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EP-4742111-A1 - COMPUTER PROGRAM, QUANTUM COMPUTING SUPPORT METHOD, AND INFORMATION PROCESSING APPARATUS

EP4742111A1EP 4742111 A1EP4742111 A1EP 4742111A1EP-4742111-A1

Abstract

An information processing apparatus expands an imaginary time evolution equation for calculating a thermal-equilibrium expectation value into equations of a plurality of degrees, generates sets of the degrees, and generates, for each set, a quantum circuit indicating quantum computation of a physical quantity value obtained by partial imaginary time evolution. A quantum computer is caused to repeatedly execute quantum computation based on the quantum circuit for each set. When doing so, a state in a stationary distribution of measurement results obtained by quantum computation based on a second quantum circuit corresponding to a second set is used as an input state at the start of quantum computation based on a first quantum circuit corresponding to a first set. The thermal-equilibrium expectation value of the physical quantity at the finite temperature is then calculated based on the values of the physical quantity after convergence for each set.

Inventors

  • Matsumoto, Norifumi

Assignees

  • FUJITSU LIMITED

Dates

Publication Date
20260513
Application Date
20251104

Claims (7)

  1. A computer program that causes a computer to execute a process comprising: expanding an imaginary time evolution equation for calculating a thermal-equilibrium expectation value of a physical quantity at a finite temperature in a calculation target system, into equations of a plurality of degrees; generating a plurality of sets of degrees obtained by extracting two degrees from the plurality of degrees; generating, for each of the plurality of sets, a quantum circuit indicating a procedure of quantum computation of a value of the physical quantity, the value being obtained by partial imaginary time evolution based on an expression of a first degree included in the set and an expression of a second degree included in the set; causing a quantum computer (1) to repeatedly execute, for each of the plurality of sets, the quantum computation based on the corresponding quantum circuit until a value of the physical quantity obtained from a result of the quantum computation converges, wherein, as an input state at a start of quantum computation based on a first quantum circuit (2a) corresponding to at least one first set out of the plurality of sets, a state in a stationary distribution of a measurement result obtained by the quantum computation based on a second quantum circuit (2b) corresponding to a second set that differs from the at least one first set out of the plurality of sets is used; and calculating the thermal-equilibrium expectation value of the physical quantity at the finite temperature, based on the values of the physical quantity after convergence for each of the plurality of sets.
  2. The computer program according to claim 1, wherein causing the quantum computer (1) to execute the quantum computation based on the quantum circuits for the plurality of sets includes setting a set of degrees lower than degrees of the at least one first set among the plurality of sets as the second set.
  3. The computer program according to claim 1, wherein causing the quantum computer (1) to execute the quantum computation based on the quantum circuits for the plurality of sets includes ranking the plurality of sets in ascending order of degree, executing the quantum computation based on the quantum circuit for each of the plurality of sets in ascending order of rank, and determining, in response to the first set being ranked N+1 th , that the set ranked N th is the second set, N being a natural number.
  4. The computer program according to claim 1, wherein causing the quantum computer (1) to execute the quantum computation based on the quantum circuits for the plurality of sets includes causing the quantum computer (1) to repeatedly execute the quantum computation based on the quantum circuit until the value of the physical quantity obtained from the result of the quantum computation converges, wherein an output state after the quantum computation according to the quantum circuit corresponding to a set is used as an input state in a following quantum computation.
  5. The computer program according to claim 1, wherein causing the quantum computer (1) to execute the quantum computation based on the quantum circuits for the plurality of sets includes selecting one state from a plurality of states indicated in a computation result of the quantum computation performed a plurality of times based on the second quantum circuit (2b) after a measurement result of the quantum computation based on the second quantum circuit (2b) has become a stationary distribution, and setting the selected one state as an input state at a start of the quantum computation based on the first quantum circuit (2a) .
  6. A quantum computing support method executed by a computer, the quantum computing support method comprising: expanding an imaginary time evolution equation for calculating a thermal-equilibrium expectation value of a physical quantity at a finite temperature in a calculation target system, into equations of a plurality of degrees; generating a plurality of sets of degrees obtained by extracting two degrees from the plurality of degrees; generating, for each of the plurality of sets, a quantum circuit indicating a procedure of quantum computation of a value of the physical quantity, the value being obtained by partial imaginary time evolution based on an expression of a first degree included in the set and an expression of a second degree included in the set; causing a quantum computer (1) to repeatedly execute, for each of the plurality of sets, the quantum computation based on the corresponding quantum circuit until a value of the physical quantity obtained from a result of the quantum computation converges, wherein, as an input state at a start of quantum computation based on a first quantum circuit (2a) corresponding to at least one first set out of the plurality of sets, a state in a stationary distribution of a measurement result obtained by the quantum computation based on a second quantum circuit (2b) corresponding to a second set that differs from the at least one first set out of the plurality of sets is used; and calculating the thermal-equilibrium expectation value of the physical quantity at the finite temperature, based on the values of the physical quantity after convergence for each of the plurality of sets.
  7. An information processing apparatus comprising: processing means (12) configured to: expand an imaginary time evolution equation for calculating a thermal-equilibrium expectation value of a physical quantity at a finite temperature in a calculation target system, into equations of a plurality of degrees; generate a plurality of sets of degrees obtained by extracting two degrees from the plurality of degrees; generate, for each of the plurality of sets, a quantum circuit indicating a procedure of quantum computation of a value of the physical quantity, the value being obtained by partial imaginary time evolution based on an expression of a first degree included in the set and an expression of a second degree included in the set; cause a quantum computer (1) to repeatedly execute, for each of the plurality of sets, the quantum computation based on the corresponding quantum circuit until a value of the physical quantity obtained from a result of the quantum computation converges, wherein, as an input state at a start of quantum computation based on a first quantum circuit (2a) corresponding to at least one first set out of the plurality of sets, a state in a stationary distribution of a measurement result obtained by the quantum computation based on a second quantum circuit (2b) corresponding to a second set that differs from the at least one first set out of the plurality of sets is used; and calculate the thermal-equilibrium expectation value of the physical quantity at the finite temperature, based on the values of the physical quantity after convergence for each of the plurality of sets.

Description

FIELD The embodiments discussed herein relate to a computer program, a quantum computing support method, and an information processing apparatus. BACKGROUND Quantum computers are prone to errors in the state of quantum bits (hereinafter "qubits") due to factors such as environmental noise. In an error correction technique for qubits (or "quantum error correction"), information is encoded with redundancy. To realize quantum error correction at a practical level, a large number of qubits, in the region of one million, are used. Quantum computers that have been currently realized are limited to medium to small scale quantum computers (or noisy intermediate scale quantum computers (NISQ)) of about several hundred qubits at the maximum and are unable to correct faults. A quantum computer that is capable of fault correction is called a "fault tolerant quantum computer (FTQC)". Small-scale FTQC are expected to be realized fairly soon, and may be referred to as "early-stage FTQC". One field in which calculation by a quantum computer is effective is the computation of a physical quantity in a quantum system. Of particular significance in practice is computation of a thermal-equilibrium expectation value at a finite temperature. To obtain a thermal-equilibrium expectation value at a finite temperature, as one example, an expectation value for an ensemble of quantum states representing a thermal equilibrium state is calculated. One example of an ensemble that represents a thermal equilibrium state at a finite temperature is a canonical ensemble. The minimally entangled typical thermal state (METTS) algorithm is known as a method of efficiently generating a canonical ensemble. Although the METTS algorithm was originally devised as a computing technique to run on a classical computer, it is possible to run an equivalent technique on a quantum computer. An algorithm equivalent to METTS that is executed on a quantum computer is distinguished by the name "quantum METTS" (or "QMETTS"). In the METTS algorithm, an imaginary time evolution algorithm is used to realize the Boltzmann weights (the same applies to QMETTS). As a quantum imaginary time evolution technique for realizing imaginary time evolution on a quantum computer, there is a technique based on linear combination of unitaries (LCU). LCU is a quantum computing method in which imaginary time evolution is expanded into polynomials, respective degrees of polynomials are expressed by quantum circuits, and a physical quantity is calculated through linear combination of the polynomials. When LCU is realized by an early-stage FTQC, a target physical quantity is calculated based on a computation result obtained by causing each of a plurality of partial circuits extracted from an original quantum circuit to act on qubits. In LCU, since execution is performed by small-scale partial circuits, computation is possible even by an early-stage FTQC. A method for obtaining an excited state of a Hamiltonian has been proposed as one example of a quantum computing technique. A combinatorial optimization computation method has also been proposed where it is possible to obtain a feasible solution even for problems where a feedback-based algorithm for quantum optimization (FALQON) does not bring about a feasible solution. Quantum algorithms have also been proposed that improve quantum optimization by utilizing peripheral data. A quantum many-body simulation method for a finite temperature system in which series expansion of a quantum imaginary time evolution is sampled has also been proposed. This quantum many-body simulation method is called "Markov-chain Monte Carlo with sampled pairs of unitaries (MCMC-SPU)". See, for example, the following literatures. International Publication Pamphlet No. WO 2020/090559 Japanese Laid-open Patent Publication No. 2023-43100 U.S. Patent Application Publication No. 2020/0057957Norifumi Matsumoto, Shoichiro Tsutsui, Yuya O. Nakagawa, Yuichiro Hidaka, Shota Kanasugi, Kazunori Maruyama, Hirotaka Oshima, Shintaro Sato, "Quantum many-body simulation of finite-temperature systems with sampling a series expansion of a quantum imaginary-time evolution", arXiv:2409.07070v1, quant-ph, 11 Sep. 2024 In MCMC-SPU, computation results of a plurality of simplified partial circuits are linearly combined by a classical computer to obtain a thermal-equilibrium expectation value for a physical quantity in a quantum system at a finite temperature. In the iterative computation of each partial circuit, the state obtained by projective measurement in the computational basis of the output state of the partial circuit in one step is used as the input state of the next step. By doing so, an appropriate statistical ensemble is efficiently generated. In MCMC-SPU, the input state of the first step (that is, the first iteration in iterative computation) in the computation by each partial circuit is randomly selected from the computational basis, for example. This is equivalent to the