EP-4738206-A1 - INFORMATION PROCESSING METHOD, INFORMATION PROCESSING SYSTEM, CALCULATION QUANTUM CIRCUIT, METHOD FOR GENERATING CALCULATION QUANTUM CIRCUIT, AND PROGRAM

EP4738206A1EP 4738206 A1EP4738206 A1EP 4738206A1EP-4738206-A1

Abstract

One aspect of the present invention provides an information processing method. The information processing method includes the following steps. In an acquisition step, information related to an input state that is represented by n calculation quantum bits, information related to a Hamiltonian, and the number K of repetitions (K is an integer of 2 or more) of an operation that is based on the Hamiltonian are acquired. In an allocation step, plurality of auxiliary bits are allocated in accordance with the number K of repetitions. The states of the n calculation quantum bits and the plurality of auxiliary bits are configured to be expressable with use of at least a first state and a second state which are observable. In a generation step, a calculation quantum circuit is generated on the basis of the acquisition result in the acquisition step. The calculation quantum circuit is configured to cause a first reflection operation, a first operation quantum circuit, a second reflection operation, and a second operation quantum circuit to act in this order. The first reflection operation is configured to act on the plurality of auxiliary bits so as to change the phase of a first reflection state, which is one of a first state component and a second state component included in the plurality of auxiliary bits. The first operation quantum circuit is configured to act on n calculation quantum bits corresponding to an input state, and includes unit gate operations corresponding to the auxiliary bits. The unit gate operations are each configured such that one of a plurality of differing auxiliary bits is a control bit, a calculation quantum bit is a target bit, and the mode of acting on the calculation quantum bit is changed in accordance with the state of an auxiliary bit. The second reflection operation is configured to act on a calculation quantum bit and an auxiliary bit so as to change the phase of a second reflection state, which is one of a first state component and a second state component included in the calculation quantum bit and the auxiliary bit. The second operation quantum circuit is configured to enable conversion into a Hermite-coupled circuit of the first operation quantum circuit using a prescribed unitary gate operation.

Inventors

NISHI, HIROFUMI
KOSUGI, TAICHI
MATSUSHITA, Yuichiro

Assignees

Quemix Inc.
INSTITUTE OF SCIENCE TOKYO

Dates

Publication Date: 20260506
Application Date: 20240423

Claims (13)

An information processing method, comprising each step including: an acquisition step of acquiring information related to an input state represented by n computational qubits, information related to a Hamiltonian, and a number of repetitions K of an operation based on the Hamiltonian, the K being an integer of 2 or more; an assignment step of assigning a plurality of ancillary bits depending on the number of repetitions K, each state of the n computational qubits and the ancillary bits being configured to be represented by using at least a first state and a second state which are observable; and a generation step of generating a computational quantum circuit based on an acquisition result obtained in the acquisition step, the computational quantum circuit being configured to allow a first reflection operation, a first operational quantum circuit, a second reflection operation, and a second operational quantum circuit to sequentially act, the first reflection operation being configured to act on the ancillary bits so as to change a phase of a first reflection state, which is one of components of the first state or the second state included in each of the ancillary bits, the first operational quantum circuit being configured to act on the n computational qubits corresponding to the input state and including unitary gate operations corresponding respectively to the ancillary bits, each of the unitary gate operations being configured to use one of the different ancillary bits as a control bit and the computational qubits as target bits, and to change a mode of action on the computational qubits depending on a state of the ancillary bits, the second reflection operation being configured to act on the computational qubits and the ancillary bits so as to change a phase of a second reflection state, which is one of components of the first state or the second state included in each of the computational qubits and the ancillary bits, the second operational quantum circuit being configured to be converted into a Hermitian conjugate circuit of the first operational quantum circuit by using a predetermined unitary gate operation.
The information processing method according to claim 1, wherein: the computational quantum circuit includes a reference circuit configured to act on the computational qubits, and the reference circuit is configured to output the input state based on a state of the initialized computational qubits.
The information processing method according to claim 1 or 2, wherein: the computational quantum circuit further includes an observation operation, the observation operation is configured to observe a state of each of the ancillary bits that functions as a control bit of the unitary gate operation, and the each step further includes an output step of outputting a state of the computational qubits as a calculation result based on an observation result of the ancillary bits.
The information processing method according to any one of claims 1 to 3, wherein: the state of the ancillary bits included in the first reflection state and the state of the ancillary bits included in the second reflection state are common, and the second operational quantum circuit is configured to be Hermitian conjugate of the first operational quantum circuit.
The information processing method according to any one of claims 1 to 4, wherein: the first reflection operation has a phase that is inverted with respect to a phase of the second reflection operation.
The information processing method according to any one of claims 1 to 5, wherein: the operation is a probabilistic operation configured to represent whether or not the operation succeeds depending on the state of the ancillary bits.
The information processing method according to any one of claims 1 to 6, wherein: each of the unitary gate operations is configured to allow either a unitary operation or a Hermitian conjugate operation of the unitary operation to act on the computational qubits depending on the state of the ancillary bits, and the unitary operation is configured to correspond to performing the operation once.
An information processing method, comprising each step including: an acquisition step of acquiring information related to an input state represented by n computational qubits, information related to a Hamiltonian, and a number of repetitions K of an operation based on the Hamiltonian, the K being an integer of 2 or more; an assignment step of assigning a plurality of ancillary bits depending on the number of repetitions K; a generation step of generating a computational quantum circuit based on an acquisition result obtained in the acquisition step, the computational quantum circuit being configured to allow an operational quantum circuit to act on the computational qubits and the ancillary bits, the operational quantum circuit being configured to act on the n computational qubits corresponding to the input state and including unitary gate operations corresponding respectively to the assigned ancillary bits, each of the unitary gate operations being configured to use one of the different ancillary bits as a control bit and the computational qubits as target bits, and to change a mode of action on the computational qubits depending on a state of the ancillary bits; and an output step of outputting a state of the computational qubits as a calculation result based on an observation result of the ancillary bits.
The information processing method according to claim 8, wherein: the computational quantum circuit is configured to further perform an observation operation on at least one of the ancillary bits after allowing the operational quantum circuit to act on the computational qubits and the ancillary bits, and the observation operation is configured to observe the state of the ancillary bits that function as control bits of the unitary gate operations.
A computational quantum circuit configured to: repeatedly perform, K times, an operation based on a Hamiltonian on an input state represented by n computational qubits, the K being an integer of 2 or more; and act on the n computational qubits and a plurality of ancillary bits depending on the K, each state of the computational qubits and the ancillary bits being configured to be represented by using at least a first state and a second state which are observable; the computational quantum circuit being configured to allow a first reflection operation, a first operational quantum circuit, a second reflection operation, and a second operational quantum circuit to sequentially act, the first reflection operation being configured to act on the ancillary bits so as to change a phase of a first reflection state, which is one of components of the first state or the second state included in each of the ancillary bits, the first operational quantum circuit being configured to act on the n computational qubits corresponding to the input state and including unitary gate operations corresponding respectively to the ancillary bits, each of the unitary gate operations being configured to use one of the different ancillary bits as a control bit and the computational qubits as target bits, and to change a mode of action on the computational qubits depending on a state of the ancillary bits, the second reflection operation being configured to act on the computational qubits and the ancillary bits so as to change a phase of a second reflection state, which is one of components of the first state or the second state included in each of the computational qubits and the ancillary bits, the second operational quantum circuit being configured to be converted into a Hermitian conjugate circuit of the first operational quantum circuit by using a predetermined unitary gate operation.
A generation method of a computational quantum circuit according to claim 10, comprising: an acquisition step of acquiring information related to the input state, information related to the Hamiltonian, and a number of repetitions of an operation based on the Hamiltonian, the number of repetitions corresponding to K, which is a number of times the unitary gate operation is performed; an assignment step of assigning the ancillary bits corresponding to the number of repetitions; and a generation step of generating a computational quantum circuit configured to allow the operation to repeatedly act on the computational qubits, based on an acquisition result obtained in the acquisition step.
An information processing system including at least one apparatus, comprising: at least one processor configured to execute a program so as to execute each step of the information processing method according to any one of claims 1 to 9.
A program that allows at least one computer to execute each step of the information processing method according to any one of claims 1 to 9.

Description

BACKGROUND The present disclosure relates to an information processing method, a computational quantum circuit, a generation method of a computational quantum circuit according to claim 10, an information processing system, and a program. RELATED ART Quantum information processing using quantum mechanics for information processing has been proposed. Furthermore, many studies have been conducted on quantum computers based on such quantum information processing. For example, Patent Document 1 discloses a conventional technique for quantum information processing. Non-patent document is a reference document. PRIOR ART DOCUMENTS Patent document [Patent Document 1] JP2015-135377 A [Non-Patent Document] [Non-Patent Document 1] H. Nishi, K. Hamada, Y. Nishiya, T. Kosugi, and Y. ichiro Matsushita, Analyzing computational cost of probabilistic imaginary-time evolution method (2023), arXiv:2305.04600 [quant-ph]. SUMMARY Problems to be solved by invention By the way, there is still room for improvement in a technique for acquiring a desired state such as a ground state of a certain Hamiltonian. Means for solving problems According to one aspect of the present disclosure, an information processing method is provided. The information processing method includes the following steps. In an acquisition step, information related to an input state represented by n computational qubits, information related to a Hamiltonian, and a number of repetitions K of an operation based on the Hamiltonian are acquired, and the K is an integer of 2 or more. In an assignment step, a plurality of ancillary bits are assigned depending on the number of repetitions K. Here, each state of the n computational qubits and the ancillary bits is configured to be represented by using at least a first state and a second state which are observable. In a generation step, a computational quantum circuit is generated based on an acquisition result obtained in the acquisition step. The computational quantum circuit is configured to allow a first reflection operation, a first operational quantum circuit, a second reflection operation, and a second operational quantum circuit to sequentially act. The first reflection operation is configured to act on the ancillary bits so as to change a phase of a first reflection state, which is one of components of the first state or the second state included in each of the ancillary bits. The first operational quantum circuit is configured to act on the n computational qubits corresponding to the input state and includes unitary gate operations corresponding respectively to the ancillary bits. Each of the unitary gate operations is configured to use one of the different ancillary bits as a control bit and the computational qubits as target bits, and to change a mode of action on the computational qubits depending on a state of the ancillary bits. The second reflection operation is configured to act on the computational qubits and the ancillary bits so as to change a phase of a second reflection state, which is one of components of the first state or the second state included in each of the computational qubits and the ancillary bits. The second operational quantum circuit is configured to be converted into a Hermitian conjugate circuit of the first operational quantum circuit by using a predetermined unitary gate operation. Accordingly, it is possible to provide a quantum algorithm that can more efficiently obtain a desired state. BRIEF DESCRIPTION OF DRAWINGS [FIG. 1] FIG. 1 is a configuration diagram representing an information processing system 1.[FIG. 2] FIG. 2 is a block diagram showing a hardware configuration of an information processing apparatus 2.[FIG. 3] FIG. 3 is a block diagram showing a hardware configuration of a quantum computer 3.[FIG. 4] FIG. 4 is a block diagram showing a hardware configuration of a user terminal 4.[FIG. 5] FIG. 5 is a block diagram showing a functional structure of a processor 23.[FIG. 6] FIG. 6 is a diagram illustrating an example of a quantum circuit QC1 of a probabilistic algorithm for preparing a ground state of a Hamiltonian.[FIG. 7] FIG. 7 is a diagram illustrating an example of a computational quantum circuit 5.[FIG. 8] FIG. 8 is a diagram illustrating an example of VRTE.[FIG. 9] FIG. 9 is a diagram illustrating a modified example of VRTE.[FIG. 10] FIG. 10 is a flowchart illustrating an overview of the information processing executed in the information processing system 1.[FIG. 11] FIG. 11 is a diagram showing simulation results of the relationship between the computational cost and the infidelity δK in each method for generating a ground state of the Hamiltonian H.[FIG. 12] FIG. 12 is a diagram showing simulation results of the relationship between the weight |c1|-1 of the probability of the ground state of the input state | ψ>, obtained using each method, and the computational cost.[FIG. 13] FIG. 13 is a quantum circuit for implementing a time-evolution operator exp(LΔt) with a