A quantum computer error correction method based on quantum circuit

Abstract

The application relates to the technical field of quantum computing, in particular to a quantum computer error correction method based on a quantum circuit, which comprises the following steps: step 1: establishing an error model according to quantum codes of quantum computer noise; step 2: measuring or obtaining data results from real quantum computer hardware according to the error model, and correcting errors of the data results, wherein the data results are composed of a plurality of syndromes and logical operators; step 3: learning and training by using the data results to obtain a decoding quantum circuit; and step 4: running the decoding quantum circuit to perform decoding, wherein when the quantum computer produces noise or new errors, the decoding quantum circuit directly outputs corresponding error correction logical operators with the syndromes as input, and real-time decoding and error correction are performed. The decoding quantum circuit after learning and training is directly deployed on the quantum computer, the logical operators required for identifying and correcting errors of the quantum computer can be directly recognized, and real-time decoding and error correction are realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of quantum computing, in particular to a quantum computer error correction method based on quantum circuit. BACKGROUND

[0002] Quantum computers need to be corrected in order to realize general quantum computing. However, the decoding of quantum error correction codes currently relies on classical computing, and in superconducting qubits, the speed of classical computing is slower than quantum operation. This difference makes the practical application of real-time quantum error correction face challenges.

[0003] An ideal quantum computer has the potential to achieve exponential acceleration over classical computing in tasks such as prime factorization. However, quantum computers are susceptible to noise at the physical level and must be corrected to ensure the accuracy of the computing results. Quantum error correction codes address this challenge by integrating multiple physical qubits into a smaller number of logical qubits, encoding logical information by redundantly measuring ancillary qubits, and when an error occurs, triggering a non-trivial measurement result and using it to infer how the logical information has changed, thereby making appropriate corrections. This inference process is called decoding and is considered a classical statistical inference problem. Various decoding algorithms have been proposed to solve this problem, including minimum weight perfect matching (MWPM), joint search, belief propagation with ordered statistical decoding (BPOSD), tensor network methods, and neural network decoders.

[0004] Despite the numerous decoders and the use of modern computing power such as GPUs and FPGAs for acceleration, it is still challenging to accurately correct actual quantum codes at a speed that matches the operation speed of superconducting qubit quantum devices under actual circuit-level noise, making real-time decoding difficult. SUMMARY

[0005] The present application provides a quantum computer error correction method based on quantum circuit, which uses quantum circuit instead of classical computing device to solve the decoding problem, so that the decoding speed matches the operation speed of the quantum circuit to be corrected.

[0006] To achieve the above objectives, this application provides a quantum computer error correction method based on quantum circuits, comprising the following steps: Step 1: Establishing an error model based on the quantum code of quantum computer noise; Step 2: Measuring or obtaining data results from real quantum computer hardware based on the error model, and correcting the errors. The data results are composed of multiple syndromes and corresponding logical operators; Step 3: Using the data results for learning and training to obtain a decoding quantum circuit; Step 4: Running the decoding quantum circuit for decoding. When the quantum computer generates noise or new errors, the decoding quantum circuit directly outputs the corresponding error correction logical operator with the syndrome as input, performing decoding and error correction in real time.

[0007] Furthermore, in step 1, the quantum code is represented using a Tanner diagram.

[0008] Furthermore, in step 2: the error model measurement is constructed by measuring the auxiliary qubits; the syndrome represents the parity check error in a specific set of error models; the error correction of the data results represents inferring the logical operator caused by the error and correcting it given the syndrome.

[0009] Furthermore, in step 3, the decoding quantum circuit involves parameterized single-qubit gates and non-parameterized two-qubit gates, meaning that the decoding quantum circuit consists of multiple qubits and multiple sets of unitary operands.

[0010] Furthermore, each unitary operation block includes multiple X-rotary doors, multiple Y-rotary doors, and multiple controlled Z-doors.

[0011] Furthermore, the parameters of the revolving door can be optimized through learning and training, which can be performed using tensor networks or by sampling with quantum computer hardware.

[0012] Furthermore, the learning and training process includes forward propagation and backward propagation, and the parameters of the rotating door are iteratively adjusted to make the conditional distribution approximate the training data distribution.

[0013] Furthermore, in step 4, decoding the quantum circuit is a pure quantum operation that does not require the participation of classical operations.

[0014] This application provides a quantum computer error correction method based on quantum circuits, which has the following beneficial effects:

[0015] This application directly deploys the trained decoding quantum circuit onto a quantum computer, enabling it to directly identify the logical operators needed to correct errors in the quantum computer, achieving real-time decoding and error correction. By directly outputting logical operators using the decoding quantum circuit, the decoding speed is fast, significantly reducing the operation time for decoding and error correction. Furthermore, quantum sampling is fast and simple, directly using the quantum circuit to sample logical operators, eliminating the need to calculate conditional probabilities as in classical sampling. Simultaneously, iterative updates of the parameters of single-qubit gates can be performed, greatly reducing the error rate in identification. Attached Figure Description

[0016] The accompanying drawings, which form part of this application, are used to provide a further understanding of the application and to make other features, objects, and advantages of the application more apparent. The illustrative embodiments and descriptions of this application are used to explain the application and do not constitute an undue limitation of the application. In the drawings:

[0017] Figure 1 It is a Tanna diagram of quantum codes provided according to embodiments of this application;

[0018] Figure 2 This is a schematic diagram illustrating the change in the surface code logic error rate with a code distance of 3 during the learning and training process of the decoding quantum circuit provided in the embodiments of this application;

[0019] Figure 3 This is a schematic diagram illustrating the change in the surface code logic error rate with a code distance of 5 during the learning and training process of the decoding quantum circuit provided in the embodiments of this application;

[0020] Figure 4 This is a schematic diagram illustrating the change in the surface code logic error rate with a code distance of 7 during the learning and training process of the decoding quantum circuit provided in the embodiments of this application;

[0021] Figure 5 This is a schematic diagram of a self-correcting repeating code quantum memory with a code distance of 3 according to an embodiment of this application. Detailed Implementation

[0022] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort should fall within the scope of protection of the present application.

[0023] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate for the embodiments of this application described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0024] In this application, the terms "upper," "lower," "left," "right," "front," "rear," "top," "bottom," "inner," "outer," "middle," "vertical," "horizontal," "lateral," and "longitudinal" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. These terms are primarily for the purpose of better describing this application and its embodiments, and are not intended to limit the indicated device, element, or component to having a specific orientation, or to be constructed and operated in a specific orientation.

[0025] Furthermore, in addition to indicating location or positional relationship, some of the aforementioned terms may also have other meanings. For example, the term "above" may also be used in some cases to indicate a certain dependency or connection relationship. Those skilled in the art can understand the specific meaning of these terms in this application based on the specific circumstances.

[0026] In addition, the term "multiple" should mean two or more.

[0027] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0028] A quantum computer is a physical device that performs high-speed mathematical and logical operations, stores and processes quantum information, following the properties and laws of quantum mechanics. When a device processes and computes quantum information and runs quantum algorithms, it is a quantum computer. With the rapid development of quantum computing technology, its applications are becoming increasingly widespread due to its powerful computing capabilities and fast operating speed. Currently, quantum computing is in its second stage, featuring dozens of noisy qubits. We have not yet implemented a complete quantum error correction scheme, primarily because the decoding method for quantum error correction codes requires classical computers, which operate slower than superconducting quantum hardware.

[0029] The quantum computer error correction method based on quantum circuits provided in this application utilizes the decoding scheme of the quantum circuit's own operation. Specifically, given a noisy quantum circuit A, a decoding quantum circuit B is trained using the obtained syntactic measurement to identify the logical operators needed to correct errors in quantum circuit A. The trained decoding quantum circuit B is then deployed on quantum devices such as quantum computers to perform real-time decoding and error correction. The specific steps include:

[0030] Step 1: Establish an error model based on the quantum code of quantum computer noise;

[0031] Specifically, such as Figure 1 As shown, the quantum code is represented using a Tanner graph. The upper left panel represents the rotating surface code under qubit noise, and the upper right panel represents the repeating code with a code distance of 3 under circuit-level noise. R represents reset, M represents measurement, and I represents idle. These correspond to the Tanner graph displayed in the upper middle panel. The error mechanism corresponds to the circle in the upper middle panel. The measurement results in the Tanner graph generate a syndrome, which is then used to decode the logic sector and perform correction. In this embodiment, only three syndrome measurements are depicted using different colors.

[0032] Step 2: Measure the data results according to the error model or obtain the data results from real quantum computer hardware, and correct the errors. The data results are composed of multiple syndromes and corresponding logical operators.

[0033] Specifically, error model measurements are constructed by measuring auxiliary qubits; the syndrome indicates whether an odd number of errors have occurred in a specific set of error models. If no errors have occurred, the syndrome will be trivial (all zeros); if an odd number of errors have occurred, some measurements will be triggered and report a nontrivial syndrome, i.e., for m measurements, there are 2 m Possible syndromes γ = {γ1, γ2, ..., γ m}∈{0,1} m Given a known syndrome, infer the logical operators caused by the error and correct them to achieve error correction of the data results.

[0034] Step 3: Use the data results for learning and training to obtain the decoded quantum circuit;

[0035] Specifically, decoding the quantum circuit involves parameterized single-qubit gates and non-parameterized two-qubit gates, ultimately indicating the logic sector through a single measurement. In the embodiments of this application, syndromes are encoded as parameters of the single-qubit gates. Figure 1 Below, taking a decoding quantum circuit consisting of 3 qubits and 2 unitary operands as an example: each unitary operand consists of a set of rotating X-gates. Followed by a set of rotating Y-doors The structure is as follows: where q∈{1,2,3} represents the qubit index in the decoding circuit, b∈{1,2} represents the block index, and i is the error symptom index. The parameters of the rotating gate are determined by the product of the learnable parameter θ and the error symptom γ. The matrix form of the X rotating gate is:

[0036]

[0037] The matrix form of the Y-shaped rotating door is:

[0038]

[0039] Here, θ and φ are learnable parameters. The parameters of the rotating gate can be optimized through learning and training, which can be performed using tensor networks or by sampling with quantum computer hardware. The learning and training process includes forward propagation and back propagation, iteratively adjusting the parameters of the rotating gate to make the conditional distribution approximate the training data distribution. In the forward propagation process, a single-qubit gate is constructed using the training checksum γ and parameters θ and φ. Then, a tensor network is used to simulate the quantum circuit to obtain the final state, and the conditional probability p(β|γ) is calculated as the output. Subsequently, a cross-entropy loss function is formulated based on this output and the corresponding label γ in the training data. In the back propagation process, the gradient of the loss function with respect to the parameters is calculated using the back propagation algorithm. Then, an optimizer uses these gradients to update the parameters.

[0040] More specifically, to verify whether the proposed decoding quantum circuit can effectively suppress errors in practical quantum codes, numerical experiments were conducted on Z-based surface code quantum memories under depolarization circuit-level noise. Surface codes with code distances of 3, 5, and 7 were tested, such as... Figures 2-4The figure shows the change in the logical error rate of the decoding quantum circuit under training steps, and compares it with the Minimum Weight Perfect Match (MWPM) algorithm. The vertical axis represents the logical error rate, and the horizontal axis represents the number of training epochs. In the experiment, the physical error rate was fixed at 0.001 to simulate the error level of current superconducting quantum devices. The decoding circuit of each code consists of 3 qubits and 10 operands, and it is assumed that the decoding circuit is noise-free. 200,000 parsers randomly generated from the error model were used to train all decoding quantum circuits, and 100,000 test parsers were randomly generated with different random seeds. As can be seen from the figure, as the number of training epochs increases, the logical error rate of both the training parsers and the test parsers initially decreases from a high value to a low value. For the surface code with a code distance of 3 and 4 rounds of measurement, the test logical error rate after 10,000 training epochs is better than the MWPM algorithm, but still below the break-even point of 0.999, which is attributed to the short code distance of the code. For the cases with a code distance of 5 and 7, it can be clearly seen that at 10... 4 After several training rounds, the test logic error rate exceeded the break-even point.

[0041] Furthermore, once the parameters are correctly learned, the resulting decoding quantum circuit can be deployed on quantum devices such as quantum computers to perform decoding. This involves applying single-qubit and two-qubit gates to the initial state to prepare the final state, followed by measurement using the computational basis. This process effectively yields the corresponding final state in the computational basis |ψ(β1, β2, ..., β...). Q )| 2 The probability distribution below represents the bit string {β1, β2, ..., β} given the error symptom γ. Q The conditional probability of} is denoted as q(β|γ). When Q>k, that is, when the number of qubits Q in the decoding circuit exceeds the number of logical qubits k, a subset of the decoding qubits can be measured or selected. For example, in the quantum memory example characterized by k=1, it is only necessary to measure one qubit in the decoding quantum circuit to obtain the conditional probability of q(β|γ1, γ2, ..., γ). m Alternatively, the process can be repeated several times to estimate the conditional probability of a logical sector given a particular error symptom, and then the logical sector that maximizes the conditional probability can be selected.

[0042] Step 4: Run the decoding quantum circuit to perform decoding. When the quantum computer generates noise or new errors, the decoding quantum circuit will directly output the corresponding error correction logic operator with the syndrome as input, and perform decoding and error correction in real time.

[0043] Specifically, the decoding speed of the decoding quantum circuit matches the operating speed of the error-correcting quantum circuit in the quantum computer. Using the quantum circuit-based quantum computer error correction method provided in this application, it is no longer necessary to measure auxiliary qubits to obtain the classical syndrome for error detection and correction. Instead, the state of the auxiliary qubits can directly control the parameters of the decoding circuit (through controlled single-qubit gates with learned parameters) to perform decoding; furthermore, the result of the decoding circuit can be directly fed back to the operating circuit using controlled gates to perform logical operations, forming a self-correcting circuit. For example... Figure 5 As shown, the blue shaded area of ​​the circuit represents the storage section, which consists of three data qubits and two auxiliary qubits. In this round, the auxiliary qubits are measured, and these auxiliary qubits are directly used to control the single-qubit gates learned in the circuit's decoding section (shown in green), which contains two decoding qubits. Finally, the second decoding qubit is used to manipulate the data qubits, introducing a controlled logic X gate to correct errors in the repetitive memory.

[0044] More specifically, the quantum computer error correction method based on quantum circuits provided in this application uses variable quantum circuits to decode quantum error-correcting codes. The decoding quantum circuit is a pure quantum operation and does not require the participation of classical operations. The proposed method is based on learning and training and can be applied to various codes under different noise conditions. The decoding time is consistent with the operation time of the noisy quantum circuit, which can correct logic errors in the noisy quantum circuit in real time.

[0045] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A quantum computer error correction method based on a quantum circuit, characterized by, The method comprises the following steps: Step 1: establishing an error model according to quantum codes of quantum computer noise; Step 2: measuring or obtaining data results from real quantum computer hardware according to the error model, and correcting errors of the data results, wherein the data results are composed of a plurality of syndromes and logical operators; The error model measurement is constructed by measuring auxiliary quantum bits; The syndrome represents the parity check of errors in a specific set of error models; That is, the syndrome represents whether an odd number of errors occurs in a specific set of error models, if no error occurs, the syndrome will be trivial; if an odd number of errors occurs, some measurements will be triggered and report a non-trivial syndrome; Correcting errors of the data results means inferring logical operators caused by errors and correcting them under the condition of known syndromes; Step 3: learning and training using the data results to obtain a decoding quantum circuit; The decoding quantum circuit involves parameterized single-qubit gates and non-parameterized two-qubit gates, that is, the decoding quantum circuit is composed of a plurality of quantum bits and a plurality of sets of unitary operation blocks; Each set of unitary operation blocks comprises a plurality of X rotation gates, a plurality of Y rotation gates and a plurality of controlled Z gates; The parameters of the rotation gates can be optimized by learning and training, which is performed by a tensor network method or by sampling using quantum computer hardware; The learning and training process comprises forward propagation and backward propagation, and the parameters of the rotation gates are adjusted by iteration to make the conditional distribution close to the training data distribution; Step 4: running the decoding quantum circuit for decoding, when the quantum computer produces noise or new errors, the decoding quantum circuit will directly output the corresponding error correction logical operator with the syndrome as the input, and real-time decoding and error correction are performed.

2. The quantum circuit based quantum computer error correction method of claim 1, wherein, In step 1, the quantum code is represented by a Tanner graph.

3. The quantum circuit based quantum computer error correction method of claim 1, wherein, In step 4, the decoding quantum circuit is a pure quantum operation and does not need the participation of classical operations.

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