Information processing program, information processing device, and information processing method

Abstract

In quantum error correction, there occurs erroneous estimation of occurred quantum error under such a condition that a connection relationship and a weight of an edge of a decoder graph used for estimating an error are not optimized and hence error correction performance deteriorates. Provided is an information processing program that causes a computer to execute processing for calculating error occurrence probabilities for a qubit on the basis of a measurement result of a surface code in error correction in a quantum computer that includes the qubit, selecting an error occurrence probability proportional to the magnitude of noise occurring to the quantum computer among the error occurrence probabilities, and generating a decoder graph, which is a weighted graph of the surface code, on the basis of the selected error occurrence probability. This can increase the error correction performance in the quantum error correction.

Description

Technical Field

[0001] The present invention relates to an information processing program, an information processing apparatus, and an information processing method for performing quantum error correction by a quantum computer.

Background Art

[0002] Quantum computers are vulnerable to environmental noise and cannot perform large-scale calculations as they are. To give quantum computers resistance to noise, for example, there is a method of redundantizing quantum information using a plurality of physical qubits.

[0003] Quantum errors may occur in the physical qubits used for redundantizing quantum information, and quantum error correction, that is, a process of detecting and correcting quantum errors without measuring (destroying) the written quantum information, is performed. Note that quantum error correction is also called quantum error correction coding.

[0004] Quantum error correction by encoding quantum information redundantly is called a quantum error correction code, and in recent years, the surface code has attracted attention due to its high error correction performance and ease of implementation.

Prior Art Documents

Patent Documents

[0005]

Patent Document 1

Patent Document 2

Patent Document 3

Patent Document 4

Summary of the Invention

Problems to be Solved by the Invention

[0006] However, in quantum error correction, if the connection relationships and edge weights of the decoder graph used for error estimation are not optimized, misestimation of the quantum error occurs, degrading the error correction performance.

[0007] One aspect of this approach is to improve the error correction performance of quantum error correction. [Means for solving the problem]

[0008] In one embodiment, an information processing program calculates the probability of error occurring in a qubit based on the measurement results of a surface code in error correction of a quantum computer, which includes qubits. The program then selects an error probability from among the probability probabilities that is proportional to the magnitude of noise generated in the quantum computer, and causes the computer to perform a process of generating a decoder graph, which is a weighted graph of the surface code, based on the selected error probability. [Effects of the Invention]

[0009] In one respect, it can improve the error correction performance of quantum error correction. [Brief explanation of the drawing]

[0010] [Figure 1] Figure 1 shows an example of the configuration of surface codes. [Figure 2] Figure 2 shows an example of a syndrome measurement circuit. [Figure 3] Figure 3 is a diagram illustrating the estimation of quantum errors using a decoder graph. [Figure 4] Figure 4 shows an example of what happens when an error occurs in the measurement qubit. [Figure 5] Figure 5 is a diagram illustrating the misestimation of quantum errors. [Figure 6] Figure 6 shows an example of a method for dealing with misestimations of quantum errors (1). [Figure 7]Figure 7 shows an example (2) of a method for dealing with misestimations of quantum errors. [Figure 8] Figure 8 is a diagram illustrating the detection of quantum errors during measurement (1). [Figure 9] Figure 9 is a diagram illustrating the detection of quantum errors during measurement (2). [Figure 10] Figure 10 is a diagram illustrating hook errors. [Figure 11] Figure 11 shows examples of successful and unsuccessful quantum error correction using existing method 1. [Figure 12] Figure 12 is a diagram illustrating the calculation of the error probability pj. [Figure 13] Figure 13 is a diagram illustrating the calculation of the probability of a single reversal of a syndrome tangent to an open boundary. [Figure 14] Figure 14 shows an example of the error probability calculation results using existing method 2. [Figure 15] Figure 15 shows an example of the configuration of the information processing device 10 according to this embodiment. [Figure 16] Figure 16 shows an example of constructing a correspondence between edges on the decoder graph and data qubits to be corrected. [Figure 17] Figure 17 is a flowchart showing an example of the quantum error correction process according to this embodiment. [Figure 18] Figure 18 is a flowchart showing an example of the decoder graph generation process according to this embodiment. [Figure 19] Figure 19 is a flowchart showing an example of the measurement sampling process according to this embodiment. [Figure 20] Figure 20 shows an example of the hardware configuration of the information processing device 10 according to this embodiment. [Modes for carrying out the invention]

[0011] The following describes in detail, with reference to the drawings, embodiments of the information processing program, information processing apparatus, and information processing method according to this embodiment. However, this embodiment is not limited to these embodiments. Furthermore, each embodiment can be combined as appropriate within a consistent scope.

[0012] First, the surface code for quantum error correction implemented in this embodiment will be described. The surface code is a quantum error correction code that is constructed by arranging qubits in a two-dimensional square lattice with open boundary conditions and causing adjacent qubits to interact with each other.

[0013] Figure 1 shows an example of the configuration of a surface code. In Figure 1, white circles (○) represent data qubits for writing quantum information, and black circles (●) represent measurement qubits (also called auxiliary qubits) for detecting quantum errors. As shown in Figure 1, there are multiple data qubits, but they are collectively referred to as data qubit 60. In surface codes, the location of a quantum error is estimated based on the measurement values ​​of each measurement qubit. As shown in Figure 1, there are also multiple measurement qubits, which are collectively referred to as measurement qubit 70 or 71. There are two types of measurement qubits because they detect different things. In Figure 1, measurement qubit 70, which is located on the shaded square, detects bit inversion, and measurement qubit 71, which is located on the dotted filled square, detects phase inversion. Measurement qubits 70 and 71 only differ in the content they detect; the decoding and other processing for them are the same. Therefore, in the following description of this embodiment, we will use measurement qubit 70, which detects bit inversion, for explanation.

[0014] Next, we will describe the measurement of the data qubit 60 and the measurement qubit 70. Figure 2 shows an example of a syndrome measurement circuit. The measurement circuit shown in Figure 2 is a circuit for measuring the state of the data qubit 60 and the state of the measurement qubit 70, i.e., bit inversion. The data qubit and the measurement qubit interact by executing a quantum circuit called a syndrome measurement circuit, and an error occurring in the data qubit can be detected by measuring the state of the adjacent measurement qubit. In the example in Figure 2, |ψ Z > indicates the state of the measurement qubit 70, |ψ a >~|ψ d The arrow indicates the state of the four data qubits 60 adjacent to the measurement qubit 70. For example, if an error occurs in a data qubit 60, the measurement result of the adjacent measurement qubit 70 will invert from +1 to -1. The measurement result of a measurement qubit is called a syndrome. A decoder graph is then generated by connecting each syndrome with an edge, and the location of the error is estimated.

[0015] Next, we will explain the decoder graph. Figure 3 is a diagram illustrating the estimation of quantum errors using a decoder graph. Figure 3 shows the decoder graph of an error correction code (repeating code) generated by arranging data qubits 60 and measurement qubits 70 alternately in a one-dimensional manner. In Figure 3, the measurement results of measurement qubits 70-1, 70-2, 70-3, etc. are shown as measurement results 80-1, 80-2, 80-3, etc. (hereinafter collectively referred to as "measurement result 80"), respectively. Each of the measurement result 80 is connected by edge 90 to generate the decoder graph. In the decoder graph, the small black circles representing the measurement result 80 are called vertices.

[0016] If an error occurs in data qubit 60, the measurement result of the adjacent measurement qubit 70 is inverted. Therefore, as shown in Figure 3, for example, if an error occurs in data qubit 60-3, the measurement results 80-2 and 80-3 of the measurement qubits 70-2 and 70-3 on either side of it are inverted. In Figure 3, measurement results 80-2 and 80-3 are shown as larger circles to indicate that they are inverted. Furthermore, measurement results 80-2 and 80-3 are correlated because they relate to the same error in data qubit 60-3, and for example, as shown in Figure 3, edge 90 is shown as thicker. From the above, it can be concluded that the quantum error estimation problem can be treated, for example, as a matching problem on a decoder graph.

[0017] Furthermore, quantum errors can occur not only in the data qubit 60 but also in the measurement qubit 70. Figure 4 shows an example of what happens when an error occurs in the measurement qubit. As shown in Figure 4, for example, if an error occurs in the measurement qubit 70-2, only the measurement result 80-2 is inverted. However, the case in which only the measurement result 80-2 is inverted can occur not only when an error occurs in the measurement qubit 70-2 but also when an error occurs in the data qubit 60, which could lead to misestimation of the quantum error.

[0018] Figure 5 illustrates the misestimation of quantum errors. As shown in Figure 5, the case in which only measurement result 80-2 is inverted can also occur if errors occur in both data qubits 60-1 and 60-2. More specifically, if an error occurs in data qubit 60-1, the measurement result 80-1 of the adjacent measurement qubit 70-1 is inverted. Then, if an error occurs in data qubit 60-2, the measurement results 80-1 and 80-2 of the adjacent measurement qubits 70-1 and 70-2 are inverted. In other words, if errors occur in both data qubits 60-1 and 60-2, measurement result 80-1 is inverted twice, resulting in a state where only measurement result 80-2 is inverted, as shown in Figure 5. Therefore, this method of estimating quantum errors using a decoder graph can lead to misestimation.

[0019] Misestions of quantum errors in such decoder graphs can be addressed by repeatedly performing syndrome measurements. Figure 6 shows an example (1) of a method for addressing misestimations of quantum errors. The decoder graph shown in Figure 6 is obtained by repeatedly performing syndrome measurements and arranging the measurement results in chronological order along time t. In the following explanation, the syndrome measurement at time t will be referred to as a round, for example, the round at time t=1 will be referred to as round 1. In the example in Figure 6, it is shown that the measurement result 80-2 of the measured qubit 70-2 is inverted only in round 1.

[0020] Figure 7 shows an example (2) of how to address misestimations of quantum errors. The decoder graph shown in Figure 7 is a continuation of Figure 6 and shows the measurement results up to round 2. In the example in Figure 7, the measurement result 80-2 of measurement qubit 70-2 is inverted in both round 1 and round 2. Since the error is reset with each round, the fact that only measurement result 80-2 is inverted in both round 1 and round 2 suggests that, for example, there is a high probability that an error has occurred in measurement qubit 70-2. In this way, by repeating syndrome measurements, it is possible to address misestimations of quantum errors in the decoder graph.

[0021] Note that errors may occur during syndrome measurement, in which case the syndrome is reversed with a time delay. Figure 8 is a diagram illustrating the detection of quantum errors during measurement (1). Figure 9 is a diagram illustrating the detection of quantum errors during measurement (2). Figures 8 and 9 are a continuation of Figure 7, with Figure 8 showing the measurement results up to round 3 and Figure 9 showing the measurement results up to round 4. For example, even if an error occurs in data qubit 60-2 during the round 3 syndrome measurement shown in Figure 8, the measurement results 80-1 and 80-2 of the measurement qubits 70-1 and 70-2 on either side of it will not be reversed. Note that the reason why the measurement result 80-2 of round 3 is reversed in Figure 8 is because an error in data qubit 60-3 was detected. If an error occurs in data qubit 60-2 during the round 3 syndrome measurement, the measurement results 80-1 and 80-2 of round 4 will be reversed with a time delay, as shown in Figure 9. Note that the measurement result for round 4, 80-2, is not inverted because two errors were detected in data qubits 60-2 and 60-3, causing it to invert twice and ultimately return to a non-inverted state.

[0022] Furthermore, in the decoder graph, if an error occurs during syndrome measurement, a single error can cause two syndromes that should have reversed in the same round to reverse in different rounds, even though they are spaced apart in time. This phenomenon is called a hook error. Figure 10 illustrates a hook error. The example in Figure 10 shows that measurement result 80-1 in round 4 and measurement result 80-2 in round 5 should have reversed in the same round due to an error in data qubit 60-2, but instead reversed in different rounds due to a hook error.

[0023] If a decoder graph is generated that does not take correlation into account due to Hook errors or other factors, it may lead to misestimation of quantum errors. For example, as shown by the diagonal dotted line in Figure 10, it is necessary to add an edge connecting the two measurement results to show that the measurement result 80-1 from round 4 and the measurement result 80-2 from round 5 are correlated. In this way, in order to address Hook errors and other factors and to perform more accurate quantum error estimation and correction, it is necessary to adjust the connection relationships and edge weights that indicate the correlation of the measurement results in the decoder graph to match the specific noise acting on them. Adjustments to the connection relationships and edges for measurement results to address Hook errors and other factors can be performed, for example, using existing methods 1 and 2 as described below.

[0024] First, as an existing method (Method 1), there is a method that models the noise generated in a quantum computer, infers the correlation of syndrome inversion from the noise model, and generates a decoder graph based on the inferences. However, Method 1 is only effective if the noise generated in the actual machine follows the assumed noise model. Therefore, if the noise that can be generated in the actual machine differs from the assumed one, there is a possibility of missing or inaccurate error correlations, which can lead to failure of quantum error correction.

[0025] Figure 11 shows successful and unsuccessful examples of quantum error correction using existing method 1. In the decoder graph shown in Figure 11, the small black circles represent the measured qubits, and each edge represents the data qubits that may be corrected. The larger circles, representing the measurement results 80-x and 80-y, represent the inverted syndrome. The line segment 91 connecting the measurement results 80-x and 80-y represents the connection relationship between the actual correct syndromes, and the line segments 92 and 93 represent the correlation of data qubit errors estimated from the inverted syndrome patterns. Thus, the correlation of data qubit errors is represented as a connection relationship on the decoder graph. In the example in Figure 11, the total length (weight) of the estimated correlation paths is assumed to be 3 (edges).

[0026] As shown on the left side of Figure 11, line segment 92 is correctly connected so that the measurement results 80-x and 80-y are correlated. On the other hand, as shown on the right side of Figure 11, line segment 93 connects each of the measurement results 80-x and 80-y to the open boundaries at both ends of the lattice. In this case, an error occurs in the estimation of the correlation of the data qubit errors, and quantum error correction fails.

[0027] As shown in Figure 11, for example, in a situation where a 2-qubit error occurs with a probability proportional to the noise level, if the decoder graph generated by the existing method 1 is used to estimate the error, quantum error correction will fail with a probability of 1 / 2. The 1 / 2 probability is because two types of estimation results for the correlation of errors in the data qubits are obtained in equal proportions.

[0028] Next, as an existing method 2, there is a method of calculating the correlation of syndrome inversion by measurement sampling and adjusting the connection relationships and edge weights of the decoder graph based on the results. For example, if there is a correlation between the inversions of two syndromes, such as measurement results 80-1 and 80-2 shown in Figure 10, it can be assumed that there is a connection relationship between the two vertices in the decoder graph. Therefore, by repeating the syndrome measurement a sufficient number of times, the error occurrence probability p, which is the correlation of syndrome inversion, can be calculated. ij The probability of an error occurring, p, can be calculated. ij In this model, i and j are sequential numbers for the syndrome, set according to the rule, for example, "(round number) × (number of measured qubits) + (row number) × (number of measured qubits per row) + (column number)". Existing Method 2 can construct a decoder graph without modeling the noise generated in the quantum computer, thus avoiding the missed correlations and errors that plagued Existing Method 1.

[0029] Error probability p ij This will be explained in detail. Figure 12 shows the error probability p. ijThis is a diagram for explaining the calculation of i p j , p ij , and p i indicate the probability of an error occurring in the edge between the corresponding syndromes, that is, the correlation of the probability of each corresponding syndrome flipping. Also, 〈x j 〉, 〈x i 〉, and 〈x j x i 〉 indicate the expected values of the measurement results of the corresponding syndromes. Also, the relationship between each expected value 〈x j 〉, 〈x i 〉, and 〈x j 〉 and each error occurrence probability p i , p j , and p ij can be expressed using the following equation (1).

[0030]

Equation

[0031] Also, by calculating equation (1) to obtain each expected value 〈x i 〉, 〈x j 〉, and 〈x i x j 〉 and applying them to the following equation (2), the error occurrence probability p ij can be calculated.

[0032]

Equation

[0033] However, in the case of the surface code, the boundary of the code is an open boundary condition, and there is a case where a syndrome flips alone. Therefore, the decoder graph cannot be created by only calculating the correlation of the flips between two syndromes. Thus, the error occurrence probability p ijBy applying the calculation of the following equation (3), the probability p of a syndrome tangent to an open boundary reversing on its own can be calculated. iB It can be calculated.

[0034]

number

[0035] In equation (3), p iΣ This is the sum of probabilities that a syndrome tangent to an open boundary will reverse due to an error occurring on the edge between the syndrome tangent to the open boundary and an adjacent syndrome. Figure 13 is a diagram illustrating the calculation of the probability of a syndrome tangent to an open boundary reversing on its own. In Figure 13, p ij1 , p ij2 , p ij3 , p ij4 , p ij5 This is the probability that an error occurs on each edge between a syndrome touching an open boundary and an adjacent syndrome. As shown in Figure 13, the probability p of an error occurring on each of these edges is... ij1 , p ij2 , p ij3 , p ij4 , p ij5 Using the following equation (4), p iΣ It can be summarized as follows.

[0036]

number

[0037] In equation (4), p iΣ The i-th syndrome has a total of k connected destination syndromes (j1, j2, ..., j k This indicates the probability that, given the existence of such connections, an error occurring on any of the edges will cause the i-th syndrome to reverse. ijk This is the i-th syndrome and j kThis shows the probability that an error occurs on an edge between the i-th syndrome. g is a function that gives the probability of the final reversal occurring when trials are performed to reverse the syndrome with probabilities p and q, respectively. The reason for subtracting 2pq is that the syndrome returns to its original state after two reversals.

[0038] However, the existing method 2 also has the following problems. Figure 14 shows an example of the error probability calculation results using the existing method 2. Also, Figure 14 shows the error probability p calculated for a surface code with a code distance d=5 using the existing method 2. ij This is a graph of the results. The code distance d is a parameter used to determine the number of errors that the code can correct. For example, the number of errors that the code can correct is "(d-1) / 2". In Figure 14, the vertical and horizontal axes of the graph represent the syndrome serial numbers i and j, respectively, and the intensity of the intensity indicates the error occurrence probability p. ij The value of is shown. Also, in the example in Figure 14, p ij This displays the components with the smallest values.

[0039] However, as shown in the lower left circle of Figure 14, for example, the calculated error probability p ij Because it contains statistical fluctuations, p ij Even for components that should be equal to 0, their values ​​will be finite. p has such components. ij When a decoder graph is generated using this method, extra connections are added to the decoder graph, which can lead to misestimation of quantum errors and thus degrade error correction performance.

[0040] Therefore, in this embodiment, the error occurrence probability p is changed to p ij This is calculated repeatedly, and only the component proportional to p is extracted. ij The average value of the component that should be =0 remains 0 even if the error probability p is changed on each side, therefore p ijThis eliminates the effect of sampling errors in components that should be equal to 0. Methods for changing the error probability p include, for example, inserting waiting periods where no operation is performed in each part of the quantum circuit, thereby increasing noise due to relaxation.

[0041] (Functional configuration of the information processing device 10) Next, the functional configuration of the information processing device 10, which is the main execution unit of this embodiment, will be described. Figure 15 is a diagram showing an example of the configuration of the information processing device 10 according to this embodiment. As shown in Figure 15, the information processing device 10 has a communication unit 20, a storage unit 30, and a control unit 40. Although not shown, the information processing device 10 may also be equipped with input devices such as a keyboard or mouse, and output devices such as a display.

[0042] The communication unit 20 is a processing unit that controls communication with other computers, etc., and is, for example, a communication interface such as a network interface card.

[0043] The storage unit 30 has the function of storing various data and programs executed by the control unit 40, and is implemented by a storage device such as memory or a hard disk. The storage unit 30 stores measurement results 31, decoder graph information 32, and estimation results 33, etc.

[0044] Measurement result 31 stores the measurement results of the surface code, for example, the measurement results of the measured qubit, i.e., information about the syndrome. Measurement result 31 also stores, for example, the correlation p of the syndrome inversion calculated from the measurement results. ij The probability p that a syndrome tangent to an open boundary reverses on its own. iB Information regarding calculated values ​​such as these is stored.

[0045] Decoder graph information 32 stores information about the decoder graph generated by connecting each syndrome with an edge, for example.

[0046] The estimation result 33 stores information such as the estimation result of the quantum error estimated using the decoder graph.

[0047] The above information stored in the memory unit 30 is merely an example, and the memory unit 30 can store various other types of information besides the above.

[0048] The control unit 40 is a processing unit that oversees the entire information processing device 10, and is, for example, a processor such as a CPU (Central Processing Unit) or a QPU (Quantum Processing Unit). The control unit 40 includes processing units such as a measurement unit 41, a calculation unit 42, a selection unit 43, a generation unit 44, an estimation unit 45, and a correction unit 46. Each processing unit is an example of an electronic circuit in the processor or an example of a process executed by the processor.

[0049] The measurement unit 41, for example, changes the error probability p to measure the surface code in error correction of a quantum computer, that is, to measure the value of the measurement qubit. In order to change the error probability p, the measurement unit 41 inserts waiting times in which no operation is performed on each part of the quantum circuit, thereby increasing the noise.

[0050] The calculation unit 42 calculates the error probability of a qubit based on the measurement results of the surface code measured by the measurement unit 41, which includes, for example, a qubit. The measurement results of the surface code measured by the measurement unit 41 may include measurement results of the surface code measured repeatedly with varying noise levels. Furthermore, the error probability is calculated based on, for example, the correlation p of syndrome inversion. ij The probability p that a syndrome tangent to an open boundary reverses on its own. iB This may include things like the following.

[0051] The selection unit 43 selects, for example, an error occurrence probability calculated by the calculation unit 42 that is proportional to the magnitude of noise generated in the quantum computer. This may include, for example, setting the error occurrence probability calculated by the calculation unit 42 that is not proportional to the magnitude of noise generated in the quantum computer to a value of 0, and selecting an error occurrence probability that is proportional to the magnitude of the noise. The determination of whether or not it is proportional to the magnitude of the noise may have a certain degree of leeway, and it may be determined whether or not it is proportional to the magnitude of the noise within a range that can be considered proportional, even if it is not exactly a constant multiple.

[0052] The generation unit 44 generates a decoder graph, which is a weighted graph of surface codes, based on the error probability selected by the selection unit 43. This may include, for example, a process of constructing a decoder graph that includes connection relationships, which are the correlation relationships of errors in the qubits in the surface codes, based on the error probability selected by the selection unit 43. The construction of the decoder graph will be described in more detail.

[0053] Figure 16 shows an example of constructing a correspondence between edges on a decoder graph and data qubits to be corrected. The grid shown in Figure 16 is an example of a decoder graph, where the vertical direction corresponds to the time direction and the direction perpendicular to the time direction corresponds to the spatial direction. The black circles on the grid represent syndromes, i.e., the measurement results of the measured qubits, and each edge represents a data qubit. The correspondence between each edge and a data qubit is, for example, the correlation p of syndrome inversion. ij The probability p that a syndrome tangent to an open boundary reverses on its own. iBThis can be determined from the above. As an example of constructing a correspondence, edges connected in the spatial direction on the lattice correspond to data qubits located at the center of the edges, while edges connected in the temporal direction do not have any particular corresponding data qubits and are not subject to quantum error correction. Furthermore, line segments 94 and 95, which are edges connected in the spatial and temporal directions, show the correlation between the connected syndromes and correspond to data particle bits located on the shortest path connecting the endpoints of the edges projected onto the lattice. For example, in the lattice shown in Figure 16, line segment 94 corresponds to the data qubit at position (i,j+1), and line segment 95 corresponds to the data qubits at positions (i,j+1) and (i+1,j+2).

[0054] Regarding the correspondence between edges on the decoder graph and the data qubits to be corrected, the estimated quantum error is given as a set of edges that connect pairs of vertices on the decoder graph via the shortest path. When performing quantum error correction using the quantum error estimation results from the decoder graph, the edges that correspond to the code data qubit are selected from the given set of edges and corrected.

[0055] The estimation unit 45 estimates the error of the qubits using, for example, the decoder graph generated by the generation unit 44.

[0056] The correction unit 46 performs quantum error correction on the error based on the estimation result of the qubit error estimated by the estimation unit 45, for example.

[0057] (Process flow) Next, the quantum error correction process according to this embodiment will be described in terms of its processing flow. Figure 17 is a flowchart showing an example of the quantum error correction process according to this embodiment.

[0058] First, the information processing device 10 repeatedly measures the surface code by changing the noise, calculates the probability of a qubit error occurring based on the surface code measurement results, and generates a decoder graph based on the said error probability (step S101). The decoder graph generation process in step S101 will be explained in more detail with reference to Figure 18.

[0059] Figure 18 is a flowchart showing an example of the decoder graph generation process according to this embodiment. First, the information processing device 10 performs measurement sampling (step S201). The measurement sampling process in step S201 will be explained in more detail using Figure 19.

[0060] Figure 19 is a flowchart showing an example of the measurement sampling process according to this embodiment. First, the information processing device 10 repeatedly performs syndrome measurements for a predetermined number of samples, such as the number of measurement qubits × the number of rounds (step S301).

[0061] Next, the information processing device 10 repeats the syndrome measurement for a predetermined number of samples, for example, by increasing the noise with each repetition (step S302). After step S302 is executed for the number of samples, the measurement sampling process shown in Figure 19 is completed, and the process returns to the decoder graph generation process shown in Figure 18.

[0062] Next, the information processing device 10 calculates the correlation p of syndrome reversal based on the measurement results of the syndrome measurement performed in steps S301 and S302. ij And the probability p that a syndrome tangent to an open boundary reverses on its own. iB The result is calculated (step S202). This yields the calculation result shown in Figure 14.

[0063] Next, the information processing device 10, for example, the p calculated in step S202 ij or p iB It is determined whether or not it is proportional to the magnitude of the noise (step S203). ij or p iBIf p is not proportional to the noise level (step S203: No), the information processing device 10, for example, p which is not proportional to the noise level ij or p iB Set the value to 0 (step S204).

[0064] p ij or p iB If it is proportional to the magnitude of the noise (step S203: Yes), or after step S204 is executed, the information processing device 10, for example, p ij and p iB Based on this, a decoder graph is generated (step S205). After step S205 is executed, the decoder graph generation process shown in Figure 18 is completed, and the process returns to the quantum error correction process shown in Figure 17.

[0065] Next, the information processing device 10 performs, for example, syndrome measurement (step S102).

[0066] Next, the information processing device 10 uses, for example, the decoder graph generated in step S101 to estimate the error of the qubits in the syndrome measurement in step S102 (step S103).

[0067] Next, the information processing device 10 performs quantum error correction on the error estimated in step S103, for example (step S104). After step S104 is executed, the quantum error correction process shown in Figure 17 is completed.

[0068] (effect) As described above, the information processing device 10 calculates the error probability of a qubit based on the measurement results of the surface code in error correction of a quantum computer, which includes qubits. It then selects an error probability from among the error probabilities that is proportional to the magnitude of the noise generated in the quantum computer, and generates a decoder graph, which is a weighted graph of the surface code, based on the selected error probability.

[0069] In this way, the information processing device 10 generates a decoder graph by selecting from the error occurrence probabilities of the qubits, which are calculated based on the measurement results of the surface code, that are proportional to the magnitude of the noise. This allows the information processing device 10 to improve the error correction performance of quantum error correction.

[0070] Furthermore, the process for calculating the probability of error occurrence, performed by the information processing device 10, includes the process of calculating the probability of error occurrence based on the measurement results of surface codes that have been repeatedly measured while varying the noise level, and the process for selecting the probability of error occurrence, also performed by the information processing device 10, includes setting the probability of error occurrence that is not proportional to the noise level to a value of 0, and selecting the probability of error occurrence that is proportional to the noise level.

[0071] This allows the information processing device 10 to improve the error correction performance of quantum error correction.

[0072] Furthermore, the process of generating a decoder graph, performed by the information processing device 10, includes the process of generating a decoder graph that includes connection relationships, which are correlations of errors in qubits in a surface code, based on the selected error occurrence probability.

[0073] This allows the information processing device 10 to improve the error correction performance of quantum error correction.

[0074] Furthermore, the information processing device 10 uses a decoder graph to estimate the error of the qubit and performs quantum error correction on the error based on the error estimation result.

[0075] This allows the information processing device 10 to improve the error correction performance of quantum error correction.

[0076] (system) The processing procedures, control procedures, specific names, and various data and parameters shown in the above documents and drawings may be changed at will unless otherwise specified. Furthermore, the specific examples, distributions, and numerical values ​​described in the embodiments are merely examples and may be changed at will.

[0077] Furthermore, the specific forms of distribution and integration of the components of the information processing device 10 are not limited to those shown in the figures. For example, the calculation unit 42 of the information processing device 10 may be distributed to multiple processing units, or the measurement unit 41 and the calculation unit 42 of the information processing device 10 may be integrated into a single processing unit. In other words, all or part of its components may be functionally or physically distributed and integrated in any unit depending on various loads and usage conditions. Moreover, each processing function of each device may be implemented, in whole or in any part thereof, by a CPU or QPU and a program that is analyzed and executed by the CPU or QPU, or by hardware using wired logic.

[0078] Figure 20 shows an example of the hardware configuration of the information processing device 10 according to this embodiment. As shown in Figure 20, the information processing device 10 has a communication interface 10a, an HDD (Hard Disk Drive) 10b, memory 10c, and a processor 10d. Furthermore, each of the parts shown in Figure 20 is interconnected by a bus or the like.

[0079] The communication interface 10a is a network interface card or the like, and communicates with other information processing devices. The HDD 10b stores, for example, programs and data that operate the various functions of the information processing device 10.

[0080] The processor 10d can be a CPU, QPU, MPU (Micro Processing Unit), GPU (Graphics Processing Unit), etc. Alternatively, the processor 10d may be implemented using an integrated circuit such as an ASIC (Application Specific Integrated Circuit) or FPGA (Field Programmable Gate Array). For example, the processor 10d reads a program that performs the same processing as the various processing units shown in Figure 15 from the HDD 10b or similar and loads it into memory 10c. This allows the processor 10d to operate as a hardware circuit that executes processes to realize each function of the information processing device 10.

[0081] Furthermore, the information processing device 10 can also achieve the same functionality as in the above embodiment by reading the above program from the recording medium using a media reader and executing the read program. It should be noted that the program referred to in this other embodiment is not limited to being executed by the information processing device 10. For example, the above embodiment may also be applied to cases where another information processing device executes the program, or where another information processing device and the information processing device 10 cooperate to execute the program.

[0082] The program may be distributed via a network such as the Internet. Furthermore, the program may be recorded on a computer-readable storage medium such as a hard disk, flexible disk (FD), CD-ROM, MO (Magneto-Optical disk), or DVD (Digital Versatile Disc). The program may then be executed by being read from the storage medium by an information processing device 10 or the like. [Explanation of symbols]

[0083] 10 Information Processing Devices 10a communication interface 10b HDD 10c memory 10d processor 20 Communications Department 30 Storage section 31 Measurement results 32 Decoder Graph Information 33 Estimation results 40 Control Unit 41 Measuring part 42 Calculation Section 43 Selection Section 44 Generation part 45 Estimation part 46 Correction Section 60 data qubits 70, 71 measurement qubits 80 Measurement results 90 sides 91-95 line segments

Claims

1. Based on the measurement results of the surface code in error correction of a quantum computer, including qubits, the probability of an error occurring in the qubit is calculated. From the aforementioned error occurrence probabilities, select the error occurrence probability that is proportional to the magnitude of the noise generated in the quantum computer, Based on the selected error probability, a decoder graph, which is a weighted graph of the surface codes, is generated. An information processing program characterized by having a computer perform the processing.

2. The process for calculating the probability of the aforementioned error occurring is: The error probability is calculated based on the measurement results of the surface code, which are repeatedly measured while varying the noise level. Including processing, The process for selecting the aforementioned error occurrence probability is: The error probability that is not proportional to the noise level is set to 0, and the error probability that is proportional to the noise level is selected. The information processing program according to claim 1, characterized by including processing.

3. The process for generating the decoder graph is as follows: Based on the selected error probability, the decoder graph is generated, which includes the connection relationships that are the correlations of errors in the qubits in the surface code. An information processing program according to claim 1 or 2, characterized by including processing.

4. Using the decoder graph, the error of the qubit is estimated. Based on the estimated error, quantum error correction is performed on the error. The information processing program according to claim 1 or 2, characterized in that it causes the computer to perform the processing.

5. Based on the measurement results of the surface code in error correction of a quantum computer, including qubits, the probability of an error occurring in the qubit is calculated. From the aforementioned error occurrence probabilities, select the error occurrence probability that is proportional to the magnitude of the noise generated in the quantum computer, Based on the selected error probability, a decoder graph, which is a weighted graph of the surface codes, is generated. An information processing device characterized by comprising a control unit that performs processing.

6. Based on the measurement results of the surface code in error correction of a quantum computer, including qubits, the probability of an error occurring in the qubit is calculated. From the aforementioned error occurrence probabilities, select the error occurrence probability that is proportional to the magnitude of the noise generated in the quantum computer, Based on the selected error probability, a decoder graph, which is a weighted graph of the surface codes, is generated. An information processing method characterized in that the processing is performed by a computer.

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