Quantum error mitigation method and device

Abstract

The present application provides a quantum error mitigation method and device, comprising obtaining a sample quantum state by linearly superposing the results of multiple first unitary transformations with a first probability acting on an exact quantum state, constructing a quantum channel model, inversely solving the quantum channel model to obtain a quasi-probabilistic model, passing a second initial state through a noisy quantum circuit to obtain an output quantum state, correcting the output quantum state using a quantum error correction code method to obtain a quantum state to be error-mitigated, and performing the operation process in the quasi-probabilistic model on the quantum state to be error-mitigated to achieve error mitigation of the sub-state to be error-mitigated. The present invention reduces the number of physical bits required to implement quantum error correction, can significantly reduce the demand for physical resources without sacrificing performance, makes the construction and maintenance of quantum computing systems more economical and efficient, and can maintain high computational accuracy even under conditions of high noise and limited operational precision.

Description

Technical Field

[0001] One or more embodiments of this specification relate to the field of quantum computers, and more particularly, to a quantum error mitigation method and apparatus. Background Art

[0002] With the rapid development of quantum computing technology, quantum computers have demonstrated superior efficiency compared to traditional computers in solving certain types of problems. However, the physical implementation of quantum computers faces challenges such as high error rates in qubits and the susceptibility of quantum states to environmental interference. Fault-tolerant quantum computing is a key research direction in quantum computing, aiming to address the problem of qubit errors during computations. Qubits are extremely fragile and susceptible to external interference, leading to computational errors. This severely limits the practicality and reliability of quantum computing. Existing methods can use quantum error correction codes for error correction. However, whether using surface codes or color codes, improving error correction accuracy requires more physical bits to encode each qubit, requiring a large number of auxiliary qubits and complex quantum gate operations, making it difficult to implement in practical quantum computers. Error mitigation techniques can also address these issues. Existing error mitigation methods include zero-noise extrapolation and quantum subspace expansion. While these methods can achieve effective error mitigation with limited physical resources, they can encounter difficulties when dealing with deep quantum circuits. As the circuit depth increases, the measurement variance increases exponentially, and the number of measurements also increases exponentially, increasing the computational overhead. Summary of the Invention

[0003] This application describes a quantum error mitigation method and device that can solve the above technical problems.

[0004] According to a first aspect, a quantum error mitigation method is provided for use in a quantum computer, the method comprising:

[0005] Constructing a quantum channel model that represents a sample quantum state as a linear superposition of multiple first results obtained by applying multiple first unitary transformations, each with a first probability of occurrence, to a precise quantum state, wherein the precise quantum state is obtained by passing the first initial state through a noise-free quantum circuit, and the sample quantum state is obtained by passing the first initial state through a noisy quantum circuit;

[0006] Inversely solving the quantum channel model to obtain a quasi-probabilistic model, which represents the resulting quantum state after error mitigation as a linear superposition of multiple second results obtained by applying multiple second unitary transformations, each with a second probability of occurrence, to the quantum state to be error mitigated;

[0007] The second initial state is passed through the noisy quantum circuit to obtain an output quantum state. After the output quantum state is corrected using a quantum error correction code method, a target quantum state is obtained. The target quantum state is used as the quantum state to be error-mitigated to execute the operation process in the quasi-probabilistic model to obtain a result quantum state of error mitigation.

[0008] In some embodiments, the second probability of occurrence is obtained by using the first probability of occurrence.

[0009] In some embodiments, the second unitary transform is the inverse operation of the first unitary transform.

[0010] In some embodiments, performing the operation process in the quasi-probabilistic model using the target quantum state as the quantum state to be error-mitigated to obtain the error-mitigated quantum state specifically includes:

[0011] A second unitary transformation is randomly selected according to the second occurrence probability, the target quantum state is operated using the second unitary transformation, the operation result is measured, and a result quantum state is obtained according to the measurement result.

[0012] In some embodiments, the expression of the quantum channel model is ,in, is the sample quantum state, i.e. the noisy quantum state, is an exact quantum state, is the first unitary transformation of i, the first probability of occurrence is the probability of the i-th first unitary transformation occurring, yes The conjugate transpose of .

[0013] In some embodiments, the expression of the quasi-probabilistic model is ,in, is the quantum state to be error-mitigated, is the resulting quantum state, is the ith second unitary transformation, the second probability of occurrence is the i-th second unitary transformation The probability of occurrence, yes The conjugate transpose of is a normalization constant used to ensure the desired quantum state Satisfy the normalization condition of the density matrix, is a sign factor that adjusts the signs of the linear combination terms.

[0014] In some embodiments, the step of correcting the output quantum state using a quantum error correction code method to obtain a target quantum state specifically includes:

[0015] The output quantum state is encoded using a quantum error correction code, errors in the encoded output quantum state are detected by measuring auxiliary quantum bits, and errors in the logical bits in the output quantum state are corrected using logical operations to obtain the target quantum state.

[0016] According to a second aspect, a quantum error mitigation device is provided for use in a quantum computer, the device comprising:

[0017] a first processing module, configured to construct a quantum channel model, wherein the sample quantum state is represented as a linear superposition of a plurality of first results obtained by applying a plurality of first unitary transformations, each having a first probability of occurrence, to a precise quantum state, wherein the precise quantum state is obtained by passing a first initial state through a noise-free quantum circuit, and the sample quantum state is obtained by passing the first initial state through the noisy quantum circuit;

[0018] a second processing module, configured to inversely solve the quantum channel model to obtain a quasi-probabilistic model, wherein the quasi-probabilistic model represents the resulting quantum state after error mitigation as a linear superposition of second results of a plurality of second unitary transformations, each having a second probability of occurrence, acting on the quantum state to be error mitigated;

[0019] A third processing module is configured to pass the second initial state through the noisy quantum circuit to obtain an output quantum state, perform error correction on the output quantum state using a quantum error correction code method, obtain a target quantum state, and use the target quantum state as the quantum state to be error-mitigated to execute the operation process in the quasi-probabilistic model to obtain a result quantum state of error mitigation.

[0020] In some embodiments, the second probability of occurrence is obtained by using the first probability of occurrence.

[0021] In some embodiments, the second unitary transform is the inverse operation of the first unitary transform.

[0022] In some embodiments, the first processing module is specifically used to randomly select one of the second unitary transformations according to the second occurrence probability, use the second unitary transformation to operate on the target quantum state, measure the operation result, and obtain a result quantum state according to the measurement result.

[0023] In some embodiments, the expression of the quantum channel model is ,in, is the sample quantum state, i.e. the noisy quantum state, is an exact quantum state, is the first unitary transformation of i, the first probability of occurrence is the probability of the i-th first unitary transformation occurring, yes The conjugate transpose of .

[0024] In some embodiments, the expression of the quasi-probabilistic model is ,in, is the quantum state to be error-mitigated, is the resulting quantum state, is the ith second unitary transformation, the second probability of occurrence is the i-th second unitary transformation The probability of occurrence, yes The conjugate transpose of is a normalization constant used to ensure that the resulting quantum state Satisfy the normalization condition of the density matrix, is a sign factor that adjusts the signs of the linear combination terms.

[0025] In some embodiments, the third processing module is specifically used to encode the output quantum state using a quantum error correction code, detect errors in the encoded output quantum state by measuring auxiliary quantum bits, and use logical operations to correct errors in logical bits in the output quantum state to obtain the target quantum state.

[0026] According to a third aspect, a computer storage medium is provided, on which a computer program is stored. When the computer program is executed by one or more processors, a quantum error mitigation method as described in any one of the above technical solutions is implemented.

[0027] According to a fourth aspect, an electronic device is provided, comprising a memory and one or more processors, wherein a computer program is stored on the memory, and when the computer program is executed by the one or more processors, a quantum error mitigation method as described in any one of the above technical solutions is implemented.

[0028] In the systems and methods described in the embodiments of this specification, a quasi-probabilistic model is used to reduce the number of physical bits required for quantum error correction. Compared to traditional quantum error-correcting codes, this significantly reduces the need for physical resources without sacrificing performance, making the construction and maintenance of quantum computing systems more economical and efficient. It also maintains high computational accuracy even under conditions of high noise and limited operational precision. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0030] Figure 1A schematic diagram of a quantum circuit illustrating a quantum error mitigation method implemented using a quantum circuit according to an embodiment of this specification;

[0031] Figure 2 A schematic diagram illustrating a flow chart of a quantum error mitigation method provided in an embodiment of this specification;

[0032] Figure 3 A schematic diagram showing a quantum error mitigation device provided by an embodiment of this specification. DETAILED DESCRIPTION

[0033] The solution provided in this specification is described below in conjunction with the accompanying drawings.

[0034] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described below with reference to the accompanying drawings.

[0035] In the description of the embodiments of the present application, words such as "exemplary," "for example," or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary," "for example," or "for example" in the embodiments of the present application should not be construed as being preferred or advantageous over other embodiments or designs. Rather, the use of words such as "exemplary," "for example," or "for example" is intended to present the relevant concepts in a concrete manner.

[0036] In the description of the embodiments of this application, the term "and / or" is merely a description of an association relationship between associated objects, indicating that three relationships may exist. For example, A and / or B can represent the following three situations: A exists alone, B exists alone, and A and B exist at the same time. In addition, unless otherwise specified, the term "plurality" means two or more.

[0037] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly identifying the technical features being referred to. Thus, features specified as "first" or "second" may explicitly or implicitly include one or more of such features. The terms "include," "comprising," "having," and their variations all mean "including but not limited to," unless otherwise specifically emphasized.

[0038] Qubits are extremely fragile and susceptible to interference from the external environment, leading to computational errors. This severely limits the practicality and reliability of quantum computing. Because the quantum no-cloning principle prohibits the direct copying of quantum information, traditional error correction methods are no longer applicable in the quantum world. One existing approach uses surface code error correction, which uses a qubit array on a two-dimensional lattice and stabilizer measurements at the lattice to detect and correct errors. This approach is very effective with large numbers of qubits, but requires complex quantum circuits and high-precision quantum operations. A second existing approach uses color code error correction, which constructs a three-dimensional lattice and exploits its topological properties to achieve error correction. Color codes offer more efficient error correction, but they also require significant physical resources and complex operations. Therefore, improving the error correction accuracy of existing methods requires increasing the code length of the error correction code, requiring more physical bits to encode each qubit. This requires a significant amount of physical resources, including auxiliary qubits and complex quantum gate operations, making it difficult to implement in a practical quantum computer.

[0039] Currently, error mitigation techniques are another strategy in quantum error correction methods, which use statistical analysis and post-processing algorithms to reduce errors in quantum computations. Specific error mitigation methods include zero-noise extrapolation and quantum subspace expansion. These methods can effectively mitigate errors under limited physical resource conditions, but they may encounter difficulties when dealing with deep quantum circuits. As the circuit depth increases, the measurement variance increases exponentially, and the number of measurements also increases exponentially, increasing the computational overhead.

[0040] In view of this, the present invention proposes a quantum error mitigation method that can solve the problem that when using error correction code methods, more physical bits are needed to encode a quantum bit to improve the error correction accuracy, and the existing error mitigation methods increase the number of measurements exponentially when processing quantum circuits with greater depth. Figure 1 Schematic diagram showing the method for implementing quantum error mitigation in quantum circuits according to the present invention. Figure 1 As shown, the process of quantum error mitigation in quantum circuits may include the following five stages / steps.

[0041] Step 1 is the encoding process of quantum error correction code. Quantum error correction code encodes the quantum state by encoding a single logical quantum bit into multiple physical quantum bits.

[0042] Step 2 is to perform logical operations on the encoded quantum state through quantum circuits. The logical operations are expressed as In this step, logical operations are performed on the encoded quantum state in the quantum circuit. The quantum circuit here is a noisy quantum circuit. Through the operation of the quantum circuit, the converted quantum state is obtained.

[0043] In step 3, it is detected whether there are errors in the converted quantum state, and if errors are detected, corresponding logical operations are applied to correct the errors.

[0044] In step 4, the error-corrected quantum state is subjected to the operation process in the quasi-probabilistic model to mitigate the quantum state error. The construction of the quasi-probabilistic model and its operation process will be described in detail below.

[0045] Step 5: Calculate the average value of the quantum state obtained in the previous step after multiple measurements, and obtain the final result based on the average value of multiple measurements.

[0046] This embodiment achieves quantum error mitigation through a quasi-probabilistic model approach, reducing the number of physical bits required in traditional error correction code methods. Without sacrificing performance, it significantly reduces the demand for physical resources, making the construction and maintenance of quantum computing systems more economical and efficient. It is particularly suitable for early fault-tolerant computing devices. Even under conditions of high noise and limited operating precision, it can maintain high computing accuracy, greatly expanding the application scope of quantum computing technology. By modeling and statistically analyzing the error characteristics of quantum operations, the accuracy of quantum computing results can be significantly improved. It does not rely on complex high-code-distance error correction codes and is easier to expand to larger-scale quantum systems. It can be applied to different types of quantum computers, including superconducting quantum bits, ion trap quantum bits, and other types of quantum bit systems. Since the demand for physical resources is reduced, the computing cost is reduced.

[0047] The following combination Figure 2 The flowchart of the quantum error mitigation method is described in detail, specifically including:

[0048] 110. Construct a quantum channel model that represents a sample quantum state as a linear superposition of multiple first results obtained by applying multiple first unitary transformations, each with a first probability of occurrence, to a precise quantum state, wherein the precise quantum state is obtained by applying the first initial state to a noise-free quantum circuit, and the sample quantum state is obtained by applying the first initial state to a noisy quantum circuit.

[0049] Specifically, the expression of the quantum channel model can be the following formula (1):

[0050] (1)

[0051] in, It is the sample quantum state, that is, the noisy quantum state, which is the quantum state obtained after a certain initial state passes through a noisy quantum circuit. is the exact quantum state, which is the quantum state obtained by assuming that the initial state passes through a quantum circuit that executes the same logic but without noise. is the first unitary transformation of i, the first probability of occurrence is the probability of the i-th first unitary transformation occurring, yes The conjugate transpose of .

[0052] It can be seen that the quantum channel model converts the sample quantum state Represented as multiple, each with a first probability of occurrence The first unitary transformation of Acting on precise quantum states The linear superposition of the multiple first results is obtained.

[0053] 120. Inversely solve the quantum channel model to obtain a quasi-probabilistic model, which represents the resulting quantum state after error mitigation as a linear superposition of multiple second results obtained by applying multiple second unitary transformations, each with a second probability of occurrence, to the quantum state to be error mitigated.

[0054] Specifically, the second occurrence probability can be obtained through the first occurrence probability.

[0055] In some applications, the second unitary transform is the inverse operation of the first unitary transform.

[0056] Specifically, the expression of the quasi-probabilistic model can be shown as formula (2):

[0057] (2)

[0058] in, is the quantum state to be error-mitigated, which corresponds to the sample quantum state in the aforementioned formula 1, i.e., the noisy quantum state. is the resulting quantum state after error mitigation, which corresponds to the exact quantum state in the aforementioned formula 1. is the ith second unitary transformation, the second probability of occurrence is the i-th second unitary transformation The probability of occurrence, yes The conjugate transpose of is a normalization constant used to ensure the desired quantum state Satisfy the normalization condition of the density matrix, is a sign factor used to adjust the sign of the linear combination term, , .

[0059] It can be seen that the quasi-probabilistic model is the inverse of the quantum channel model. That is, the quantum channel model expresses the potentially error-containing quantum state (i.e., the sample quantum state) obtained by a noisy quantum circuit as a function of the exact quantum state; whereas the quasi-probabilistic model expresses the exact quantum state (the resulting quantum state after error mitigation) as a function of the quantum state to be error-mitigated. Specifically, the quasi-probabilistic model expresses the resulting quantum state after error mitigation as a linear superposition of multiple second results obtained by applying multiple second unitary transformations, each with a second probability of occurrence, to the quantum state to be error-mitigated.

[0060] Specifically, the method for inversely solving the quantum channel model includes constructing a quasi-probabilistic model through quantum process tomography. The functional form of the first unitary transformation Determine the second unitary transform , according to the i-th first unitary transformation The probability of occurrence determines the second unitary transformation The probability of occurrence, calculate the normalization constant , according to the characteristics of the noise and the effect of the unitary transformation, adjust the sign factor .

[0061] When implementing the above steps on actual quantum hardware, the effect of the inversion can be verified by collecting the resulting data, and the quasi-probabilistic model can be further optimized by iteratively adjusting the unitary transformation, quasi-probability, and sign factor.

[0062] 130. The second initial state is passed through a noisy quantum circuit to obtain an output quantum state. The output quantum state is corrected using a quantum error correction code method to obtain a target quantum state. The target quantum state is used as the quantum state to be error-mitigated to execute the operation process in the quasi-probabilistic model to obtain a resultant quantum state of error mitigation.

[0063] Specifically, if Figure 1 As shown, a quantum error-correcting code is used to encode the second initial state. This encoded quantum state is then input into a noisy quantum circuit to obtain an output quantum state. Errors in this output quantum state are detected by measuring auxiliary qubits and corrected to obtain a corrected logical bit. This quantum state is referred to as the target quantum state. As can be seen, even after correction, the target quantum state still contains errors, requiring error mitigation.

[0064] Therefore, the target quantum state can be used as the quantum state to be error-mitigated in the quasi-probabilistic model, and the operation process in the quasi-probabilistic model is performed on it to obtain the error-mitigated result quantum state.

[0065] Specifically, on a quantum computer, using a classical random number generator, according to the second probability Randomly select a second unitary transformation And execute, that is, the second unitary transformation Apply to the target quantum state to be error-mitigated, measure the execution result, and obtain the measurement result. Multiply each measurement result by the corresponding sign factor , to reverse the effect of noise. All measurement results are summed and multiplied by the normalization constant , and obtain the desired quantum state.

[0066] After the unitary transformation is performed, the quantum state is measured. Since the measurement results are affected by the selected unitary transformation, all measurement results can be collected by repeating the procedure multiple times and then analyzed according to their probabilities. After weighted averaging, the final quantum state is obtained.

[0067] The following is an illustration of a specific case.

[0068] In this example, it is assumed that the initial state , the error correction code is a simple 3-qubit repetition code, namely , , logical operations Pauli Operation, the noise channel is a depolarized noise line , is the error rate. Assume that the observable quantity to be measured is . Combined Figure 1 The relevant steps to mitigate quantum errors are as follows.

[0069] In step 1, using quantum error correction code, the physical bits Mapped to logical bits , to encode the quantum state.

[0070] In step 2, a logical operation is performed based on the noisy quantum circuit N. At this time, the line noise has been taken into account. That is, the above logic bits are After that, the output quantum state is obtained: .

[0071] In step 3, error detection and error correction are performed on the line to obtain the corrected logical bits. Even the corrected logical bits still have errors. Assume that the quantum state obtained at this time is represented by the quantum channel model as follows: in, is the exact quantum state. In this case, the exact quantum state , the sample quantum state at this time .

[0072] In step 4, the corrected logical bits are subjected to error mitigation using a quasi-probabilistic model. The quasi-probabilistic model is obtained by inversely solving the quantum channel model, and is specifically expressed as:

[0073]

[0074] Applied to this example, it is expressed as ,

[0075] in, , , .

[0076] The above formula shows that the process of error mitigation operation of quasi-probabilistic model includes: The probability performs the identity transformation to The probability of performing zero transformation is as follows. The identity transformation and zero transformation are the specific implementations of the aforementioned second unitary transformation in this example.

[0077] For other initial states Through the depolarized noise line , the quantum state to be processed is obtained, and the error correction code is a simple 3-qubit repetitive code, that is , After encoding the quantum state to be processed, the encoded quantum state is subjected to Pauli Operations are performed to detect and correct quantum state errors and obtain the quantum state after error correction. The quasi-probabilistic model is applied to the quantum state after error correction. , respectively The probability performs the identity transformation to Probabilistically perform a zeroing transformation to obtain the resulting quantum state.

[0078] In step 5, the resulting quantum state is measured, and the average value is calculated after multiple measurements. The result is multiplied by That is, you can get the final result.

[0079] This embodiment achieves quantum error mitigation through a quasi-probabilistic model approach, reducing the number of physical bits required in traditional error correction code methods. Without sacrificing performance, it significantly reduces the demand for physical resources, making the construction and maintenance of quantum computing systems more economical and efficient. It is particularly suitable for early fault-tolerant computing devices. Even under conditions of high noise and limited operating precision, it can maintain high computing accuracy, greatly expanding the application scope of quantum computing technology. By modeling and statistically analyzing the error characteristics of quantum operations, the accuracy of quantum computing results can be significantly improved. It does not rely on complex high-code-distance error correction codes and is easier to expand to larger-scale quantum systems. It can be applied to different types of quantum computers, including superconducting quantum bits, ion trap quantum bits, and other types of quantum bit systems. Since the demand for physical resources is reduced, the computing cost is reduced.

[0080] like Figure 3 A quantum error mitigation device is shown for use in a quantum computer, the device comprising:

[0081] a first processing module, configured to construct a quantum channel model, wherein the sample quantum state is represented as a linear superposition of a plurality of first results obtained by applying a plurality of first unitary transformations, each having a first probability of occurrence, to a precise quantum state, wherein the precise quantum state is obtained by passing a first initial state through a noise-free quantum circuit, and the sample quantum state is obtained by passing the first initial state through the noisy quantum circuit;

[0082] a second processing module, configured to inversely solve the quantum channel model to obtain a quasi-probabilistic model, wherein the quasi-probabilistic model represents the resulting quantum state after error mitigation as a linear superposition of second results of a plurality of second unitary transformations, each having a second probability of occurrence, acting on the quantum state to be error mitigated;

[0083] A third processing module is configured to pass the second initial state through the noisy quantum circuit to obtain an output quantum state, perform error correction on the output quantum state using a quantum error correction code method, obtain a target quantum state, and use the target quantum state as the quantum state to be error-mitigated to execute the operation process in the quasi-probabilistic model to obtain a result quantum state of error mitigation.

[0084] In some embodiments, the second probability of occurrence is obtained by using the first probability of occurrence.

[0085] In some embodiments, the second unitary transform is the inverse operation of the first unitary transform.

[0086] In some embodiments, the first processing module is specifically used to randomly select one of the second unitary transformations according to the second occurrence probability, use the second unitary transformation to operate on the target quantum state, measure the operation result, and obtain a result quantum state according to the measurement result.

[0087] In some embodiments, the expression of the quantum channel model is ,in, is the sample quantum state, is an exact quantum state, is the first unitary transformation of i, the first probability of occurrence is the probability of the i-th first unitary transformation occurring, yes The conjugate transpose of .

[0088] In some embodiments, the expression of the quasi-probabilistic model is ,in, is the quantum state to be error-mitigated, is the resulting quantum state, is the ith second unitary transformation, the second probability of occurrence is the i-th second unitary transformation The probability of occurrence, yes The conjugate transpose of is a normalization constant used to ensure the desired quantum state Satisfy the normalization condition of the density matrix, is a sign factor that adjusts the signs of the linear combination terms.

[0089] In some embodiments, the third processing module is specifically used to encode the output quantum state using a quantum error correction code, detect errors in the encoded output quantum state by measuring auxiliary quantum bits, and use logical operations to correct errors in logical bits in the output quantum state to obtain the target quantum state.

[0090] This embodiment achieves quantum error mitigation through a quasi-probabilistic model approach, reducing the number of physical bits required in traditional error correction code methods. Without sacrificing performance, it significantly reduces the demand for physical resources, making the construction and maintenance of quantum computing systems more economical and efficient. It is particularly suitable for early fault-tolerant computing devices. Even under conditions of high noise and limited operating precision, it can maintain high computing accuracy, greatly expanding the application scope of quantum computing technology. By modeling and statistically analyzing the error characteristics of quantum operations, the accuracy of quantum computing results can be significantly improved. It does not rely on complex high-code-distance error correction codes and is easier to expand to larger-scale quantum systems. It can be applied to different types of quantum computers, including superconducting quantum bits, ion trap quantum bits, and other types of quantum bit systems. Since the demand for physical resources is reduced, the computing cost is reduced.

[0091] The present invention also provides a computer storage medium, on which a computer program is stored. When the computer program is executed by one or more processors, the quantum error mitigation method as described in any one of the above technical solutions is implemented.

[0092] The present invention also provides an electronic device, comprising a memory and one or more processors, wherein the memory stores a computer program, and when the computer program is executed by the one or more processors, the quantum error mitigation method as described in any one of the above technical solutions is implemented.

[0093] The specific implementation methods described above further illustrate the purpose, technical solutions and beneficial effects of this application. It should be understood that the above description is only the specific implementation methods of this application and is not intended to limit the scope of protection of this application. Any modifications, equivalent replacements, improvements, etc. made on the basis of the technical solutions of this application should be included in the scope of protection of this application.

Claims

1. A quantum error mitigation method, characterized in that: For use in a quantum computer, the method comprises: Constructing a quantum channel model that represents a sample quantum state as a linear superposition of multiple first results obtained by applying multiple first unitary transformations, each with a first probability of occurrence, to a precise quantum state, wherein the precise quantum state is obtained by passing the first initial state through a noise-free quantum circuit, and the sample quantum state is obtained by passing the first initial state through a noisy quantum circuit; Inversely solving the quantum channel model to obtain a quasi-probabilistic model, which represents the resulting quantum state after error mitigation as a linear superposition of multiple second results obtained by applying multiple second unitary transformations, each with a second probability of occurrence, to the quantum state to be error mitigated; Passing the second initial state through the noisy quantum circuit to obtain an output quantum state, performing error correction on the output quantum state using a quantum error correction code method to obtain a target quantum state, and executing the operation process in the quasi-probabilistic model using the target quantum state as the quantum state to be error-mitigated to obtain an error-mitigated result quantum state; The inverse solution of the quantum channel model to obtain a quasi-probabilistic model specifically includes: determining the second unitary transform from the first unitary transform, determining a probability of the second unitary transform occurring based on a probability of the first unitary transform occurring, calculating a normalization constant, and adjusting a sign factor based on characteristics of noise and an effect of the unitary transform; The expression of the quasi-probabilistic model is ,in, is the quantum state to be error-mitigated, is the resulting quantum state, is the ith second unitary transformation, the second probability of occurrence is the i-th second unitary transformation The probability of occurrence, yes The conjugate transpose of is a normalization constant used to ensure that the resulting quantum state satisfies the normalization condition of the density matrix, is a sign factor that adjusts the signs of the linear combination terms.

2. The method according to claim 1, characterized in that The second occurrence probability is obtained through the first occurrence probability.

3. The method according to claim 1, characterized in that The second unitary transform is an inverse operation of the first unitary transform.

4. The method according to claim 1, wherein The step of executing the operation process in the quasi-probabilistic model using the target quantum state as the quantum state to be error-mitigated to obtain the error-mitigated quantum state specifically includes: A second unitary transformation is randomly selected according to the second occurrence probability, the target quantum state is operated using the second unitary transformation, the operation result is measured, and a result quantum state is obtained according to the measurement result.

5. The method according to claim 1, wherein The expression of the quantum channel model is ,in, is the sample quantum state, i.e. the noisy quantum state, is an exact quantum state, is the first unitary transformation of i, the first probability of occurrence is the probability of the i-th first unitary transformation occurring, yes The conjugate transpose of .

6. The method according to claim 1, characterized in that After performing error correction on the output quantum state using a quantum error correction code method, obtaining a target quantum state specifically includes: The output quantum state is encoded using a quantum error correction code, errors in the encoded output quantum state are detected by measuring auxiliary quantum bits, and errors in the logical bits in the output quantum state are corrected using logical operations to obtain the target quantum state.

7. A quantum error mitigation device, characterized in that For use in a quantum computer, the device comprises: a first processing module, configured to construct a quantum channel model, wherein the sample quantum state is represented as a linear superposition of a plurality of first results obtained by applying a plurality of first unitary transformations, each having a first probability of occurrence, to a precise quantum state, wherein the precise quantum state is obtained by passing a first initial state through a noise-free quantum circuit, and the sample quantum state is obtained by passing the first initial state through the noisy quantum circuit; a second processing module, configured to inversely solve the quantum channel model to obtain a quasi-probabilistic model, wherein the quasi-probabilistic model represents the resulting quantum state after error mitigation as a linear superposition of second results of a plurality of second unitary transformations, each having a second probability of occurrence, acting on the quantum state to be error mitigated; a third processing module, configured to pass the second initial state through the noisy quantum circuit to obtain an output quantum state, perform error correction on the output quantum state using a quantum error correction code method to obtain a target quantum state, and execute an operation process in the quasi-probabilistic model using the target quantum state as the quantum state to be error-mitigated to obtain a result quantum state of error mitigation; a second processing module, specifically configured to determine the second unitary transform from the first unitary transform, determine a probability of the second unitary transform occurring based on the probability of the first unitary transform occurring, calculate a normalization constant, and adjust a sign factor based on characteristics of noise and an effect of the unitary transform; The expression of the quasi-probabilistic model is ,in, is the quantum state to be error-mitigated, is the resulting quantum state, is the ith second unitary transformation, the second probability of occurrence is the i-th second unitary transformation The probability of occurrence, yes The conjugate transpose of is a normalization constant used to ensure that the resulting quantum state satisfies the normalization condition of the density matrix, is a sign factor that adjusts the signs of the linear combination terms.

8. A computer storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by one or more processors, the quantum error mitigation method according to any one of claims 1 to 6 is implemented.

9. An electronic device, characterized in that: The method comprises a memory and one or more processors, wherein a computer program is stored in the memory, and when the computer program is executed by the one or more processors, the quantum error mitigation method according to any one of claims 1 to 6 is implemented.

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