Information processing device, parallel quantum computing method, parallel quantum computing program, and parallel quantum computing system

Abstract

To provide an information processing device, a parallel quantum computing method, a parallel quantum computing program, and a parallel quantum computing system that enable improved efficiency of quantum computing using quantum computers. [Solution] The information processing device according to the embodiment comprises a division unit, an instruction unit, an acquisition unit, and a partitioning unit. The division unit divides a plurality of qubits into a specified number of independent parts in an arrangement layout representing the connection relationships between a plurality of qubits implemented in a quantum computer. The instruction unit transmits instructions to the quantum computer for executing a specified number of quantum computations in parallel, corresponding to each of the specified number of independent parts.

Description

Technical Field

[0001] Embodiments of the present invention relate to an information processing apparatus, a parallel quantum computing method, a parallel quantum computing program, and a parallel quantum computing system.

Background Art

[0002] In recent years, with the progress of quantum computer processors, NISQ (Noisy Intermediate-Scale Quantum) devices with more than 100 qubits have become available on the cloud (as of February 2024) (Non-Patent Document 1). With the progress of quantum hardware, there is a shift from quantum-classical hybrid algorithms executed using a small number of qubits to quantum computing executed by superimposing dozens to 100 qubits. However, in order to perform high-precision calculations using a large number of 100-qubit-class qubits, advanced quantum circuit design and transpilation techniques are required, which are difficult for users to implement. Moreover, many of these large-scale calculations are dynamics simulations in limited Hamiltonians and remain in the realm of basic research (Non-Patent Documents 2, 3, 4).

[0003] On the other hand, quantum chemistry calculations and quantum circuit learning based on the variational quantum eigensolver (VQE) (Non-Patent Documents 5, 6) reported so far require a small number of qubits and are useful for exploring the use cases of quantum computers. Also, since the scale of the quantum circuit is small, relatively high-precision quantum calculations can be performed on current NISQ devices without advanced circuit design techniques, so quantum calculations with a small number of qubits are easy for users to use. However, for quantum computers equipped with processors with more than 100 qubits, quantum calculations using only a small number of qubits cannot be said to effectively utilize the computing resources of the quantum computer.

Prior Art Documents

Non-Patent Documents

[0004] [Non-Patent Document 1] IBM Quantum Platform. https: / / quantum.ibm.com / . [Non-Patent Document 2] Youngseok Kim, Andrew Eddins, Sajant Anand, Ken Xuan Wei, Ewout Van Den Berg, Sami Rosenblatt, Hasan Nayfeh, Yantao Wu, Michael Zaletel, Kristan Temme, et al. Evidence for the utility of quantum computing before fault tolerance. Nature, Vol. 618, No. 7965, pp. 500-505, 2023. [Non-Patent Document 3] Edward H Chen, Guo-Yi Zhu, Ruben Verresen, Alireza Seif, Elisa Baumer, David Lay-den, Nathanan Tantivasadakarn, Guanyu Zhu, Sarah Sheldon, Ashvin Vishwanath, et al. Realizing the nishimori transition across the error threshold for constant-depth quantum circuits. arXiv preprint arXiv:2309.02863, 2023. [Non-Patent Document 4] Oles Shtanko, Derek S Wang, Haimeng Zhang, Nikhil Harle, Alireza Seif, Ramis Movassagh, and Zlatko Minev. Uncovering local integrability in quantum many-body dynamics. arXiv preprint arXiv:2307.07552, 2023. [Non-Patent Document 5] Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Pe-ter J Love, Alan Aspuru-Guzik, Jeremy LO brien. A variational eigenvalue solver on a photonic quantum processor. Nature communications, Vol. 5, No. 1, p. 4213, 2014. [Non-Patent Document 6] Jarrod R McClean, Jonathan Romero, Ryan Babbush, and Alan Aspuru-Guzik. The theory of variational hybrid quantum-classical algorithms. New Journal of Physics, Vol. 18, No. 2, p. 023023, 2016. [Non-Patent Document 7] Sam McArdle, Suguru Endo, Alan Aspuru-Guzik, Simon C Benjamin, and Xiao Yuan. Quantum computational chemistry. Reviews of Modern Physics, Vol. 92, No. 1, p. 015003, 2020. [Overview of the project] [Problems that the invention aims to solve]

[0005] The problem that this invention aims to solve is to provide an information processing device, a parallel quantum computing method, a parallel quantum computing program, and a parallel quantum computing system that enable improved efficiency of quantum computing by quantum computers. [Means for solving the problem]

[0006] The information processing apparatus according to the embodiment comprises a division unit, an instruction unit, an acquisition unit, and a partitioning unit. The division unit divides a plurality of qubits implemented in a quantum computer into a specified number of independent parts in an arrangement layout representing the connection relationships between the plurality of qubits. The instruction unit transmits instructions to the quantum computer for executing a specified number of quantum computations in parallel, corresponding to each of the specified number of independent parts. [Brief explanation of the drawing]

[0007] [Figure 1] A diagram showing an example configuration of a parallel quantum computing system. [Figure 2] A diagram showing an example configuration of a classical computer (information processing device). [Figure 3] A diagram illustrating the processing procedure of a classical computer in parallel quantum computing. [Figure 4] A diagram showing an example of a display screen for the layout. [Figure 5] Diagram showing the display screen of the layout after division. [Figure 6] A diagram showing an example of a display screen for classical calculation results. [Figure 7] A diagram showing the circuit configuration of the parallel quantum circuit according to Example 1. [Figure 8] A diagram showing the number of measurements for each measurement result of the parallel quantum circuit according to Example 1. [Figure 9] This figure shows the circuit configuration of a parameterized quantum circuit with 4 quantum bits of the Unitary Coupled Cluster type according to Example 2. [Figure 10] This figure shows the error between the energy expectation value obtained from a noise-free, ideal simulator and the energy expectation value obtained from parallel quantum computation using a Qasm simulator, when the number of measurements in Example 2 is varied. [Figure 11] This figure shows the circuit configuration of a hardware-efficient type 4-qubit parameterized quantum circuit according to Example 3. [Figure 12]Figure showing the comparison between the energy expectation value obtained by parallel quantum calculation of the energy expectation value of water molecules according to Example 3 and the exact solution of the model obtained from quantum chemical calculation using a classical computer [Figure 13] Figure showing the error between the exact solution according to Example 4 and the average of 10 samples [Figure 14] Figure showing the measurement results of 10 parallel quantum calculations in FIG. 13 according to Example 4 [Figure 15] Figure showing the change in the accuracy of the sample average with an increase in the number of qubits according to Example 4

Mode for Carrying Out the Invention

[0008] Hereinafter, an information processing apparatus, a parallel quantum calculation method, a parallel quantum calculation program, and a parallel quantum calculation system according to the present embodiment will be described with reference to the drawings.

[0009] FIG. 1 is a diagram showing a configuration example of a parallel quantum calculation system 100 according to the present embodiment. As shown in FIG. 1, the parallel quantum calculation system 100 includes a classical computer (information processing apparatus) 1 and a quantum computer 2. The classical computer 1 and the quantum computer 2 communicate data with each other via a network.

[0010] As an example, the parallel quantum computing system 100 assumes a network system in which a classical computer 1, acting as a local terminal, utilizes a quantum computer 2 provided via the cloud. In this case, the classical computer 1 transmits instructions containing data for the quantum circuit to be executed to the quantum computer 2. The quantum circuit data is assumed to be the data for the circuit diagram and / or the program code of the quantum circuit. Quantum computer 2 is an example of a quantum computing unit. As an example, quantum computer 2 is assumed to be a Noisy Intermediate-Scale Quantum (NISQ) device, which is a noisy intermediate-scale quantum computer. Quantum computer 2 implements hardware such as qubits and quantum gates for executing quantum circuits (hereinafter referred to as quantum hardware) and a control computer that controls the quantum hardware. The implementation method for the quantum hardware may be any method, such as a superconducting circuit method, an ion trap method, a quantum dot method, an optical lattice method, or any other method. The control computer receives the quantum circuit data from the classical computer 1 and converts the received quantum circuit data into a control sequence optimized for the quantum hardware of quantum computer 2. Optimization items include conversion to primitive quantum circuits, scheduling of quantum gates, and mapping of qubits. The control computer then operates the quantum hardware according to the control sequence. This executes the target quantum circuit. The data of the quantum circuit's execution result is transmitted from the control computer to classical computer 1. Classical computer 1 uses the received execution result for various purposes.

[0011] Figure 2 shows an example configuration of classical computer 1. As shown in Figure 2, classical computer 1 has a processor 11, a storage device 12, an input device 13, a display device 14, and a communication device 15. Data and various signals are transmitted and received between the processor 11, storage device 12, input device 13, display device 14, and communication device 15 via a bus.

[0012] The processor 11 is an integrated circuit that controls the overall operation of the classical computer 1. For example, the processor 11 has a CPU (Central Processing Unit), a GPU (Graphics Processing Unit), a DSP (Digital Signal Processor), and / or an FPU (Floating-Point Unit). The processor 11 may also have internal memory and I / O interfaces. The processor 11 performs various processes by interpreting and calculating programs pre-stored in the storage device 12, etc. The processor 11 may be partially or entirely implemented by hardware such as an ASIC (Application Specific Integrated Circuit) or an FPGA (Field Programmable Gate Array).

[0013] The storage device 12 is a volatile memory and / or non-volatile memory that stores various types of data. For example, the storage device 12 stores data and settings used by the processor 11 when it performs various processes, and data generated by various processes performed by the processor 11. The storage device 12 is composed of ROM (Read Only Memory), RAM (Random Access Memory), HDD (Hard Disk Drive), SSD (Solid State Drive), integrated circuit memory, etc. The storage device 12 may also have a non-temporary computer-readable storage medium that stores programs executed by the processor 11.

[0014] The input device 13 receives various operation inputs from the operator. The input device 13 can include a keyboard, mouse, various switches, touchpad, touch panel display, etc. Electrical signals corresponding to the received operation inputs (hereinafter referred to as operation signals) are supplied to the processor 11.

[0015] The display device 14 displays various data according to the control of the processor 11. The display device 14 can be a CRT (Cathode-Ray Tube) display, a liquid crystal display, an organic EL (Electro-Luminescence) display, an LED (Light-Emitting Diode) display, a plasma display, or any other display as appropriate. The display device 14 may also be a projector.

[0016] The communication device 15 includes a communication interface such as a network interface card (NIC) for data communication with various devices connected to the classical computer 1 via a network. Operation signals may be supplied from a computer connected via the communication device 15 or from an input device provided by that computer, and various data may be displayed on a display device provided by a computer connected via the communication device 15. However, for the sake of simplicity in the following explanation, unless otherwise specified, the source of the operation signals will be the input device 13, and the destination for the display of various data will be the display device 14. The input device 13 can be replaced by a computer connected via the communication device 15 or from an input device provided by that computer, and the display device 14 can be replaced by a display device provided by a computer connected via the communication device 15.

[0017] Classical computer 1 does not need to have all of the processor 11, storage device 12, input device 13, display device 14, and communication device 15. Some of the storage device 12, input device 13, display device 14, and communication device 15 may be omitted as needed. Classical computer 1 may be provided with any additional hardware devices useful for executing the processing according to this embodiment. Classical computer 1 does not need to consist of a single physical computer; it may consist of a computer system having multiple computers connected communicably via wired or network lines, etc. The assignment of the series of processes according to this embodiment to the multiple processors 11 implemented in each of the multiple computers can be arbitrarily configured. All processors 11 may execute all processes in parallel, or specific processes may be assigned to one or some of the processors 11, and the series of processes according to this embodiment may be executed by the entire computer system.

[0018] As shown in Figure 2, the processor 11 has the following functional configuration: a division unit 111, an allocation unit 112, an instruction unit 113, an acquisition unit 114, a division unit 115, a classical calculation unit 116, and a display control unit 117.

[0019] The partitioning unit 111 divides a plurality of qubits into a specified number of independent parts in the arrangement layout representing the connection relationships between multiple qubits implemented in the quantum computer 2. The partitioning unit 111 sets the specified number to a number according to the user's instructions. The partitioning unit 111 sets the number of qubits contained in each of the specified number of independent parts to a number according to the user's instructions. Hereinafter, these independent parts will be referred to as clusters.

[0020] The allocation unit 112 assigns calculation conditions to each of the specified number of clusters separated by the division unit 111. The calculation conditions include quantum circuits and samples. A quantum circuit means a sequence of quantum gate operations on the qubits contained in the quantum circuit. A sample means input data to the quantum circuit. Since a quantum circuit is assigned to each cluster, each cluster corresponds to one quantum circuit.

[0021] The instruction unit 113 transmits quantum computation instructions to the quantum computer 2 via the communication device 15. For example, the instruction unit 113 transmits instructions to the quantum computer 2 for executing a specified number of quantum computations in parallel, each corresponding to a specified number of clusters. The quantum computer 2 executes the specified number of quantum computations in parallel in response to the instructions. A single sequence containing a specified number of measurement results corresponding to the executed specified number of quantum computations is transmitted to the classical computer 1.

[0022] The acquisition unit 114 acquires various types of information from the quantum computer 2 via the communication device 15. For example, the acquisition unit 114 acquires a single sequence from the quantum computer 2 that includes a specified number of measurement results corresponding to a specified number of quantum computations.

[0023] The splitting unit 115 divides a single sequence acquired by the acquisition unit 114 into a specified number of measurement results. The splitting unit 115 divides a single sequence into a specified number of measurement results based on the specified number, the order of the specified number of clusters, and the number of qubits contained in each of the specified number of clusters. Each of the specified number of measurement results corresponds to the quantum state of the corresponding cluster or quantum circuit.

[0024] The classical calculation unit 116 performs classical calculations on a specified number of measurement results obtained by the division unit 115. For example, the classical calculation unit 116 calculates the expected value of an arbitrary observable based on the specified number of measurement results.

[0025] The display control unit 117 displays various information on the display device 14. For example, the display control unit 117 displays an arrangement layout on the display device 14 in which a specified number of independent parts are drawn. In this case, the display control unit 117 can also highlight the specified number of independent parts. As another example, the display control unit 117 displays the results of classical calculations obtained by the classical calculation unit 116.

[0026] Figure 3 shows the processing procedure of classical computer 1 in relation to parallel quantum computing. As shown in Figure 3, first, the display control unit 117 displays the arrangement layout of multiple qubits to be implemented in quantum computer 2 on the display device 14 (step S1). The arrangement layout is displayed for the partitioning process performed in step S2. The arrangement layout data is supplied from quantum computer 2 to classical computer 1.

[0027] Figure 4 shows an example of the display screen I1 of the arrangement layout 4. As shown in Figure 4, the display screen I1 shows the arrangement layout 4, which represents the connection relationships (topology) between multiple qubits 40 installed in the quantum computer 2. The multiple qubits 40 displayed in the arrangement layout 4 represent the qubits contained in one quantum chip (quantum processor) that is the target of processing and installed in the quantum computer 2. In the case of quantum hardware where the qubits are not implemented on a quantum chip, the qubits only need to be spatially arranged within the quantum computer 2. In Figure 4, 127 qubits 40 are displayed.

[0028] When step S1 is performed, the partitioning unit 111 divides the multiple qubits into a specified number (m) clusters (step S2). The partitioning unit 111 divides the multiple qubits into m clusters based on the error rate of the multiple qubits.

[0029] Figure 5 shows the display screen I1 of the arrangement layout 5 after partitioning. Partitioning is performed according to user instructions via input device 13. As an example, the user performs the partitioning work by referring to a list of error rates for each qubit provided by the quantum computer 2. This list is displayed on the display device 14 by the display control unit 117. Qubits with error rates greater than a threshold are excluded, and qubits 41 to be included in each cluster 50 are selected. In this case, the error rate of connections between qubits may also be considered when selecting the qubits 41 to be included in each cluster 50. The partitioning work is performed so that the number of qubits 41 included in a cluster 50 matches the number of qubits required for the quantum circuit to be implemented. Clusters 50 must contain interconnected qubits 41, and it is prohibited to include unconnected qubits in a single cluster 50. Two adjacent clusters 50 should be placed with one or more qubits 42 separating them to reduce interference to each other's quantum computations. In this embodiment, the partitioning unit 111 is configured to partition multiple qubits into clusters 50 according to user instructions, but this embodiment is not limited to this. The partitioning unit 111 may also automatically partition multiple qubits into clusters 50 according to the rules described above. Specifically, the partitioning unit 111 can automatically partition multiple qubits into clusters 50 according to an optimization algorithm based on error rate, arrangement layout and / or connection relationships, etc. As another example, the partitioning unit 111 may partition some of the multiple qubits into clusters 50 according to user instructions, and then automatically partition the remaining qubits into clusters 50 according to the algorithm described above.

[0030] Figure 5 illustrates an example where there are 25 clusters 50, and each cluster 50 has the same number of qubits 41, 4. As shown in Figure 5, the display control unit 117 can highlight the clusters 50 in red or another color in the arrangement layout 5. This makes it easy to understand the location of the clusters 50 in the arrangement layout 5. Furthermore, it is preferable that the display control unit 117 display the qubits 41 belonging to the cluster 50 and the qubits 42 not belonging to the cluster 50 in different colors. For example, qubit 41 could be displayed in black and qubit 42 in blue. This makes it easy to visually distinguish between qubit 41 and qubit 42. In addition, the cluster number 50, such as "1", "2", ..., "25", may be displayed near each cluster 50.

[0031] The clustering process may be performed using the list above or using arrangement layout 5. Each qubit may be assigned to one of the clusters using either the list or the arrangement layout, or multiple qubits may be selected to belong to a cluster, thereby assigning the selected qubits to that cluster.

[0032] When step S2 is performed, the allocation unit 112 assigns computational conditions such as quantum circuits and samples to each cluster (step S3). A quantum circuit means a sequence of quantum operations on the qubits contained in the quantum circuit. Quantum circuits are assigned to clusters that each contain the same number of qubits. Since a quantum circuit is assigned to each cluster, each cluster can be considered as a single independent quantum circuit. The configuration of the quantum gate and / or circuit parameters can be set arbitrarily. A sample means input data to the quantum circuit.

[0033] As a first example, the same quantum circuit and different samples may be assigned to multiple clusters. In this case, the accuracy of the measurement results can be improved by obtaining the sample mean of multiple measurement results corresponding to each of the multiple clusters. As a second example, quantum circuits with the same quantum gate configuration but different rotation parameters may be assigned to multiple clusters. For the samples, the same sample may be assigned to multiple clusters, or different samples may be assigned. In this case, it is possible to perform quantum computations with different rotation parameters in parallel. As a third example, different quantum circuits may be assigned to multiple clusters. For the samples, the same sample may be assigned to multiple clusters, or different samples may be assigned. In this case, it is possible to perform quantum computations with different quantum circuits in parallel.

[0034] When step S3 is performed, the instruction unit 113 sends a parallel quantum computation instruction to the quantum computer 2 (step S4). The parallel quantum computation instruction is an instruction to cause the quantum computer 2 to execute in parallel the quantum computation defined by the quantum circuits and samples assigned in step S3 for the m clusters determined in step S2. The parallel quantum computation instruction includes information such as the instruction to execute the quantum computation, the number of clusters m, and the quantum circuits and samples for each cluster.

[0035] In response to a parallel quantum computation instruction, quantum computer 2 executes the quantum computation defined by the quantum circuits and samples assigned in step S3 in parallel for m clusters. That is, a parallel circuit of m quantum circuits is executed with a single instruction. A parallel circuit of m quantum circuits can also be called a parallel quantum circuit.

[0036] Specifically, first, quantum computer 2 converts the data from the quantum circuit into a control sequence for each of the m clusters, and operates the quantum hardware according to the control sequence. Specifically, the samples are encoded into qubits by the encoding gates provided in the quantum circuit. This forms an encoded quantum state. Quantum operations are performed on the encoded quantum state by various quantum gates provided in the quantum circuit to form an output quantum state. The output quantum state is measured by a measuring instrument. The m measurement results, corresponding to each of the m clusters, are transmitted to classical computer 1 as a single bit string. Hereafter, a single bit string containing m measurement results will be referred to as a parallel qubit string.

[0037] When step S4 is performed, the acquisition unit 114 acquires one parallel qubit sequence from the quantum computer 2 (step S5). When step S5 is performed, the division unit 115 divides the one parallel qubit sequence into m measurement results (step S6). The division unit 115 divides one bit sequence into m measurement results based on the number of clusters m, the order of the m clusters, and the number of qubits contained in each cluster.

[0038] As an example, consider a 15-qubit parallel quantum circuit, which is a parallel circuit of three quantum circuits. Assume the first quantum circuit has 6 qubits, the second has 5 qubits, and the third has 4 qubits. The measured parallel qubit sequence of this parallel quantum circuit is composed of a single sequence of 15 qubits, for example, as shown below.

[0039] 001101011001111

[0040] Assuming that the measurements of each of the three quantum circuits constituting the quantum parallel circuit are independent, a single measurement of the quantum parallel circuit can yield measurement results corresponding to the measurements of each individual quantum circuit. That is, the division unit 115 divides the parallel qubit sequence of all 15 qubits into 6 qubits, 5 qubits, and 4 qubits in the order of the number of qubits contained in each quantum circuit, as shown below.

[0041] 001101|01100|1111

[0042] As a result, the measurement result for the first quantum circuit is "001101", the measurement result for the second quantum circuit is "01100", and the measurement result for the third quantum circuit is "1111". By dividing the parallel qubit sequence in this way, the output quantum state of each quantum circuit (cluster) can be reproduced.

[0043] When step S6 is performed, the classical calculation unit 116 performs classical calculations based on the measurement results obtained in step S6 (step S7). Classical calculations can include the calculation of probability distributions and expected values ​​of observables in quantum chemistry calculations, and the calculation of the optimal combination in combinatorial optimization problems. When step S7 is performed, the display control unit 117 displays the results of the classical calculations performed in step S7 on the display device 14 (step S8).

[0044] Figure 6 shows an example of the display screen I2 for classical calculation results. In Figure 6, the number of quantum circuits (clusters) is m=4, the number of qubits in each cluster is n=4, and the measurement target is an arbitrary energy expectation value in quantum chemical calculations. The four quantum circuits are common but the samples are different, and the sample mean of the energy expectation value for each cluster is calculated by the classical calculation unit 116. As shown in Figure 6, the display screen I2 has display fields for the number of qubits, measurement result, and energy expectation value for each cluster. For example, the number of qubits for cluster 1 is "4", the measurement result is "0011", and the energy expectation value is "AAAA". The sample mean display field shows the sample mean "EEEE" based on the four energy expectation values ​​"AAAA", "BBBB", "CCCC", and "DDDD". In this way, it becomes possible to check the number of qubits, measurement result, and energy expectation value for multiple clusters obtainable in a single parallel quantum calculation, for each cluster. Furthermore, it becomes possible to check the sample mean obtainable in a single parallel quantum calculation on the same screen.

[0045] With the above steps completed, the processing procedure of the classical computer 1 related to parallel quantum computing according to this embodiment is finished.

[0046] The above parallel quantum computing process is merely an example, and various steps can be deleted, added, and / or modified. For example, if cluster partitioning is performed automatically, the display of the arrangement layout (S1) does not necessarily have to be performed. In this case, the arrangement layout after partitioning may be displayed as needed. As another example, if the quantum circuits and samples are determined before cluster partitioning, the order of the cluster partitioning process (S2) and the quantum circuit and sample assignment process (S3) may be reversed. Alternatively, the quantum circuit assignment process may be performed before the cluster partitioning process (S2), and the sample assignment process may be performed after the cluster partitioning process (S2). The order of the quantum circuit assignment process and the sample assignment process may also be reversed. As yet another example, if classical computation is not required, the classical computation process (S7) and the display process (S8) may be omitted. In this case, the display control unit 117 may perform a display process in which it displays m measurement results on the display device 14.

[0047] As another example, the classical computation unit 116 may perform other classical computations based on a specified number of measurement results obtained in step S7 or on classical computation results based on those measurement results. For example, when performing quantum machine learning on a parameterized quantum circuit, the parameterized quantum circuit is assigned to m clusters, different circuit parameters and training input samples are assigned to each parameterized quantum circuit, and parallel quantum computation of the m parameterized quantum circuits is performed. As a classical computation result, the classical computation unit 116 calculates a model output value for each of the m measurement results based on the measurement results and calculates a cost function value that evaluates the difference between the model output and the ground truth output. As another classical computation, the classical computation unit 116 estimates the optimal values ​​of the circuit parameters from the m cost function values ​​using parametric or nonparametric optimization methods based on Bayesian estimation or the like that utilize prior information. The estimated optimal values ​​are assigned to the circuit parameters of the parameterized quantum circuit. This completes the quantum machine learning. In this way, by applying this embodiment to quantum machine learning, it becomes possible to perform quantum machine learning with high efficiency.

[0048] As another example, the instruction unit 113 may send instructions to the quantum computer 2 to perform other quantum computations based on m measurement results or classical computation results based on those measurement results. For example, in the case of the quantum machine learning described above, it is preferable that trained quantum circuits with optimal values ​​for circuit parameters assigned to m clusters are assigned to each trained quantum circuit, and instructions are sent to the quantum computer 2 to perform parallel quantum computations of the m trained quantum circuits.

[0049] The classical computer (information processing device) 1 according to the above embodiment comprises a partitioning unit 111 and an instruction unit 113. The partitioning unit 111 divides the multiple qubits into m clusters in an arrangement layout representing the connection relationships between multiple qubits implemented in the quantum computer 2. The instruction unit 113 transmits instructions to the quantum computer 2 for executing m quantum computations in parallel, each corresponding to one of the m clusters.

[0050] According to the above configuration, by dividing multiple qubits into m clusters, each allocated with m quantum computations, it becomes possible to execute m quantum computations in a single parallel quantum computation. As a result, this embodiment can execute m quantum computations more efficiently than conventional methods that perform m quantum computations separately one by one. Furthermore, since it is possible to increase the number of qubits used per job, it is possible to improve the efficiency of qubit utilization or resource allocation.

[0051] The parallel quantum computing system 100 according to the above embodiment includes a division unit 111, a quantum computer 2, and a partitioning unit 115. The division unit 111 divides a plurality of qubits into m clusters in an arrangement layout representing the connection relationships between a plurality of qubits implemented in the quantum computer 2. The quantum computer 2 executes m quantum computations in parallel, each corresponding to one of the m clusters, and outputs a single parallel qubit sequence containing m measurement results corresponding to the m quantum computations. The partitioning unit 115 divides the single parallel qubit sequence into m measurement results.

[0052] According to the above configuration, by performing a single parallel quantum computation on m clusters to which m quantum computations are assigned, it is possible to efficiently obtain m measurement results compared to the conventional method of performing m quantum computations separately one by one. Furthermore, since the m measurement results are obtained from quantum computer 2 as a single parallel qubit sequence, and classical computer 1 divides this single parallel qubit sequence into m measurement results, it is possible to reduce the number of communications between quantum computer 2 and classical computer 1 compared to the conventional method of individually transmitting the m measurement results from quantum computer 2 to classical computer 1. In addition, this embodiment, which executes m quantum computations in parallel, can improve the uniformity of the noise environment for each quantum computation compared to the conventional method of performing m quantum computations separately. Accordingly, this embodiment can also improve the accuracy of the sample mean compared to the conventional method of obtaining the sample mean of separate quantum computations by obtaining the sample mean based on the m measurement results obtained by parallel quantum computation. Furthermore, according to this embodiment, since quantum computation with a small number of qubits is performed in parallel as a single job, it is possible to increase the number of qubits used per job compared to the conventional method in which quantum computation with a small number of qubits is divided into m jobs, thereby improving the efficiency of qubit utilization or resource allocation.

[0053] Various examples will be described below.

[0054] <Example 1> Example 1 is a parallel quantum computation on a single quantum chip. Consider m independent quantum circuits, each consisting of n qubits. Parallel quantum computation is performed by performing quantum computation on an m × n qubit quantum circuit, which is formed by combining the m n qubit quantum circuits into a single circuit.

[0055] Figure 7 shows the circuit configuration of the parallel quantum circuit according to Example 1. As shown in Figure 7, the parallel quantum circuit according to Example 1 has a number of quantum circuits (Circ) m=4 and the number of qubits n=4 for each quantum circuit. Conventionally, to obtain the results of four 4-qubit quantum circuits, the calculation of the 4-qubit quantum circuit is performed four times on one quantum chip. In contrast, in this example, a 4×4=16-qubit quantum parallel circuit is constructed, and by performing this quantum parallel circuit once on one quantum chip, it is possible to obtain the results of four quantum circuits at once.

[0056] Next, the measurement of the quantum parallel circuit according to Example 1 will be described. When the above 16-qubit quantum parallel circuit is measured, it is possible to obtain, for example, the following single parallel qubit sequence.

[0057] 0011001100110011

[0058] Assuming that the measurements of each of the four quantum circuits constituting the quantum parallel circuit are independent, a single measurement of the quantum parallel circuit can yield measurement results corresponding to the measurements of each individual quantum circuit. That is, the measurement results of each quantum circuit divide the entire 16-qubit parallel qubit sequence into groups of four qubits, as shown below.

[0059] 0011|0011|0011|0011

[0060] The measurement results for the first quantum circuit, the second, third, and fourth are "0011", "0011", "0011", and "0011", respectively. This makes it possible to obtain the measurement results for each quantum circuit.

[0061] It is also possible to observe the number of measurements of a parallel qubit sequence by performing parallel quantum computations multiple times on the same or different samples. The method for performing multiple parallel quantum computations can be to execute a single parallel quantum circuit multiple times, or to execute multiple parallel quantum circuits connected in series once or in several separate executions.

[0062] Figure 8 shows the number of measurements (Count) for each measurement result of the parallel quantum circuit according to Example 1. The horizontal axis of Figure 8 represents the parallel qubit sequence, and the vertical axis represents the number of measurements for each parallel qubit sequence. By performing parallel quantum computation multiple times in this way, it becomes possible to observe the number of measurements more efficiently. For example, when the parallel quantum circuit is composed of four identical quantum circuits or four different quantum circuits, it becomes possible to observe the number of measurements with four times the efficiency compared to executing a single quantum circuit.

[0063] Next, we will discuss parallel quantum computation of the expectation value of an observable. From a 16-bit parallel qubit sequence, it is also possible to compute four expectation values ​​corresponding to four qubit sequences simultaneously. As an example, we will explain how to compute the expectation value of a 4-qubit observable given by IIIZ from the measurement of a quantum parallel circuit. Note that I is the identity matrix, Z is the Pauli Z, and unless otherwise specified, all qubits are arranged in little-endian notation.

[0064] The expectation value of the Pauli operator of IIIZ is the same as the expectation value of the Pauli Z of the 0th qubit in the individual 4-qubit circuits obtained from the measurement of the quantum parallel circuit. Here, the |0> state of the i-th qubit is |0> i , |1> state |1> i Therefore, the expected value of the Pauli Z for the 0th qubit is equal to the difference in the number of measurements between |0>0 and |1>0. <iiiz>This can be expressed by the following equation (1).

[0065]

number

[0066] The procedure for obtaining the IIIZ expectation value for each of the four 4-qubit sequences from a 16-qubit quantum parallel circuit is as follows: 1. Store a parallel qubit sequence of 1.16 qubits 2. Divide the parallel qubit sequence into four 4-qubit sequences (measurement result). 3. For each 4-qubit sequence, extract the number of measurements for both the |0> state and the |1> state of the 0th qubit. 4. According to equation (1), each 4-qubit sequence <iiiz>Calculate

[0067] The expected value of the i-th Pauli Z can be calculated according to equation (2) below.

[0068]

number

[0069] As described above, when the observable consists only of Pauli Z, the expected value can be calculated using the methods of equations (1) and (2).

[0070] Furthermore, observables generally include bases other than Pauli Z. In this case, all measurements can be reduced to Z bases by performing appropriate gate operations.

[0071] Examples of 4-qubit observables other than Pauli Z include YXXY, YYXX, XXYY, XYYX, etc. From the Clifford operation, if X is Hadamard gate, and if Y is R X If a rotation gate of (π / 2) is applied to each qubit in a quantum circuit, the expectation values ​​of Pauli X and Pauli Y become equivalent to the expectation value of Pauli Z. In other words, the expectation values ​​of observables other than the 4-qubit Pauli Z are equivalent to the expectation values ​​of the Hadamard gate and R X By appropriately applying a (π / 2) rotation gate to the qubit, everything can be reduced to a ZZZZ measurement.

[0072] In other words, the calculation of the expected value of any observable can be reduced to the calculation of the expected value in the measurement of an IZ···ZI··· type Z basis, and all that is needed is to count the number of measurements of the quantum states |0> and |1> of the qubits on which Pauli Z is acting.

[0073] specifically, <iiiz>The calculation is performed according to equation (1). As an example of the expected value of other observables, <iizz>Note that in this case, the expected value is +1 when the 0th and 1st quantum states are the same, and -1 otherwise, the calculation can be performed according to equation (3) below.

[0074]

number

[0075] The above method can be extended to the expectation value of an n-qubit observable containing an arbitrary Pauli operator, and can be similarly calculated from the number of measurements of the quantum state measured in the Z basis. In this way, the expectation value of m n-qubit observables can be obtained by measuring a quantum parallel circuit with m × n qubits.

[0076] The parallel quantum computation of the expected value of the observable described above can also be applied to quantum parallel circuits constructed by combining any number of arbitrary qubit circuits on a single quantum chip. For example, a quantum parallel circuit with (m1×n1+m2×n2) qubits can be set up, which includes m1 n1 qubit quantum circuits and m2 n2 qubit quantum circuits.

[0077] <Example 2> Example 2 is an application of this embodiment to quantum chemical calculations, performing parallel quantum computation of the expectation value of the hydrogen molecule Hamiltonian. As an example, the energy expectation value E of the hydrogen molecule is calculated. The eigenstates of the hydrogen molecule can be represented by a parameterized quantum circuit of the Unitary Coupled Cluster type with 4 quantum bits (Non-Patent Literature 7).

[0078] Figure 9 shows the circuit configuration of a Unitary Coupled Cluster type 4-qubit parameterized quantum circuit according to Example 2. Example 2 demonstrates that the energy expectation value E(θ) can be obtained in a single calculation by performing parallel quantum computation on the angle θ of the Rz rotation gate included in the quantum circuit.

[0079] The Hamiltonian of a hydrogen molecule consists of 15 different Pauli operator terms of 4 qubits: IIII, ZIII, IZII, IIZI, IIIZ, ZZII, IIZZ, ZIZI, ZIIZ, IZZI, IZIZ, YXXY, YYXX, XXYY, and XYYX. Therefore, from the parallel quantum computation of the expected values ​​of the observables mentioned above, everything can be reduced to measurements in the Z basis, and it is possible to calculate the energy expected value of each quantum circuit from the number of measurements of the quantum state of each qubit.

[0080] The parallelization procedure is the same as the calculation procedure shown in the parallel quantum computation of the observable expectation value described above: the measurement result of m × n qubits is divided into m n qubit sequences, and m energy expectation values ​​are calculated from each n qubit sequence.

[0081] For verification, 10 4 The results of calculating the θ dependence of hydrogen molecules using a noisy simulator (Qasm simulator) in shots are shown. Note that "shots" refers to the number of measurements. For hydrogen molecules, the interatomic distance is 1.0 × 10⁻¹⁶. -10 Let m be the value of the Rz rotation gate of the Unitary Coupled Cluster type quantum circuit shown in Figure 9. The angle θ of the Rz rotation gate was swept to eight values: π / 5, 2π / 5, 3π / 5, 4π / 5, π, 6π / 5, 7π / 5, and 8π / 5, thereby constructing eight Unitary Coupled Cluster type quantum circuits. To verify whether the expectation values ​​can be calculated using parallel quantum computing, the table below shows a comparison between the results of independently calculating the eight Unitary Coupled Cluster type quantum circuits using a simulator (Non-Parallel) and the results of calculating the eight expectation values ​​simultaneously using a 4×8=32 qubit quantum circuit with the Qasm simulator (Parallel). As can be seen from the results in the table, the expectation value calculations performed individually and independently (Non-Parallel) and the results of calculating the expectation values ​​simultaneously using 32 qubits (Parallel) agree within an error range of approximately 1%.

[0082] [Table 1]

[0083] Figure 10 shows the results of the error between the energy expectation value obtained in a noise-free, ideal simulator and the energy expectation value obtained in parallel quantum computation using the Qasm simulator, when the number of measurements is varied. In the graph of Figure 10, the vertical axis represents the error in the energy expectation value (ΔEnergy(Hr)), and the horizontal axis represents the number of measurements (shots). The dotted line represents the chemical precision (approximately 0.0015 Hr). As shown in Figure 10, it can be confirmed that increasing the number of measurements reduces the systematic error and satisfies the chemical precision, indicating that the parallel quantum computation according to this embodiment is being performed correctly.

[0084] <Example 3> Example 3 performed sample parallel testing of the ground state energy of a water molecule. For simplicity, Example 3 treats the water molecule as a 4-qubit model with 2 electrons and 2 orbitals. The coordinates of each atom in the water molecule were set as follows. O[0.0,0.0,0.11779] H[0.0,0.75545,-0.47116] H[0.0,-0.75545,-0.47116]

[0085] The basis set used for the calculation was set to the minimal basis STO3G. In this case, the Hamiltonian of a water molecule is obtained, consisting of all 15 types of 4-qubit Pauli operator terms: IIII, ZIII, IZII, IIZI, IIIZ, ZZII, IIZZ, ZIZI, ZIIZ, IZZI, IZIZ, YXXY, YYXX, XXYY, and XYYX. Since this is the same observable as in Example 2, the procedure for parallel quantum computation of a hydrogen molecule can be applied directly.

[0086] To verify parallel quantum computing, the ground state energy of a water molecule is obtained beforehand using VQE. Therefore, a parameterized quantum circuit describing the quantum state of a water molecule is defined. Here, a type of quantum circuit called a Hardware-Efficient type, suitable for actual experiments, is used.

[0087] Figure 11 shows the circuit configuration of a hardware-efficient 4-qubit parameterized quantum circuit according to Example 3. As shown in Figure 11, the hardware-efficient quantum circuit is a quantum circuit consisting of an Rx gate, a Ry gate, and a CX gate, and includes 16 circuit parameters θ[0] to θ

[15] .

[0088] By performing VQE in a simulator, optimized circuit parameters were obtained. A quantum parallel circuit was constructed using multiple quantum circuits, as shown in Figure 11, with the optimized circuit parameters substituted in. Parallel quantum computation of energy was then performed using this quantum parallel circuit. This represents a sample-parallel expectation value on a single quantum chip.

[0089] Figure 12 shows a comparison of the energy expectation value of a water molecule obtained by parallel quantum computation with the exact solution of a model obtained from quantum chemical calculations using a classical computer. In the graph in Figure 12, the vertical axis represents the energy expectation value (Energy(Hr)), and the horizontal axis represents the quantum circuit number (n_circ). The energy expectation value obtained by parallel quantum computation is shown as a black circle, and the exact solution is shown as a straight line. The parallel quantum computation was performed using eight 4-qubit quantum circuits with optimized circuit parameters, i.e., a 32-qubit parallel quantum circuit. Since the parallel quantum computation was performed using Qasm simulation, sampling errors due to the number of measurements are included. As is clear from Figure 12, the energy expectation value obtained by parallel quantum computation is found to be scattered within less than 1% error around the exact solution of the model using a classical computer, confirming the validity of the results of parallel quantum computation.

[0090] <Example 4> Example 4 investigated whether sample parallelism improves the accuracy of expected value calculations by calculating the average of eight results obtained from parallel quantum computation. To more clearly observe the effect of variance from the correct value, parallel quantum computation was performed with the number of measurements (shots) reduced from 10,000 to 100. Eight parallel quantum computations of 100 shots were performed 10 times. In other words, parallel quantum computations equivalent to a total of 80 quantum circuit calculations were performed, and the average of the expected values ​​obtained from 10 parallel quantum circuit executions (the average of the results of the eight parallel quantum computations) was calculated.

[0091] Figure 13 shows the error between the exact solution and the mean of 10 samples. In the graph in Figure 13, the vertical axis represents the error in the energy expectation value (ΔEnergy(Hr)), and the horizontal axis represents the sample number. The dotted line represents chemical precision (approximately 0.0015 Hr), and the black circles represent the error between the exact solution and the mean of the samples. As shown in Figure 13, in all 10 calculations, the average value of the parallel quantum calculations yields a solution with precision below chemical precision. Since each of the 10 parallel quantum calculations consists of 100 shots, the systematic error varies with precision approximately 1 / (√number of shots), that is, the reciprocal of the square root of the number of shots. Therefore, it is difficult to obtain individual results from parallel quantum calculations with precision below chemical precision, but chemical precision can be satisfied by taking the sample mean of the individual results obtained from the parallel quantum calculations.

[0092] Figure 14 shows the measurement results of the 10 parallel quantum computations in Figure 13. In Figure 14, the vertical axis of each graph represents the energy expectation value, and the horizontal axis represents the circuit number of the quantum circuit. As shown in Figure 14, the results of each parallel quantum computation vary within a certain range in terms of positive and negative values. By taking the average of these values, the positive and negative errors cancel each other out, and a value close to the exact solution is obtained.

[0093] Figure 15 shows the change in the accuracy of the sample mean as the number of qubits increases. In each graph shown in Figure 15, the vertical axis represents the probability density, and the horizontal axis represents the energy expectation value. Note that E * represents the energy expectation value (mean value) when the probability density takes its maximum value, ave represents the sample mean, and e represents the electron's energy. The left figure in Figure 15 represents one quantum computation (4 qubits), the center figure represents eight parallel quantum computations (100 qubits), and the right figure represents N (many) parallel quantum computations (~1000 qubits). As shown in Figure 15, it can be seen that as the number of quantum computations executed in parallel increases, the sample mean approaches the mean value.

[0094] By applying the parallel quantum computation according to this embodiment to sample parallelism in a quantum circuit and taking the sample mean of the obtained results, more accurate results can be obtained than those obtained with conventional non-parallel quantum computation. As the number of qubits implemented in quantum computer 2 increases, the number of parallel processes that can be performed increases, making it possible to perform quantum computation with higher accuracy.

[0095] Thus, it becomes possible to provide an information processing device, a parallel quantum computing method, a parallel quantum computing program, and a parallel quantum computing system that enable improved efficiency of quantum computing by quantum computers.

[0096] While several embodiments of the present invention have been described, these embodiments are presented as examples only and are not intended to limit the scope of the invention. These novel embodiments can be carried out in a variety of other forms, and various omissions, substitutions, and modifications can be made without departing from the spirit of the invention. These embodiments and their variations are included in the scope and spirit of the invention, as well as in the claims of the invention and its equivalents. [Explanation of Symbols]

[0097] 1...Classical computer (information processing device), 2...Quantum computer, 11...Processor, 12...Storage device, 13...Input device, 14...Display device, 15...Communication device, 111...Division unit, 112...Allocation unit, 113...Instruction unit, 114...Acquisition unit, 115...Partition unit, 116...Classical calculation unit, 16...Display control unit, 100...Parallel quantum computing system.< / iizz> < / iiiz> < / iiiz> < / iiiz>

Claims

1. In an arrangement layout representing the connection relationships between multiple qubits implemented in a quantum computer, a division unit divides the multiple qubits into a specified number of independent parts, An instruction unit that transmits instructions to the quantum computer for executing a specified number of quantum computations in parallel, corresponding to each of the specified number of independent parts, An information processing device equipped with the following.

2. The aforementioned division section is The specified number is set to the number indicated by the user's instructions. The number of qubits contained in each of the specified number of independent parts is set to a number according to the user's instructions. The information processing apparatus according to claim 1.

3. The information processing apparatus according to claim 1, wherein the division unit divides the plurality of qubits into a specified number of independent parts based on the error rate of the plurality of qubits.

4. The information processing apparatus according to claim 1, wherein the partitioned portion is arranged such that adjacent independent portions of the specified number of independent portions are separated by one or more qubits.

5. An acquisition unit that acquires a sequence from the quantum computer that includes a specified number of measurement results corresponding to the specified number of quantum computations, The system further comprises a division unit that divides the aforementioned single series into the specified number of measurement results, The information processing apparatus according to claim 1.

6. The information processing apparatus according to claim 5, further comprising a classical calculation unit that calculates the expected value of the observables based on the measurement results of the specified number of items.

7. The information processing apparatus according to claim 1, further comprising an allocation unit that individually allocates quantum circuits and samples to the specified number of independent parts.

8. It also includes a classical calculation section, The allocation unit assigns the same quantum circuit and different samples to two or more independent parts out of the specified number of independent parts. The classical calculation unit calculates the sample mean based on the expected value of each of the two or more independent parts. The information processing apparatus according to claim 7.

9. It also includes a classical calculation section, The allocation unit assigns different quantum circuits and the same sample to two or more independent parts out of the specified number of independent parts. The classical calculation unit calculates the sample mean based on the expected value of each of the two or more independent parts. The information processing apparatus according to claim 7.

10. The information processing apparatus according to claim 1, wherein the instruction includes information relating to the specified number.

11. The information processing apparatus according to claim 5, wherein the division unit divides the single sequence into the specified number of measurement results based on the specified number, the order of the independent parts of the specified number, and the number of qubits contained in each of the independent parts of the specified number.

12. The information processing apparatus according to claim 6, wherein the classical calculation unit performs other classical calculations based on the specified number of measurement results or classical calculation results based on said measurement results.

13. The information processing apparatus according to claim 1, wherein the instruction unit transmits instructions to the quantum computer for performing other quantum calculations based on a specified number of measurement results or classical calculation results based on said measurement results.

14. The information processing apparatus according to claim 1, further comprising a display control unit that displays the arrangement layout in which the specified number of independent parts are drawn on a display device.

15. The information processing apparatus according to claim 14, wherein the display control unit displays the qubits belonging to the specified number of independent portions of the plurality of qubits included in the arrangement layout in different colors from the qubits not belonging to the specified number of independent portions.

16. In an arrangement layout representing the connection relationships between multiple qubits implemented in a quantum computer, a division step is made to divide the multiple qubits into a specified number of independent parts, An instruction step of sending instructions to the quantum computer for executing a specified number of quantum computations in parallel, each corresponding to a specified number of independent parts; A parallel quantum computing method that possesses the following features.

17. Classical computers, A function to divide the multiple qubits into a specified number of independent parts in an arrangement layout representing the connection relationships between multiple qubits implemented in a quantum computer, A function to cause the quantum computer to send instructions to perform a specified number of quantum computations in parallel, corresponding to each of the specified number of independent parts, A parallel quantum computing program that makes this possible.

18. In an arrangement layout representing the connection relationships between multiple qubits, a division section divides the multiple qubits into a specified number of independent parts, A quantum computing unit that executes a specified number of quantum computations in parallel, corresponding to each of the specified number of independent parts, and outputs a single sequence containing a specified number of measurement results corresponding to the specified number of quantum computations, A division unit that divides the aforementioned single series into the specified number of measurement results, A parallel quantum computing system equipped with the following features.

Images