Quantum operation device and method for quantum operation

Abstract

To efficiently use a quantum bit.SOLUTION: A quantum operation device includes: a setting unit configured to set, as a processing target, an evaluation function including a polynomial containing third- or higher-degree terms; a determination unit for determining, in a quantum circuit corresponding to the evaluation function, whether a qubit used in the operation of one term and not used in the operation of subsequent terms is to be reused; a generation unit for generating a quantum circuit in which the qubit determined to be reused is reused in place of another qubit; and a quantum operation unit for executing a quantum operation using the generated quantum circuit.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present disclosure relates to a quantum processing device and a quantum processing method. [Background technology]

[0002] In recent years, there has been much research being done on using quantum computers to perform high-speed calculations to find solutions to specific problems. Quantum computers achieve faster calculations than classical computers by controlling and measuring the states of qubits.

[0003] One example of a problem that can be solved by a quantum computer is a combinatorial optimization problem. Many combinatorial optimization problems can be handled using the QUBO (Quadratic Unconstrained Binary Optimization) format, which expresses the evaluation function as a quadratic polynomial.

[0004] In addition, instead of formulating the problem in the QUBO format, it is being considered to reduce the number of quantum bits required for quantum computation by formulating it in the HUBO (Higher-Order Unconstrained Binary Optimization) format, which allows evaluation functions of orders higher than quadratic. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] JP 2023-057945 A [Patent Document 2] Patent Publication No. 2022-090249 [Non-patent literature]

[0006] [Non-Patent Document 1] A. Glos, A. Krawiec and Z. Zimboras, "Space-efficient binary optimization for variational quantum computing", npj Quantum Information 8, 39 2022 [Non-Patent Document 2] M. DeCross, E. Chertkov, M. Kohagen and M. Foss-Feig, "Qubit-reuse compilation with mid-circuit measurement and reset", arXiv Quantum Physics arXiv:2210.08039, 2022 Summary of the Invention [Problem to be solved by the invention]

[0007] However, since the influence of noise also increases as the number of quantum bits used in a quantum computer increases, it is preferable to further reduce the number of quantum bits used. For example, general-purpose quantum computers currently in practical use are called NISQ (Noisy Intermediate-Scale Quantum Device) devices, and since they have only a few to several hundred quantum bits available, it is required to reduce the number of quantum bits used for calculations as much as possible.

[0008] Even if the number of quantum bits available in quantum computers increases in the future, it will be important to use the limited number of quantum bits efficiently.

[0009] The present disclosure has been made in view of the above, and has an object to provide a quantum processing device and a quantum processing method that can efficiently utilize quantum bits. [Means for solving the problem]

[0010] According to one aspect of the present disclosure, a quantum computing device has a setting unit that sets an evaluation function consisting of a polynomial including third- or higher-order terms as an object of computation, a determination unit that determines, in a quantum circuit corresponding to the evaluation function, to reuse quantum bits used in the computation of one term that are not used in the computation of a subsequent term, a generation unit that generates a quantum circuit that reuses the quantum bits determined to be reused in place of other quantum bits, and a quantum computing unit that performs quantum computations using the generated quantum circuit. [Brief description of the drawings]

[0011] [Figure 1] FIG. 1 is a block diagram showing a configuration of a quantum processing device according to an embodiment. [Diagram 2] FIG. 2 is a flow diagram showing a quantum computing method according to an embodiment. [Diagram 3] FIG. 3 is a diagram showing a specific example of shading in a graph. [Figure 4] FIG. 4 is a diagram showing a specific example of a quantum gate corresponding to a higher-order term. [Diagram 5] FIG. 5 is a flow diagram showing a measurement order determination method. [Figure 6] FIG. 6 is a diagram illustrating a quantum circuit for quantum operations. [Figure 7] FIG. 7 is a diagram showing a specific example of a quantum circuit. [Figure 8] FIG. 8 is a diagram showing a specific example of a causal cone. [Figure 9] FIG. 9 is a diagram for explaining the interchange of terms. [Figure 10] FIG. 10 is a diagram illustrating the reuse of quantum bits. [Figure 11] FIG. 11 is a diagram showing a specific example of the number of quantum bits used. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0012] Hereinafter, an embodiment according to the present disclosure will be described with reference to the accompanying drawings. The embodiment described below is merely an example, and should not be construed as being limited by this description.

[0013] Fig. 1 is a block diagram showing a configuration of a quantum processing device 100 according to an embodiment. The quantum processing device 100 shown in Fig. 1 includes an evaluation function setting unit 110, a quantum bit reduction unit 120, a quantum circuit generation unit 130, and a quantum processing unit 140. This quantum processing device 100 is a quantum computer that quickly finds a solution to a graph coloring problem, which is an example of a combinatorial optimization problem. The graph coloring problem is a problem of coloring each node in a graph having multiple nodes with a color different from the adjacent nodes connected by an edge.

[0014] The evaluation function setting unit 110 sets an evaluation function for obtaining a solution to the graph coloring problem. That is, the evaluation function setting unit 110 accepts an input of an evaluation function that expresses a condition that a node is colored with a color different from that of adjacent nodes connected by an edge, and sets the accepted evaluation function as a calculation processing target. At this time, the evaluation function setting unit 110 sets an evaluation function that is a polynomial including a cubic or higher order term. A binary optimization problem using such an evaluation function including a cubic or higher order term is also called HUBO (Higher-order Unconstrained Binary Optimization). Therefore, the evaluation function setting unit 110 sets a HUBO format evaluation function as a calculation processing target.

[0015] Here, a specific example of an evaluation function in the HUBO format will be described. For example, when expressing the color of a node s in binary, the set of values ​​for each digit is b s =(b s (K-1) , b s (K-2) , …, b s (0) ), the condition for coloring the neighboring node t of node s with a different color from that of node s is to minimize (i.e., to 0) the following equation (1): t This can be expressed as determining

number

[0016] In equation (1), K is the smallest integer greater than or equal to the logarithm to the base 2 of the number of colors C that can be used in the coloring (K=ceil(log2C)). If the number of colors that can be used in the coloring is C, then each color can be expressed by a K-digit binary number.

[0017] Since minimizing equation (1) for all nodes is the solution to the graph coloring problem, the evaluation function here is as shown in equation (2) below.

number

[0018] In formula (2), E(G) is the set of all edges in the graph. Therefore, by determining the combination of binary numbers representing the color of each node so as to minimize the evaluation function of formula (2), it is possible to make the colors of the nodes s and t on both sides of every edge different.

[0019] As is clear from equation (1), the evaluation function shown in equation (2) includes third- or higher-order terms if K is 2 or greater. In other words, the evaluation function shown in equation (2) is a HUBO-type evaluation function.

[0020] The evaluation function setting unit 110 sets, for example, the evaluation function of the above-mentioned formula (2) as the calculation processing target. Note that, in addition to the evaluation function of formula (2), the evaluation function setting unit 110 may set, as the calculation processing target, an evaluation function that is an upper limit value of a binary number representing a color and indicates an upper limit value condition according to the number C of colors that can be used for coloring.

[0021] The quantum bit reduction unit 120 reduces the number of quantum bits used in the calculation process of the evaluation function in the HUBO format. Specifically, when the calculation process of the evaluation function, which is a polynomial, is executed, the quantum bit reduction unit 120 reuses the quantum bits used in the calculation of one term that are not used in the calculation of the subsequent term, thereby reducing the number of quantum bits used in the entire calculation process. For this reason, the quantum bit reduction unit 120 appropriately rearranges the order of the terms of the evaluation function, and selects the quantum bits that are not used in the calculation of the subsequent term as the quantum bits to be measured. Then, the quantum bit reduction unit 120 determines the quantum bits to reuse the quantum bits that have been measured.

[0022] The quantum circuit generation unit 130 generates a quantum circuit for performing calculation processing of the evaluation function based on the content determined by the quantum bit reduction unit 120. That is, the quantum circuit generation unit 130 generates a quantum circuit in which quantum gates that perform calculations corresponding to the evaluation function are arranged for the quantum bits reduced by the quantum bit reduction unit 120.

[0023] The quantum operation unit 140 executes a quantum operation using the quantum circuit generated by the quantum circuit generation unit 130. That is, the quantum operation unit 140 executes a quantum operation according to the quantum gates arranged in the quantum circuit, measures the state of each quantum bit at the timing indicated by the quantum circuit, and obtains a quantum operation result. Therefore, for example, when the evaluation function of formula (2) is the object of the operation process, the quantum operation unit 140 obtains a combination of binary numbers that minimizes the evaluation function of formula (2) as the quantum operation result.

[0024] Next, a quantum processing method using the quantum processing device 100 configured as above will be described with reference to the flow chart shown in FIG.

[0025] When the graph coloring problem is formulated and necessary information is input to the quantum computing device 100, the evaluation function to be processed is set by the evaluation function setting unit 110 (step S101). This evaluation function is a HUBO format evaluation function that expresses the color of a node in binary, and for example, the evaluation function of the above formula (2) is set. Since the evaluation function is in the HUBO format, it is possible to reduce the number of quantum bits used compared to when the evaluation function is in, for example, the QUBO format.

[0026] Below, we will explain, using specific examples, how HUBO can reduce the number of quantum bits.

[0027] In QUBO, for example, when eight nodes are colored in four colors, the color of each node is expressed by four color representation bits by one-hot representation. That is, for each of nodes t0 to t7, as shown in FIG. 3(a), the color number is expressed by a color representation bit c0 indicating whether to color in a first color, a color representation bit c1 indicating whether to color in a second color, a color representation bit c2 indicating whether to color in a third color, and a color representation bit c3 indicating whether to color in a fourth color. For this reason, in QUBO, 32 quantum bits are used to perform operations related to the color representation bits of the eight nodes.

[0028] On the other hand, in HUBO, when eight nodes are similarly colored in four colors, the color of each node is expressed by two color representation bits in binary notation. That is, for example, as shown in FIG. 3(b), for each of the nodes t0 to t7, the color representation bit b (1) and color representation bit b indicating the lowest digit (0) Therefore, in HUBO, 16 quantum bits are used to perform operations on the color representation bits of the 8 nodes.

[0029] In this way, compared to QUBO, HUBO can reduce the number of quantum bits used from 32 to 16. Therefore, by using the HUBO format evaluation function as the computation target, it is possible to reduce the number of quantum bits used in quantum operations.

[0030] In addition, the evaluation function of the HUBO format includes third-order or higher terms, and the quantum circuit that performs quantum operations on third-order or higher terms can be configured with quantum gates corresponding to the terms arranged as shown in Figures 4(a) and 4(b). That is, for third-order terms using quantum bits q0, q1, and q2, for example, it is possible to construct a quantum gate with the configuration shown in Figure 4(a), and for fourth-order terms using quantum bits q0, q1, q2, and q3, for example, it is possible to construct a quantum gate with the configuration shown in Figure 4(b).

[0031] Once the evaluation function is set, the quantum bit reduction unit 120 executes a process of reducing the quantum bits used in the quantum operation (step S102). That is, when the calculation process of the evaluation function, which is a polynomial, is executed, it is decided to perform a quantum operation on each term while reusing quantum bits, and the quantum bits to be used are reduced. At this time, it is decided to reuse the quantum bits that are not used in the calculation of the subsequent term among the quantum bits used in the calculation of one term, and the quantum bits to which the quantum bits are to be reused are determined. Such reuse of quantum bits is sometimes called MCMR (Mid-Circuit Measurement and Reset). The quantum bit reduction process will be described in detail later.

[0032] When the quantum bit reduction process is performed, a quantum circuit in which the number of quantum bits used is reduced is generated by the quantum circuit generation unit 130 (step S103). The quantum circuit generated here can be a quantum circuit used in, for example, a quantum approximate optimization algorithm (QAOA). This quantum circuit is, for example, a quantum circuit having a configuration shown in FIG. 5.

[0033] In the quantum circuit shown in Figure 5, U(H1, γ k )=exp(-iγ k H1), U(H0, β k )=exp(-iβ k H0), where H1 is a Hamiltonian with the optimal solution as its ground state, and H0 is a Hamiltonian with the trivial ground state as its solution. By performing quantum operations using such a quantum circuit, the optimal solution that minimizes the evaluation function can be obtained.

[0034] Then, the quantum operation unit 140 executes a quantum operation using a quantum circuit (step S104). In the quantum operation, the state of the quantum bit controlled by the quantum gate is measured to obtain an optimal solution. That is, here, for example, a combination of the binary representations b of colors that minimizes the evaluation function of formula (2) is determined.

[0035] In this way, the evaluation function formulated by HUBO is used as the target of calculation, and quantum operations are performed to find the optimal solution while reusing quantum bits, making it possible to use quantum bits efficiently.

[0036] Next, a quantum bit reduction process for reducing quantum bits used in quantum computation will be specifically described with reference to the flow diagram shown in Fig. 6. The quantum bit reduction process is mainly executed by quantum bit reduction unit 120.

[0037] Since the evaluation function of the HUBO format includes a third or higher order term, a quantum circuit corresponding to this evaluation function has a quantum gate across three or more quantum bits, for example, as shown in Fig. 7. That is, the quantum circuit shown in Fig. 7 corresponds to an evaluation function having a first term 210 related to the quantum bits q0, q3, and q4, a second term 220 related to the quantum bits q0, q1, q2, and q3, and a third term 230 related to the quantum bits q1, q2, and q4, among five quantum bits q0, q1, q2, q3, and q4. Although five quantum bits are used in the quantum circuit shown in Fig. 7, the number of quantum bits used can be reduced by a quantum bit reduction process described below.

[0038] First, a set of qubits Q that reuses other qubits among the qubits corresponding to all terms of the evaluation function is R is initialized (step S201). That is, here, since all the quantum bits q0, q1, q2, q3, and q4 may reuse other quantum bits, the set Q R is initialized with the set Q = {q0, q1, q2, q3, q4} of all qubits.

[0039] Then, the quantum bit p to be measured first is selected according to the strategy of the following equation (3) (step S202).

number

[0040] In formula (3), C p , C q are the causal cones of the quantum bits p and q, respectively, and indicate a set of quantum bits that affect the measurement of the quantum bits p and q. For example, FIG. 8(a) is a diagram showing the causal cone 240 of the quantum bit q1. In the quantum circuit shown in FIG. 8(a), the quantum bit q1 is influenced by the quantum bit q2, the quantum bit q2 is influenced by the quantum bit q3, and the quantum bit q3 is influenced by the quantum bits q0 and q4, so the causal cone 240 of the quantum bit q1 includes the quantum bits q0, q2, q3, and q4. Similarly, FIG. 8(b) is a diagram showing the causal cone 250 of the quantum bit q4. In the quantum circuit shown in FIG. 8(b), the quantum bit q4 is influenced by the quantum bits q0 and q3, so the causal cone 250 of the quantum bit q4 includes the quantum bits q0 and q3.

[0041] The above formula (3) shows that the qubit p to be measured is selected so that the union of the causality cones of each qubit, including the qubit already selected as the measurement target, is minimized. However, since the size of the causality cone changes depending on the arrangement order of the quantum gates corresponding to the terms in the quantum circuit, the causality cone C pAs small as possible, a quantum bit p is selected that satisfies equation (3) after advancing the order of quantum gates across the quantum bit p.

[0042] For example, in the quantum circuit shown in FIG. 9(a), quantum gates 310, 320, and 330 are arranged in this order from the left. In this case, the causal cone of the quantum bit q1, for example, includes the quantum bits q0, q2, q3, and q4 as shown in FIG. 8(a). Here, if the order of the quantum gate 330 across the quantum bit q1 is advanced and moved to the left, for example, the quantum circuit shown in FIG. 9(b) is obtained. In the quantum circuit shown in FIG. 9(b), quantum gates 330, 320, and 310 are arranged in this order from the left. In this case, the causal cone of the quantum bit q1 includes only the quantum bit q2.

[0043] Thus, the causal cone C of qubit p p As small as possible, a quantum bit p that satisfies the above formula (3) is selected, and this quantum bit p is measured at an early stage as the measurement target. This makes it possible to measure a quantum bit that does not affect other quantum bits at an early stage and reuse this quantum bit.

[0044] For example, in the example shown in FIG. 9(b), if quantum bit q1 is selected as the quantum bit to be measured, the measurement of quantum bit q1 is accelerated, as shown in FIG. 10(a), and quantum bit q1 after the measurement becomes reusable.

[0045] When a qubit p is selected for measurement, a set of qubits Q R is updated (step S203). That is, the quantum bit p and the quantum bits included in the causal cone of the quantum bit p are updated in the set Q R This can be expressed as the following formula (4): R will be updated.

number

[0046] Then, the set of qubits q that reuse the measured qubit p is Q R (Step S204). Specifically, the set Q R Among the quantum bits included in, the quantum bit that is spanned by the smallest number of other quantum bits in the quantum gate is determined to be quantum bit q.

[0047] For example, in the example shown in FIG. 9(b), when the qubit q1 is selected as the qubit to be measured, the set of qubits to be reused Q R belongs to quantum bits q0, q3, and q4, excluding quantum bits q1 and q2. Of these, quantum bit q3 spans quantum bits q2, q0, and q4 in quantum gates 320 and 310, respectively, spanning three quantum bits. On the other hand, quantum bits q0 and q4 span two quantum bits in quantum gate 310. For this reason, the quantum bit q to be reused is determined to be quantum bit q0 or quantum bit q4. Here, for example, if quantum bit q0 is determined to be the quantum bit to be reused, quantum bit q0 is deleted and measured quantum bit q1 is initialized and reused in place of quantum bit q0, as shown in FIG. 10(b).

[0048] When the number of qubits used is reduced in this way, the set of qubits to be reused Q R It is determined whether Q is an empty set (step S205). R If the set Q is not an empty set (step S205 No), the process is repeated from the selection of the quantum bit p to be measured (step S202). R When becomes an empty set (Yes in step S205), the quantum bit reduction process ends.

[0049] In this way, by reusing the measured quantum bits, the number of quantum bits used in the quantum operation can be reduced. FIG. 11 is a diagram showing the number of quantum bits used when solving a graph coloring problem for coloring ladder-shaped graphs with various numbers of nodes. FIG. 11 shows the number of quantum bits used when solving the graph coloring problem by QUBO, by solving it by HUBO, and by solving it by the quantum operation method according to the present embodiment. As shown in this figure, by solving the graph coloring problem by HUBO, the number of quantum bits used can be halved compared to solving it by QUBO, and the number of quantum bits used can be significantly reduced by further performing the quantum bit reduction process described above.

[0050] As described above, according to this embodiment, a HUBO-format evaluation function including third-order or higher-order terms is set as the calculation target, and in a quantum circuit corresponding to this evaluation function, quantum bits used in the calculation of one term that are not used in the calculation of the subsequent term are reused to execute quantum calculation. Therefore, the number of quantum bits used in the quantum calculation can be reduced, and the quantum bits can be used efficiently. [Explanation of symbols]

[0051] 100 Quantum computing device 110 Evaluation function setting section 120 qubit reduction section 130 Quantum circuit generation section 140 Quantum operation section

Claims

1. A setting unit that sets an evaluation function consisting of a polynomial including third-order or higher-order terms as a calculation target; A determination unit that determines to reuse a quantum bit that is used in an operation of one term but is not used in an operation of a subsequent term in a quantum circuit corresponding to the evaluation function; A generator for generating a quantum circuit that reuses the quantum bit determined to be reused in place of other quantum bits; A quantum operation unit that executes quantum operations using the generated quantum circuit; A quantum computing device having the above structure.

2. The determination unit is The quantum computing device according to claim 1 , wherein the quantum bits to be reused are selected so that the union of the causality cones of the quantum bits to be reused is minimized.

3. The determination unit is 3. The quantum computing device according to claim 2, wherein a quantum bit to be reused is selected so that the union of the causality cones when the order of the quantum gates related to the quantum bit is advanced so that the causality cone of the quantum bit is minimized.

4. The generation unit is 2. The quantum computing device according to claim 1, which generates a quantum circuit in which the quantum bit with the smallest number of quantum bits spanned in a quantum gate is the quantum bit to be reused, among the quantum bits other than the quantum bit determined to be reused by the determination unit and the quantum bits included in the causal cone of the quantum bit, is selected.

5. Setting an evaluation function consisting of a polynomial including third or higher degree terms as an object of calculation; determining that, in a quantum circuit corresponding to the evaluation function, a quantum bit used in an operation of one term that is not used in an operation of a subsequent term is reused; generating a quantum circuit that reuses the determined qubit in place of other qubits; Executing a quantum operation using the generated quantum circuit; and A quantum computing method comprising:

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