047] The given set of processing schemes includes K processing schemes, which can be K gate insertion schemes or K noise channel amplification factors. Specifically, when the given set of processing schemes includes K gate insertion schemes, each gate insertion scheme specifies a different quantum gate insertion position and quantum gate type in the target quantum program; when the given set of processing schemes includes K noise channel amplification factors, each processing scheme defines a different amplification factor for the noise channel of the target quantum program.

[0048] A new program is constructed based on the processing schemes in the set of program processing schemes. The set of program processing schemes includes K processing schemes, and each processing scheme corresponds to a new program. Therefore, K new programs are constructed.

[0049] In this context, where the K processing schemes are K gate insertion schemes, constructing a new program based on the processing schemes means, given the target quantum program, inserting quantum gates of the corresponding type at the appropriate positions according to the insertion positions and types of quantum gates in the gate insertion schemes, thereby constructing a new program.

[0050] With K processing schemes representing K noise channel amplification factors, the logic circuit of the target quantum program is not changed. Instead, the noise level of the entire target quantum program is systematically amplified through physical means. Specifically, constructing a new program based on the processing scheme means uniformly amplifying the noise channels after all quantum gates constituting the target quantum program according to the noise channel amplification factor defined in the processing scheme, so as to obtain the corresponding processed program, i.e., constructing a new program.

[0051] Each processing scheme defines an amplification factor α to amplify the noise channel of the target quantum program. Different processing schemes correspond to different α values ​​(e.g., α = 1.0, 1.1, 1.34, 1.58, where α = 1.0 represents the original target quantum program). For a given processing scheme, the noise channel amplification factor... If the noise channel behind a quantum gate in the target quantum program is This amplifies the noise intensity, making the noise channel appear as... By processing all noise channels in the target quantum program as described above, a new program is constructed. This program processing method can be called the noise extrapolation method. In experiments, this method can be implemented by extending the circuit's running time, alternating the operation of quantum gates, and combining inverse quantum gates and probabilistic sampling. Theoretically, the noise amplification factor α can be adjusted to obtain arbitrarily large program processing sets. However, this method requires significant resources to execute in experiments. Therefore, only four schemes with noise amplification factors α = 1.0, 1.1, 1.34, and 1.58 are used to construct four processed programs.

[0052] In some embodiments, the K processing schemes in the set of program processing schemes can be obtained through the following steps, that is, how to learn the K insertion schemes in the set of program processing schemes included in the error mitigation scheme.

[0053] S1011: Determine candidate gate positions in the target quantum program, wherein the candidate gate positions include positions before and after each quantum gate in the target quantum program. It is necessary to identify all possible positions in the target quantum program where quantum gates can be inserted, i.e., candidate insertion positions, also known as candidate insertion positions. In this application, candidate insertion positions include positions before and after each quantum gate in the target quantum program.

[0054] like Figure 3 As shown, Figure 3 This is a schematic diagram illustrating a candidate door position according to an embodiment of this application. Figure 3 Taking the target quantum program as an example, this target quantum program contains two quantum gates and has three types of candidate gate insertion positions. The first type of candidate gate insertion position is the position between the initialization operation of a qubit and the first quantum gate on that qubit, such as... Figure 3 Positions 1 and 2 in the qubit. The second type of candidate insertion position is the position between two adjacent quantum gates on a qubit, such as... Figure 3 Position 3 in the middle. The third type of candidate gate position is the position between a measurement operation of a qubit and the previous qubit gate of that measurement operation, such as... Figure 3 Position 4 in the middle.

[0055] S1012: Based on the candidate insertion gate positions and the predefined set of insertable quantum gate types, generate a set of candidate insertion gate schemes.

[0056] First, we can enumerate all unique combinations of door insertion positions from the candidate positions. Specifically, we can select C distinct positions from the candidate positions to generate all possible combinations, where C is an integer between 0 and the total number of candidate positions. Here, C can be called the order of the insertion scheme, defined as the number of door insertion positions involved. Starting from order 0, we increment the order C (C=0, 1, 2, ...) until we reach the total number of candidate positions or a preset maximum order. From all candidate positions, we select C distinct positions to generate all possible combinations. For example, if there are 3 candidate positions, namely position 1, position 2, and position 3, for C=2, the corresponding combinations are position 1 and position 2, position 1 and position 3, and position 2 and position 3.

[0057] Secondly, for each candidate insertion position in each combination of insertion positions, a quantum gate type is selected by traversing the set of insertable quantum gate types to generate all candidate insertion schemes corresponding to the combination of insertion positions. For example, the predefined set of insertable quantum gate types may include Pauli X, Y, and Z gates. Of course, in actual implementation, other quantum operations besides the aforementioned Pauli X, Y, and Z gates can also be selected, and this embodiment does not specifically limit this.

[0058] Finally, the candidate door insertion schemes corresponding to all door insertion position combinations are merged to generate a set of candidate door insertion schemes.

[0059] It is important to emphasize that a specific door insertion scheme can be represented by "{(position, door type), ...}". For example, {(1,X),(2,Y)} represents a door insertion scheme that inserts door X at position 1 and door Y at position 2. The order of a door insertion scheme is defined as the number of door positions involved in the scheme. For example, {(1,Z)} is a first-order door insertion scheme, and {(1,X),(2,Y)} is a second-order door insertion scheme. Typically, there are many door insertion schemes of the same order. The first-order door insertion scheme is special; there is only one, which is the original program itself.

[0060] For example, suppose the target quantum program has only two candidate gate positions (position 1 and position 2), and the set of gate types G is {Pauli X gate, Pauli Y gate}.

[0061] When C is 0, i.e., a 0th-order gate insertion scheme, one candidate gate insertion scheme is generated, i.e., an empty set {}, representing the target quantum program itself.

[0062] When C is 1, it is a first-order door insertion scheme. There are two combinations of door insertion positions: Door insertion position combination 1: [position 1], which generates two candidate door insertion schemes by assigning door type: {(1,X)} and {(1,Y)}; Door insertion position combination 2: [position 2], which generates two candidate door insertion schemes by assigning door type: {(2,X)} and {(2,Y)}.

[0063] When C is 2, it is a 2nd order door insertion scheme. There is only one door insertion position combination 1: [position 1, position 2]. Assigning door type generates 4 candidate door insertion schemes: {(1,X),(2,X)}, {(1,X),(2,Y)}, {(1,Y),(2,X)} and {(1,Y),(2,Y)}.

[0064] The candidate door insertion schemes corresponding to all door insertion position combinations are merged, and the final set of candidate door insertion schemes contains 1+2+2+4=9 candidate door insertion schemes.

[0065] S1013: Select K insertion schemes from the candidate insertion scheme set to obtain the program processing scheme set. In this embodiment, the number K of the insertion schemes is predetermined.

[0066] In this embodiment, S1011-S1013 can be referred to as "program processing method", which is used to generate K insertion schemes in the program processing scheme set.

[0067] S102: Input the K processed programs into the quantum computer for execution to obtain K actual measurement results.

[0068] The K processed programs are then input into a quantum computer (or quantum processing unit, QPU) for execution. Through the final measurement operation, K corresponding measurement results are obtained, denoted as... ,…, .

[0069] S103: Process the K actual measurement results using the given combination scheme to obtain an estimate of the ideal measurement result of the target quantum program.

[0070] The combined scheme defines the transformation relationship from K actual measurement results to a single estimate. The combined scheme is a K-input, 1-output function; it takes K actual measurement results of a new program as input and outputs an estimate of the ideal measurement result of a given target quantum program. Since the ideal measurement result of the target quantum program cannot always be accurately obtained, the result obtained through the combined scheme is called the estimate of the ideal measurement result.

[0071] The general form of the combination scheme is: ,in, , ,…, This represents K actual measurement results. The function represents the estimate of the ideal measurement result of the target quantum program. The choice can be either linear or nonlinear. Linear form, for example... ,in, These are parameters to be determined. The nonlinear form can be leveraged, for example, by using neural networks to fit nonlinear functions and recover the desired output, given their powerful representational capabilities. Neural networks come in various forms; any structure that satisfies K inputs and 1 output is acceptable.

[0072] The combination scheme is obtained by solving for the minimum of the mean squared error on a reference program set, which contains multiple reference programs with the same structure as the target quantum program.

[0073] In some embodiments, the calculation of the mean squared error depends on the ideal measurement results of each reference program and the actual measurement results of the program obtained by applying each processing scheme in the set of program processing schemes to each reference program.

[0074] In some embodiments, a combination scheme can be obtained through the following steps, namely, how to learn the combination schemes included in the error mitigation scheme.

[0075] S1031: For each rotating gate in the target quantum program, replace it with one of a plurality of pre-set Clifford gates with equal probability to obtain the plurality of reference programs with the same structure as the target quantum program.

[0076] In this embodiment, the quantum gates used in the target quantum program are Clifford gates and rotation gates. This type of quantum program can implement arbitrary quantum operations and the device is highly efficient.

[0077] The structure of a quantum program is defined by: 1. the placement and order of quantum gates; and 2. the qubits involved in the observables. The structure of a quantum program as defined above is independent of the specific type of quantum gate (e.g., X-gate or H-gate) and the form of the observables (e.g., Z-operator or Y-operator).

[0078] like Figure 4 As shown, Figure 4 This is a schematic diagram of a quantum program structure provided in an embodiment of this application, to... Figure 4 Based on quantum program (a), quantum programs (b) and (c) have the same structure as quantum program (a), differing only in the type of single-bit gate or the form of observable. Quantum program (d) differs from quantum program (a) in the location of the single-bit gate, and quantum program (e) differs from quantum program (a) in the number of qubits involved in the observable. Therefore, quantum programs (d) and (e) are quantum programs with different structures from quantum program (a).

[0079] In this embodiment, for a given target quantum program, the Clifford gates are retained, and for the rotation gates... The gate is randomly replaced with one of the following four Clifford gates with equal probability: , , and After replacing all the rotating gates in the target quantum program as described above, a program with the same structure as the target quantum program is generated, which is called the reference program.

[0080] Repeat the above steps to generate multiple reference programs with the same structure as the target quantum program, forming a reference program set, denoted as T. The number of reference programs in the reference program set is typically five to ten times the number of gate schemes K. In this embodiment, the above-mentioned reference program set T can also be called the training set, and step S1031 can be called the "training set generation method".

[0081] S1032: For each reference program, the ideal measurement result corresponding to the reference program is obtained through classical computation simulation, and the reference program is processed by the K processing schemes respectively to obtain K processed reference programs. The K processed reference programs are then input into the quantum computer for execution to obtain K actual measurement results corresponding to the reference program.

[0082] For each reference program in the reference program set, denoted as ( This must be a quantum program whose entire set of quantum gates consists of Clifford gates. For this type of quantum program, its output can be classically simulated using the Gottesman–Knill algorithm.

[0083] At the same time, each reference program in the reference program assembly Treating it as a "new target quantum program," it is processed using each of the given program processing schemes to obtain K processed reference programs. Each processed reference program is then input into the quantum computer for execution to obtain the reference program. The corresponding K actual measurement results are denoted as follows: , ,…, .

[0084] S1033: Using a combination scheme containing K undetermined parameters, process the K actual measurement results corresponding to each reference program to obtain an estimate of the ideal measurement result corresponding to the reference program.

[0085] By using a combination scheme containing K undetermined parameters, the K actual measurement results corresponding to each reference program are merged into an estimate of the ideal measurement result corresponding to that reference program.

[0086] In this embodiment, the combination scheme takes the form of a linear combination. Specifically, the expression for the combination scheme is as follows: ,in, , ,…, This represents the actual measurement result of the program after processing by the 1st, 2nd, ..., Kth processing scheme in the set of program processing schemes. , ,…, These are K undetermined parameters in the combined scheme. Each undetermined parameter corresponds to a specific processing scheme, and its value reflects the contribution or credibility of the actual measurement results obtained by the processing scheme in the final estimate. These K undetermined parameters need to be solved.

[0087] For each reference program in reference assembly T The estimated values ​​of the corresponding ideal measurement results are calculated as follows: Obtain this reference program The corresponding K actual measurement results: , ,…, Each actual measurement result Its corresponding undetermined parameters Multiply them to get K products. Sum these K products to get the result of the reference procedure. Estimate of the ideal measurement result .

[0088] S1034: The average of the sums of the squares of the differences between the ideal measurement result and the estimated value of the ideal measurement result for each reference program is obtained by averaging the sums of the squares of the differences.

[0089] Mean squared error is used to assess the average degree of difference between the estimated value and the true value. In this application, mean squared error is defined as the average of the squares of the differences between the ideal measurement results of all reference procedures and their corresponding estimates of the ideal measurement results. The smaller the value of mean squared error, the more accurately the combined scheme can recover the ideal value from noisy actual measurement results, i.e., the better the error mitigation effect.

[0090] Suppose that reference assembly T contains M reference programs, denoted as Mreference. First, calculate the squared error of each reference program. For each reference program in the set... Its known ideal measurement result is denoted as (Obtained through classical simulation in S1032), the estimated value of its corresponding ideal measurement result is denoted as... (Obtained via S1033), the squared error of this reference procedure is Next, calculate the mean squared error on the reference program set. This involves summing the squared errors of all M reference programs and then dividing by the total number of reference programs, M, to obtain the mean squared error L on the reference program set. The expression for L is: ,in, This indicates a summation operation.

[0091] S1035: Under the premise that the K undetermined parameters meet the preset constraints, with the goal of minimizing the mean square error on the reference program set, solve for the values ​​of the K undetermined parameters to obtain the combined scheme.

[0092] This step is the core of learning the combination schemes included in the error mitigation scheme. Through mathematical optimization methods, it automatically finds the optimal set of parameters that minimizes the mean squared error, thereby determining the final combination scheme.

[0093] In this embodiment, the problem of finding the optimal parameters is formalized as a constrained objective optimization problem. The optimization objective (objective function) is to minimize the mean squared error L calculated in S1034. The optimization problem can be expressed as follows: .

[0094] The optimization problem requires that the K undetermined parameters satisfy a preset constraint. In this embodiment, this constraint can be an L1 norm constraint, and the expression for the constraint can be... ,in, γ is a preset positive real hyperparameter used to control the variance of the linear combination form. For example, γ = 5 or 10, etc. Of course, this embodiment does not specifically limit the constraint condition; for example, the constraint condition could also be an L2 norm constraint, etc.

[0095] To solve the aforementioned constrained objective optimization problem, a series of numerical optimization algorithms, such as gradient descent and least squares, can be used. These algorithms automatically and iteratively adjust the parameters to be determined. , ,…, The value. For example, step a, can initialize a set of undetermined parameter values; step b, calculate the mean squared error L under the current parameters; step c, check whether the K undetermined parameters meet the preset constraints (such as...). Step d: According to the rules of the optimization algorithm, update the parameters in the direction that satisfies the constraints to reduce the value of the mean squared error L; Step e: Repeat steps b to d until a set of parameters is found that makes the mean squared error L reach the minimum (or close to the minimum) under the premise of satisfying the constraints.

[0096] The optimization process ultimately outputs a set of definite, optimal parameter values, denoted as... Substituting these parameter values ​​into the expression of the combination scheme yields a definite combination scheme for estimating the ideal measurement results used to generate the target quantum program.

[0097] In the embodiments of this application, the target quantum program is processed using K processing schemes from a given set of program processing schemes to obtain K processed programs. Each of the K processing schemes defines a different quantum gate insertion position and quantum gate type, or defines a different noise channel amplification factor. The K processed programs are then input into a quantum computer for execution, yielding K actual measurement results. A given combination scheme is used to process the K actual measurement results to obtain an estimate of the ideal measurement result of the target quantum program. This application, based on white-box methods such as probabilistic errors and zero-noise extrapolation, inherits the theoretical advantage of effectively suppressing errors. Furthermore, it introduces machine learning, a black-box method, to achieve better error mitigation with low overhead, mitigating the impact of noise in the era of noisy medium-scale quantum computing and making the attainment of quantum advantage possible.

[0098] Based on the training set generation method described in this application, it can be theoretically proven that the optimal error mitigation scheme (in an average sense) under the corresponding program processing method can be learned. Simultaneously, it can be proven that the required number of noisy quantum programs increases only linearly with the number of processing schemes K. Theoretically, this ensures that this application can achieve more effective mitigation of quantum errors at extremely low cost, thereby improving the fidelity of quantum program execution and accelerating the practical application of quantum computing.

[0099] This effect is illustrated using a variable quantum circuit program defined on a one-dimensional chain as an example. Figure 5 As shown, Figure 5 This is a circuit diagram of a variable quantum circuit program defined on a one-dimensional chain, provided in an embodiment of this application. The program involves 6 qubits, comprising 4 cycles and a single-qubit rotation gate layer; each block represents one... The rotating gate has a rotation angle randomly selected in [0, 2π]. The two bit gates are both controlled Pauli Z gates (CZ). The dashed box represents one cycle.

[0100] The final measured mean of the Hamiltonian is as follows: .

[0101] Each qubit corresponds to a diagram. Let V be a point in graph G, where V is the set of points in graph G and E is the set of edges in graph G. Point and Connected in the diagram, in this quantum program This is a one-dimensional chain. When executing the program in a simulation environment, a single-bit gate error is selected as a single-bit depolarization error with an error rate of 0.001, and a two-bit gate error is selected as a two-bit depolarization error with an error rate of 0.01. Let... For error rate, The depolarization error on a qubit is defined as: ,in, for Maximumly Mixed State on a qubit.

[0102] The following comparisons are divided into two categories. The first is a comparison between the average-mean-optimal quantum computer error mitigation method proposed in this application and a previous machine learning-based error mitigation method (since this method replaces all non-Clifford gates in the original program with all Clifford gates, it will be referred to as the Clifford training method). Specifically, low-order (0th order + all 1st order + 200 2nd order + 200 3rd order) gate schemes are used to generate training sets in different ways. The same optimization method is used to obtain the ideal output of the linear function recovery, to compare the advantages and disadvantages of the proposed method and the Clifford training method. To verify the optimality of the linear function obtained by the proposed method, non-Clifford circuits are used for training, and the mean squared error (MSE) is observed to be consistent with the result obtained by the proposed method. The second category compares different processing schemes, specifically comparing the error mitigation effects of low-order gates and noise extrapolation, and also comparing it with the original zero-noise extrapolation method to demonstrate the advantages of the proposed method.

[0103] 1. Comparison with Clifford training method like Figure 6 As shown, Figure 6 This is a comparison diagram of the error mitigation effects of the method proposed in this application and the Clifford training method provided in the embodiments of this application.

[0104] The results in the figure show that the linear combination function obtained based on the method proposed in this application is significantly better than the Clifford training method. When using 200 gate schemes, the error is reduced by an order of magnitude compared to the Clifford training method. Furthermore, based on the curves corresponding to the method proposed in this application and the curves corresponding to the optimal error mitigation scheme in the figure, the error of the error mitigation scheme obtained by the method proposed in this application is almost the same as that of the optimal error mitigation scheme obtained by directly using non-Clifford gates to generate the training set, verifying the optimality of this method in the sense of average error. It should be mentioned that the method proposed in this application has scalability. When the circuit scale is further increased, the results of the ideal program can still be classically simulated, but the results of the ideal program using the method of non-Clifford gates will not be efficiently calculated.

[0105] 2. Comparison between the door insertion method and the noise extrapolation method like Figure 7 As shown, Figure 7 This is a comparison diagram of the error mitigation effects of the door insertion method and the noise extrapolation method provided in the embodiments of this application.

[0106] The results are as follows Figure 7 As shown, the insertion method is still a low-order insertion method, and the noise extrapolation method uses four noise extrapolation processing schemes. Figure 7 The dashed line pointed to by ZNE in the middle is the mean square error obtained by using the original zero-noise extrapolation ZNE on the evaluation set.

[0107] Figure 7 This reflects two main phenomena: First, when resources available for error mitigation are limited, using the noise extrapolation method to process the target quantum program can achieve better error mitigation results. When the acceptable cost increases, the gate-based program processing method can better reduce the impact of errors. Second, the original ZNE method is far weaker than machine learning-based error mitigation schemes, reflecting that the method proposed in this application can significantly improve the error mitigation effect compared to white-box methods.

[0108] Compared to existing white-box and black-box methods, the method proposed in this application has significant advantages: it achieves better error mitigation at the same cost. This makes it easier to mitigate errors and achieve quantum advantage in the NISQ era with tolerable overhead. Furthermore, Comparison 2 illustrates that when tolerable overhead is low, the procedure using noise extrapolation is a better choice.

[0109] The above description describes the method provided in this application. The following description describes the apparatus provided in this application: Please see Figure 8 This is a schematic diagram of an average-valued quantum computer error mitigation device provided in an embodiment of this application.

[0110] like Figure 8 As shown, the device may include: The first processing unit 810 is used to process the target quantum program using K processing schemes from a given set of program processing schemes to obtain K processed programs. The K processing schemes define different quantum gate insertion positions and quantum gate types, or define different noise channel amplification factors. The second processing unit 820 is used to input the K processed programs into the quantum computer for execution to obtain K actual measurement results; The estimation unit 830 is used to process the K actual measurement results using a given combination scheme to obtain an estimate of the ideal measurement result of the target quantum program. The combination scheme defines the transformation relationship from the K actual measurement results to a single estimate. The combination scheme is obtained by solving for the minimum of the mean square error on a reference program set, which contains multiple reference programs with the same structure as the target quantum program.

[0111] Optionally, the apparatus further includes a first determining unit, which is specifically used for: Determine candidate gate positions in the target quantum program, wherein the candidate gate positions include positions before and after each quantum gate in the target quantum program; Based on the candidate insertion gate positions and the predefined set of insertable quantum gate types, a set of candidate insertion gate schemes is generated; K insertion schemes are selected from the candidate insertion scheme set to obtain the program processing scheme set.

[0112] Optionally, the first determining unit is specifically used for: From the candidate door positions, enumerate all unique combinations of door positions; For each candidate insertion position in each combination of insertion positions, quantum gate types are selected by traversing the set of insertable quantum gate types to generate all candidate insertion schemes corresponding to the combination of insertion positions. All candidate door insertion schemes corresponding to the combinations of all door insertion positions are merged to generate the candidate door insertion scheme set.

[0113] Optionally, when the K processing schemes define different noise channel amplification factors, the first processing unit is specifically used for: For each processing scheme in the set of program processing schemes, the noise channels after all quantum gates constituting the target quantum program are uniformly amplified according to the noise channel amplification factor defined in the processing scheme, so as to obtain the corresponding processed program.

[0114] Optionally, the estimation unit 830 is specifically used for: The calculation of the mean squared error depends on the ideal measurement results of each reference program and the actual measurement results of the program obtained by applying each processing scheme in the set of program processing schemes to each reference program.

[0115] Optionally, the device further includes a second determining unit, which is specifically used for: For each rotating gate in the target quantum program, it is randomly replaced with one of a plurality of pre-set Clifford gates with equal probability to obtain the plurality of reference programs with the same structure as the target quantum program; For each reference program, the ideal measurement result corresponding to the reference program is obtained through classical computational simulation. The reference program is then processed using the K processing schemes to obtain K processed reference programs. The K processed reference programs are then input into the quantum computer for execution to obtain K actual measurement results corresponding to the reference program. By using a combination scheme containing K undetermined parameters, the K actual measurement results corresponding to each reference program are processed to obtain the estimated value of the ideal measurement result corresponding to the reference program. The average of the sums of the squares of the differences between the ideal measurement result and the estimated value of the ideal measurement result for each reference program is obtained by averaging the sums of the squares of the differences. Under the premise that the K undetermined parameters meet the preset constraints, the values ​​of the K undetermined parameters are solved with the goal of minimizing the mean squared error, and the combined scheme is obtained.

[0116] The specific implementation process of the functions and roles of each unit in the above device can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.

[0117] This application also provides a hardware structure. See [link to relevant documentation]. Figure 9 , Figure 9 This is a structural diagram of an electronic device provided in an embodiment of this application. Figure 9 As shown, the hardware structure may include a processor 910 and a machine-readable storage medium 920. The machine-readable storage medium 920 stores machine-executable instructions 921 that can be executed by the processor; the processor 910 executes the machine-executable instructions 921 to implement the method disclosed in the above example of this application.

[0118] Based on the same application concept as the above method, this application embodiment also provides a machine-readable storage medium storing a plurality of computer instructions, which, when executed by a processor, can implement the method disclosed in the above examples of this application.

[0119] For example, the aforementioned machine-readable storage medium can be any electronic, magnetic, optical, or other physical storage device that can contain or store information such as executable instructions, data, etc. For instance, machine-readable storage media can be: RAM (Random Access Memory), volatile memory, non-volatile memory, flash memory, storage drives (such as hard disk drives), solid-state drives, any type of storage disk (such as optical discs, DVDs, etc.), or similar storage media, or combinations thereof.

[0120] It should be noted that, in this document, relational terms such as "objective" and "target" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0121] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. An average-optimal error mitigation method for quantum computers, characterized in that, The method includes: Using K processing schemes from a given set of program processing schemes, the target quantum program is processed to obtain K processed programs. The K processing schemes define different quantum gate insertion positions and quantum gate types, or define different noise channel amplification factors. K processed programs were input into a quantum computer for execution, resulting in K actual measurement results; By processing the K actual measurement results using a given combination scheme, an estimate of the ideal measurement result of the target quantum program is obtained. The combination scheme defines the transformation relationship from the K actual measurement results to a single estimate. The combination scheme is obtained by solving for the minimum of the mean squared error on a reference program set, which contains multiple reference programs with the same structure as the target quantum program.

2. The method according to claim 1, characterized in that, The method further includes: Determine candidate gate positions in the target quantum program, wherein the candidate gate positions include positions before and after each quantum gate in the target quantum program; Based on the candidate insertion gate positions and the predefined set of insertable quantum gate types, a set of candidate insertion gate schemes is generated; K insertion schemes are selected from the candidate insertion scheme set to obtain the program processing scheme set.

3. The method according to claim 2, characterized in that, The generation of a candidate gate insertion scheme set based on the candidate insertion gate positions and a predefined set of insertable quantum gate types includes: From the candidate door positions, enumerate all unique combinations of door positions; For each candidate insertion position in each combination of insertion positions, quantum gate types are selected by traversing the set of insertable quantum gate types to generate all candidate insertion schemes corresponding to the combination of insertion positions. All candidate door insertion schemes corresponding to the combinations of all door insertion positions are merged to generate the candidate door insertion scheme set.

4. The method according to claim 1, characterized in that, Given that the K processing schemes each define different noise channel amplification factors, the process of using the K processing schemes from the given set of program processing schemes to process the target quantum program, resulting in K processed programs, includes: For each processing scheme in the set of program processing schemes, the noise channels after all quantum gates constituting the target quantum program are uniformly amplified according to the noise channel amplification factor defined in the processing scheme to obtain the corresponding processed program.

5. The method according to claim 1, characterized in that, The calculation of the mean squared error depends on the ideal measurement results of each reference program and the actual measurement results of the program obtained by applying each processing scheme in the set of program processing schemes to each reference program.

6. The method according to claim 5, characterized in that, The method further includes: For each rotating gate in the target quantum program, it is randomly replaced with one of a plurality of pre-set Clifford gates with equal probability to obtain the plurality of reference programs with the same structure as the target quantum program; For each reference program, the ideal measurement result corresponding to the reference program is obtained through classical computational simulation. The reference program is then processed using the K processing schemes to obtain K processed reference programs. The K processed reference programs are then input into the quantum computer for execution to obtain K actual measurement results corresponding to the reference program. By using a combination scheme containing K undetermined parameters, the K actual measurement results corresponding to each reference program are processed to obtain the estimated value of the ideal measurement result corresponding to the reference program. The average of the sums of the squares of the differences between the ideal measurement result and the estimated value of the ideal measurement result for each reference program is obtained by averaging the sums of the squares of the differences. Under the premise that the K undetermined parameters meet the preset constraints, the values ​​of the K undetermined parameters are solved with the goal of minimizing the mean squared error, and the combined scheme is obtained.

7. An average-optimal quantum computer error mitigation device, characterized in that, The device includes: The first processing unit is used to process the target quantum program using K processing schemes from a given set of program processing schemes to obtain K processed programs. The K processing schemes define different quantum gate insertion positions and quantum gate types, or define different noise channel amplification factors. The second processing unit is used to input the K processed programs into the quantum computer for execution, and obtain K actual measurement results; An estimation unit is used to process the K actual measurement results using a given combination scheme to obtain an estimate of the ideal measurement result of the target quantum program. The combination scheme defines the transformation relationship from the K actual measurement results to a single estimate. The combination scheme is obtained by solving for the minimum of the mean squared error on a reference program set, which contains multiple reference programs with the same structure as the target quantum program.

8. An electronic device, characterized in that, It includes a processor and a memory, the memory storing machine-executable instructions that can be executed by the processor, the processor being used to execute the machine-executable instructions to implement the method as described in any one of claims 1-6.

9. A machine-readable storage medium, characterized in that, The machine-readable storage medium stores machine-executable instructions, which, when executed by a processor, implement the method as described in any one of claims 1-6.

10. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1-6.

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