Information processing system, information processing method, and information processing program

Abstract

According to one aspect of the present invention, an information processing system is provided. The information processing system comprises at least one processor capable of executing a program so as to carry out each of the following steps. An acquisition step involves performing a process of acquiring substance information relating to a substance including at least one atomic nucleus and at least one electron. The substance information includes: a plurality of disposition candidates for the atomic nucleus; and interactions that act on the atomic nucleus and the electron. The interactions at least include an electron-atomic nucleus interaction that acts between the atomic nucleus and the electron. An allocation step involves performing a process of allocating each of the acquired disposition candidates for the atomic nucleus to one of one or more first quantum bit states. The first quantum bit states are configured by one or more first quantum bits and can be observed through observation operation on the first quantum bits. A superposition step involves performing a process of generating a superposition state of a plurality of the first quantum bit states, by performing a prescribed first quantum gate operation on the first quantum bits. An interaction step involves performing a process of, by performing a second quantum gate operation, including the acquired interactions, on the first quantum bits representing the superposition state and on one or more second quantum bits representing the state of the electron of the substance, generating a correlated quantum bit state in which the first quantum bits and the second quantum bits are correlated with each other. An identification step involves performing a process of identifying, on the basis of a result of observation on the first quantum bits in the generated correlated quantum bit state, a disposition where the minimum energy eigenvalue is relatively low, from among the disposition candidates for the atomic nucleus.

Description

Information processing system, information processing method, and information processing program

[0001] The present invention relates to an information processing system, an information processing method, and an information processing program.

[0002] a potential energy calculation unit that calculates the total potential energy based on the nuclear coordinates, the internal coordinates, the bond order, and the coordination state; a first-order differential calculation unit that calculates the force acting on each nuclear coordinate and internal coordinate by first-order differential processing of the potential energy; a simulation unit that calculates the amount of movement over a specified short time period based on the nuclear coordinates and the force acting on the internal degree of freedom that determines the direction of the covalent bond of each atom, and updates the coordinate information, and performs molecular dynamics calculations on the time evolution of the nuclear coordinates and the internal degree of freedom variables while repeating the bond order calculation, potential energy calculation, and differential calculation a specified number of times based on the coordinate information; and an output unit that outputs the simulation results.

[0003] By applying the technology described in Patent Document 1, in a molecular dynamics simulation of a large-scale system dealing with a group of several thousand atoms or more, it is possible to efficiently reproduce the structural changes that accompany the rearrangement of covalent bonds in a substance having a complex composition in which multiple elements are mixed, while faithfully reproducing the structural energy changes that depend on the coordination state of each atom.

[0004] Japanese Patent Application Laid-Open No. 2008-052308

[0005] When simulating a material, the arrangement of particles that make up the material can be important. Therefore, it is desirable to accurately determine the arrangement of particles. However, when there are multiple particle arrangement candidates, it is necessary to perform dynamics simulation for each of the multiple particle arrangement candidates in sequence, which may increase the calculation time.

[0006] According to one aspect of the present invention, there is provided an information processing system. The information processing system includes at least one processor capable of executing a program to perform the following steps: In the acquisition step, a process is performed to acquire substance information about a substance including at least one atomic nucleus and at least one electron. The substance information includes a plurality of candidate atomic nucleus configurations and interactions acting on the atomic nucleus and the electron. The interactions include at least the electron-nucleus interaction acting between the atomic nucleus and the electron. In the assignment step, a process is performed to assign each of the acquired candidate atomic nucleus configurations to one of at least one first quantum bit state. The first quantum bit state is constituted by at least one first quantum bit and is a state that can be observed by an observation operation on the first quantum bit. In the superposition step, a process is performed to generate a superposition state of a plurality of first quantum bit states by performing a predetermined first quantum gate operation on the first quantum bit. In the interaction step, a process is performed to generate a correlated quantum bit state in which the first quantum bit and the second quantum bit are correlated by performing a second quantum gate operation including the obtained interaction on the first quantum bit representing the superposition state and at least one second quantum bit representing the electronic state of the material. In the identification step, a process is performed to identify a configuration having a relatively low minimum energy eigenvalue from among candidate configurations of atomic nuclei based on observation results for the first quantum bit in the generated correlated quantum bit state.

[0007] According to this information processing system, it is possible to improve the calculation efficiency when identifying an appropriate particle arrangement from among a plurality of particle arrangement candidates.

[0008] 1 is a configuration diagram showing an information processing system 1. FIG. 1 is a block diagram showing the hardware configuration of an information processing device 2. FIG. 2 is a block diagram showing the hardware configuration of a quantum computer 3. FIG. 3 is a block diagram showing the hardware configuration of a user terminal 4. FIG. 4 is a block diagram showing the functional configuration of a processor 23. FIG. 5 is an activity diagram showing an overview of information processing executed in the information processing system 1. FIG. 6 is a diagram showing an example of a computational quantum circuit QC1. FIG. 7 is a diagram for explaining an example of a first quantum gate operation QC11. FIG. 8 is a diagram for explaining an example of a reference quantum gate operation QC12. FIG. 9 is a diagram for explaining a computational quantum circuit QC1 based on a stochastic imaginary time evolution method. FIG. 10 is a diagram showing an example of an expression of the contribution exp(-iVΔt) of the interaction V in a unit quantum circuit QC131. FIG. 11 is a diagram showing an example of a quantum circuit for implementing a real-time evolution operator exp(-iV_enΔt) when n_e=4, n_nucl=3. FIG. 12 is a diagram showing an example of a search quantum circuit C_PITE for performing imaginary time evolution. FIG. 13 is a diagram showing an example of a quantum amplitude amplification circuit Q in the imaginary time evolution method. FIG. 14 is a diagram showing a simulation result of the first step (i.e., initial state). FIG. 15 is a diagram showing a simulation result of the eighth step. 1 is a diagram showing the simulation results of the 14th step. It is a diagram showing the simulation results of the weights of each candidate structure immediately after the 19th step has passed. It is an activity diagram showing an overview of information processing in this embodiment executed in the information processing system 1. It is an example of a computational quantum circuit QC1 for VQE. It shows a differential circuit QC2 for calculating the differential (-2i)·∂|φ(θ)> / ∂θ_k with respect to θ_k. It is a diagram showing the simulation results of the sum of the weights of the energy eigenstates in each nucleus configuration (Geom 0 to Geom 7). It is a diagram showing the weights of the energy eigenstates of the ground state (1st lowest), first excited state (2nd lowest), second excited state (3rd lowest), and sum (Total) of the electron wave function in the optimal configuration (Geom 4). It is a diagram showing an example of a unit quantum circuit QC131 for performing an information processing method on a quantum bit system that considers only the nucleus configuration. 10 is a diagram showing an example of a second quantum gate operation QC13 that generates a Gibbs state for performing finite temperature calculations. FIG. 11 is a diagram showing an example of a maximally entangled state generation circuit U_ME.1 is a flowchart showing the flow of quantum circuit generation processing in this embodiment. FIG. 2 is a diagram showing an example of an input generation circuit QC10 in this embodiment. FIG. 3 is a diagram showing an example of a quantum circuit representing a virtual Hamiltonian as a second quantum gate operation QC13. FIG. 4 is a diagram showing an example of a computational quantum circuit QC1 in this embodiment. FIG. 5 is a diagram showing the relationship between the observation probability of each candidate and the number of steps, as a simulation result when an adiabatic time evolution method is adopted as the ground state search method. FIG. 6 is a diagram showing components included in a wave function in a final state. FIG. 7 is a flowchart showing the flow of a fourth information processing. FIG. 8 is a flowchart showing the flow of a fifth information processing.

[0009] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will be described below with reference to the accompanying drawings. Various features shown in the following embodiments can be combined with each other.

[0010] Incidentally, the program for realizing the software appearing in this embodiment may be provided as a non-transitory computer-readable recording medium, or may be provided so as to be downloadable from an external server, or may be provided so that the program is started on an external computer and its functions are realized on a client terminal (so-called cloud computing).

[0011] In this embodiment, the term "unit" may include, for example, a combination of hardware resources implemented by a circuit in the broad sense and software information processing that can be specifically realized by these hardware resources. In addition, various types of information are handled in this embodiment, and this information may be represented by, for example, physical values ​​of signal values ​​representing voltages and currents, high and low signal values ​​as a binary bit set consisting of 0 or 1, or quantum superposition (so-called quantum bits), and communication and calculations may be performed on a circuit in the broad sense.

[0012] Furthermore, a circuit in the broad sense is a circuit realized by at least an appropriate combination of a circuit, circuitry, a processor, a memory, etc. That is, it includes an application specific integrated circuit (ASIC), a programmable logic device (e.g., a simple programmable logic device (SPLD), a complex programmable logic device (CPLD), and a field programmable gate array (FPGA)), etc.

[0013] 1. Hardware Configuration In this section, the hardware configuration of an information processing system 1 according to this embodiment will be described. <Information Processing System 1> FIG. 1 is a configuration diagram showing the information processing system 1. The information processing system 1 includes an information processing device 2, at least one quantum computer 3, and a user terminal 4. The information processing device 2, the quantum computer 3, and the user terminal 4 are configured to be able to communicate with each other via a telecommunications line. In one embodiment, the information processing system 1 is made up of one or more devices or components. For example, if the information processing system 1 is made up of only the information processing device 2, the information processing system 1 can be the information processing device 2. These components will be described below.

[0014] 2 is a block diagram showing the hardware configuration of the information processing device 2. The information processing device 2 includes a communication unit 21, a storage unit 22, and a processor 23, and these components are electrically connected via a communication bus 20 inside the information processing device 2. Each component will be further described.

[0015] <Communication Unit 21> The communication unit 21 is preferably a wired communication means such as USB, IEEE 1394, Thunderbolt (registered trademark), or wired LAN network communication, but may also include wireless LAN network communication, mobile communication such as 3G / LTE / 5G, or BLUETOOTH (registered trademark) communication as needed. In other words, it is more preferable to implement the communication unit 21 as a collection of multiple communication means. In other words, the information processing device 2 may communicate various information from the outside via the communication unit 21 and the network.

[0016] <Storage Unit 22> The storage unit 22 stores various pieces of information defined above. This may be implemented, for example, as a storage device such as a solid state drive (SSD) that stores various programs and the like related to the information processing device 2 executed by the processor 23, or as a memory such as a random access memory (RAM) that stores temporarily required information (arguments, arrays, etc.) related to program calculations. The storage unit 22 stores various programs, variables, etc. related to the information processing device 2 executed by the processor 23.

[0017] <Processor 23> The processor 23 processes and controls the overall operations related to the information processing device 2. The processor 23 is, for example, a central processing unit (CPU) not shown. The processor 23 realizes various functions related to the information processing device 2 by reading out predetermined programs stored in the storage unit 22. In other words, information processing by software stored in the storage unit 22 is specifically realized by the processor 23, which is an example of hardware, and can be executed as each functional unit included in the processor 23. These will be described in more detail in the next section. Note that the processor 23 is not limited to being single, and multiple processors 23 may be provided for each function. A combination of these may also be used.

[0018] <Quantum Computer 3> Fig. 3 is a block diagram showing the hardware configuration of the quantum computer 3. As shown in Fig. 3, the quantum computer 3 has a communication unit 31, a quantum memory 32, and a quantum processor 33, and these components are connected via a communication bus 30 inside the quantum computer 3. Note that the quantum computer 3 may include an error-tolerant quantum computer, an NISQ device, or both. The quantum computer 3 of this embodiment is a gate type. Each component will be further described below.

[0019] <Communication Unit 31> The communication unit 31 is used by the quantum computer 3 to communicate information with other information processing devices (including classical computers, quantum computers, or computers that combine these) or peripheral devices.

[0020] <Quantum Memory 32> The quantum memory 32 stores various pieces of information defined above. In particular, the quantum memory 32 stores various programs that can be read by the quantum processor 33, which will be described next. The quantum memory 32 also stores, as needed, information on the physical properties of specific materials related to calculations by the quantum computer 3. The quantum memory 32 includes multiple qubits 320. The qubits 320 can be implemented using any method, such as nuclear spins, photons, ions, atoms, quantum dots, or superconducting Josephson devices. The qubits 320 include a computation qubit 321 and an ancillary bit 322. The computation qubit 321 includes at least one first qubit 321n and at least one second qubit 321e. The first qubit 321n functions as a qubit for representing the arrangement of atomic nuclei contained in a material. The second qubit 321e functions as a qubit for representing the electronic state of the material. In particular, the second quantum bit 321e functions as a quantum bit that represents the arrangement of electrons contained in a substance, for example. Note that the quantum memory 32 may include a classical memory device.

[0021] <Quantum Processor 33> The quantum processor 33 processes and controls the overall operations related to the quantum computer 3. The quantum processor 33 realizes various functions related to the quantum computer 3 by reading out a program stored in the quantum memory 32 or a predetermined program input via the communication unit 31. Note that while Fig. 3 shows a single quantum processor 33, in practice this is not limited to this, and multiple quantum processors 33 may be implemented for each function. A combination of these may also be used.

[0022] Quantum processor 33 is configured to be able to perform various quantum operations on quantum bits 320 that can be implemented on a quantum circuit. For example, the quantum circuit is configured to define a series of quantum operations on quantum bits 320. Quantum operations include, for example, quantum gate operations and observation operations. A quantum gate operation corresponds to a unitary operation on the quantum state of quantum bits 320. An observation operation corresponds to a projection operation on the quantum state of quantum bits 320.

[0023] <User Terminal 4> Next, the hardware configuration of the user terminal 4 will be described. Fig. 4 is a block diagram showing the hardware configuration of the user terminal 4. The user terminal 4 includes a communication unit 41, a memory 42, a processor 43, a display unit 44, and an input unit 45, and these components are electrically connected via a communication bus 40 inside the user terminal 4. The description of the communication unit 41, the memory 42, and the processor 43 is omitted because they are the same as the description of each unit in the information processing device 2.

[0024] <Display Unit 44> The display unit 44 may be included in the housing of the user terminal 4 or may be externally attached. The display unit 44 displays a graphical user interface (GUI) screen that can be operated by the user. This is preferably implemented by selectively using display devices such as a CRT display, a liquid crystal display, an organic EL display, or a plasma display depending on the type of user terminal 4.

[0025] <Input Unit 45> The input unit 45 may be included in the housing of the user terminal 4, or may be externally attached. For example, the input unit 45 may be implemented as a touch panel integrated with the display unit 44. A touch panel allows the user to input tapping, swiping, and the like. Of course, a switch button, a mouse, a QWERTY keyboard, or the like may be used instead of a touch panel. That is, the input unit 45 accepts an operation input made by the user. The input is transferred as a command signal to the processor 43 via the communication bus 40, and the processor 43 can execute predetermined control or calculation as necessary.

[0026] 2. Functional Configuration of the Processor 23 In this section, the functional configuration of the processor 23 of the information processing device 2 according to this embodiment will be described. Fig. 5 is a block diagram showing the functional configuration of the processor 23. The processor 23 includes an acquisition unit 231, a candidate generation unit 232, an allocation unit 233, a quantum operation unit 234, and an identification unit 235.

[0027] <Acquisition unit 231> The acquisition unit 231 is configured to be able to acquire various pieces of information related to quantum computing from the quantum computer 3 and the user terminal 4. The acquisition unit 231 is configured to be able to acquire various pieces of information by reading out various pieces of information stored in a storage area that is at least a part of the memory unit 22 and writing the read out information to a working area that is at least a part of the memory unit 22. The storage area is, for example, an area of ​​the memory unit 22 that is implemented as a storage device such as an SSD. The working area is, for example, an area that is implemented as a memory such as a RAM.

[0028] <Candidate Generator 232> The candidate generator 232 generates various information related to quantum computing. For example, the candidate generator 232 generates candidates for the arrangement of atomic nuclei based on the information acquired by the acquirer 231.

[0029] <Assignment Unit 233 > The assignment unit 233 is configured to be able to assign various pieces of information, for example, candidates for the arrangement of atomic nuclei, to the state of the quantum bit 320 .

[0030] <Quantum Operation Unit 234> The quantum operation unit 234 is configured to be able to perform various quantum operations on the quantum bits 320. The quantum operation unit 234 may be configured to perform quantum operations directly on the quantum bits 320, or may be configured to send a command to cause the quantum processor 33 to perform a quantum operation. The quantum operation unit 234 of this embodiment causes the quantum processor 33 to perform a quantum operation by sending various quantum circuits to the quantum processor 33.

[0031] <Identification Unit 235> The identification unit 235 is configured to be able to identify various pieces of information based on the results of quantum computation using the quantum bits 320. For example, the identification unit 235 identifies the optimal atomic nucleus arrangement under predetermined conditions from among the generated candidate atomic nucleus arrangements based on the results of quantum computation.

[0032] 3. Information Processing Method This chapter describes the flow of information processing executed in the above-described information processing system 1. The information processing described in this chapter may be referred to as first information processing.

[0033] 3.1. Information Processing Flow FIG. 6 is an activity diagram showing an overview of information processing executed in the information processing system 1. Note that the information processing may include any exception handling not shown in the activity diagram. Exception handling includes interruption of the information processing or omission of each process. Selection or input performed in the information processing may be based on a user operation or may be performed automatically without relying on a user operation.

[0034] In this information processing, the quantum processor 33 initializes the quantum bits 320 as necessary. When the quantum bits 320 are in two states, a ground state and an excited state, for example, the quantum processor 33 sets the states of all the quantum bits 320 to the ground state. Hereinafter, for convenience of explanation, the ground state of a single quantum bit 320 may be expressed as |0> and the excited state as |1> using bracket notation.

[0035] The information processing method can be used, for example, to identify the optimal arrangement of atomic nuclei in any substance. In the following description, the natural unit system is used, but other unit systems, such as the SI unit system or the CGS unit system, can also be used.

[0036] [Activity A1] First, in activity A1, the user terminal 4 transmits information about a substance to the processor 23. The information includes information that can identify the substance, such as the substance name of the substance. The information may include the substance information IF1 itself, which will be described later. The information may be input by the user or automatically input by the user terminal 4.

[0037] [Activity A2] Next, the processing proceeds to activity A2, where the acquisition unit 231 acquires substance information IF1. The acquisition unit 231 acquires substance information IF1 transmitted from, for example, the user terminal 4. The acquisition unit 231 may acquire substance information IF1 from any database, such as a chemical substance database or a crystal structure database, based on the transmitted information about the substance. Note that the acquisition unit 231 may acquire each of the partial information constituting substance information IF1 from separate information sources. In other words, the information included in substance information IF1 is not limited to information stored as a single data file.

[0038] <Substance Information IF1> The substance information IF1 is information about a substance that includes at least one atomic nucleus and at least one electron. The substance information IF1 includes candidates for the arrangement of multiple atomic nuclei and interactions V acting on each of the atomic nuclei and electrons. The substance information IF1 may also include the electric charges Z of each of the multiple atomic nuclei. In this embodiment, the substance information IF1 includes information about the reference position R_ν0 of the atomic nuclei. The acquisition unit 231 then acquires candidates for the arrangement of atomic nuclei that are generated based on the reference position R_ν0 of the atomic nuclei by a candidate generation process described below.

[0039] The substance of this embodiment is composed of at least one molecular system. Specifically, the substance is composed of a molecular system consisting of n_nucl atomic nuclei and n_e electrons. Each particle has three spatial degrees of freedom: the x-direction, the y-direction, and the z-direction. In the following description, electrons are treated quantum mechanically, and atomic nuclei are treated as classical point charges. That is, candidate atomic nuclei arrangements are described as classical point charges. In particular, atomic nuclei are assumed to be fixed in space. Furthermore, atomic nuclei and electrons may be collectively referred to simply as particles. Furthermore, atomic nuclei are not limited to atomic nuclei contained in atoms, but may also include atomic nuclei contained in ions.

[0040] The processor 23 generates a Hamiltonian H corresponding to the energy of the matter from such an interaction V. The Hamiltonian H may further include the kinetic energy T of the particle or the external potential V_ext for the particle.

[0041] The interaction V includes at least an electron-nucleus interaction V_en. In this embodiment, the interaction V further includes an electron-electron interaction V_ee and an atomic nucleus interaction V_nn. The interactions V_en, V_nn, and V_ee in this embodiment are isotropic, determined by the distance between particles, but are not limited to this and may also have anisotropy, determined by the orientation of the particles.

[0042] For ease of explanation, let us assume that the charge and position of the vth nucleus are Z_ν and R_ν, respectively, and that a common interaction V(d) acts on each pair of these (n_e + n_nucl) particles (electron-electron, electron-nucleus, nucleus-nucleus). d is the distance between the pair of particles. For example, in the case of the Coulomb interaction, V(d) = 1 / d. Also, let us assume that each electron is subjected to an external potential V_ext. The external potential V_ext can be provided by, for example, an electric field, a magnetic field, heat, or external disturbance.

[0043] The Hamiltonian H in this embodiment is expressed as in Equation 1, with the position R_ν of the atomic nucleus as a parameter. m_e is the electron mass. r_l with a hat symbol is the position operator of the l-th electron. In the following description, the hat symbol may be omitted in the component numbers.

[0044] In this embodiment, since the nuclei are treated as classical point charges, the internuclear interaction V_nn in the Hamiltonian H can be set to a scalar quantity E_nn. This reduces the calculation load on the processor 23.

[0045] [Activity A3] Next, processing proceeds to activity A3, where the candidate generation unit 232 performs the acquired candidate generation process. As a result, the candidate generation unit 232 generates candidates for the arrangement of multiple atomic nuclei. For example, the candidate generation unit 232 generates candidates for the arrangement of multiple atomic nuclei by adding a predetermined displacement ΔR to the acquired reference position R_ν0. More specifically, the candidate generation unit 232 generates candidates for the arrangement of multiple atomic nuclei from the reference position R_ν0 by combining displacements ΔR_ν (ν=0, 1, ..., n_nucl-1) of the νth nucleus from the reference position R_ν0. Then, the acquisition unit 231 acquires the generated candidates for the arrangement of atomic nuclei.

[0046] As an example, the candidate generator 232 first sets the maximum value ΔR_νμmax of the displacement of the ν-th nucleus ν in the μ direction (μ=x, y, z). For convenience of explanation, only the case where μ=x will be described here, but the same applies to the case where μ=y, z.

[0047] Next, the candidate generator 232 sets a nucleus position operator R_{νx} for the state |j_νx>_n_{qn} of the first quantum bit 321n as shown in Equation 2, where j_νx=0, 1, ..., N_{qn-1}, and N_qn≡2^{n_qn} corresponds to the number of candidates for the arrangement of the nuclei generated for one degree of freedom.

[0048] As a result, the position operator of the nuclei represents discrete displacements from the reference position R_ν0. n_qn is the number of first quantum bits 321n used to generate candidate nuclei arrangements for one degree of freedom. The n_qn first quantum bits 321n form a quantum state |j_νx>_n_qn, which is represented by the Kronecker product of 2^{n_qn} independent quantum bit states. Each of these independent quantum states is also called a computational basis. These computational bases are eigenstates of the position operator R_νx, as shown in Equation 2. n_qn is a parameter that determines the search resolution and does not necessarily have a direct relationship to the actual size of the target molecule. Since the spatial degrees of freedom of the molecular system in this embodiment are three, 3×n_qn first quantum bits 321n are used to represent candidate nuclei arrangements included in the molecular system. Therefore, the number of computational bases required to represent the position of one nucleus is 2^{3n_qn}.

[0049] At least one of the obtained candidate nucleus configurations is assigned to each of these computational bases by the process described below. Therefore, each state |j_ν>_3n_qn of these computational bases corresponds to the first quantum bit state. For convenience of explanation, the first quantum bit state corresponding to the Jth candidate nucleus configuration may be expressed as |J>_{3n_{nucl}}_{n_qn} or simply |J>.

[0050] The Hamiltonian H shown in Equation 1 includes a set of position coordinates of the nuclei {R_ν} as a parameter. Therefore, in this embodiment, the processor 23 can generalize the Hamiltonian H shown in Equation 1 to the Hamiltonian H∼ shown in Equation 3 by replacing the parameter with a position operator of the nuclei.

[0051] In the above generalization, the positions of the nuclei included in the electron-nucleus interaction V_en, the nuclear interaction energy E_nn, and the external potential V_ext, which are included in the original Hamiltonian H, are replaced as operators to define V_en~, E_nn~, and V_ext~, respectively. For convenience of explanation, the tilde symbol (~) in V_en~, E_nn~, and V_ext~ may be omitted below.

[0052] [Activity A4] Next, the process proceeds to activity A4, where the allocation unit 233 performs an allocation process. As a result, the allocation unit 233 assigns each of the acquired candidate nucleus configurations to at least one first quantum bit state |J> (i.e., computational basis). The first quantum bit state is composed of at least one first quantum bit 321n and is a state that can be observed by an observation operation on the first quantum bit. In this embodiment, the allocation unit 233 assigns each candidate nucleus configuration described as a classical point charge to at least one first quantum bit state. In this embodiment, the allocation unit 233 assigns one candidate nucleus configuration to each of multiple computational bases. The first quantum bit 321n functions as a computation quantum bit 321 for expressing the configuration of the atomic nuclei. The process of activity A4 corresponds to a process including an allocation step in this embodiment.

[0053] [Activity A5] Next, the process proceeds to activity A5, where the processor 23 performs a quantum circuit generation process based at least on the above-described Hamiltonian H to generate a computational quantum circuit QC1 that defines a series of quantum operations to be performed on the quantum bit 320. The computational quantum circuit QC1 of this embodiment is generated as an instruction to cause the quantum computer 3 to perform quantum operations.

[0054] <Computational Quantum Circuit QC1> An example of the computational quantum circuit QC1 will now be described. Fig. 7 is a diagram showing an example of the computational quantum circuit QC1.

[0055] The computational quantum circuit QC1 defines a series of quantum operations for optimizing the structure of a target system (i.e., a substance). Specifically, the computational quantum circuit QC1 is composed of gate operations and measurements on a first quantum bit 321n representing a nuclear configuration and a second quantum bit 321e representing a multi-electron wave function. Specifically, the computational quantum circuit QC1 includes a first quantum gate operation QC11, a reference quantum gate operation QC12, a second quantum gate operation QC13, and an observation operation QC14. In particular, the computational quantum circuit QC1 is configured to sequentially apply the first quantum gate operation QC11, the reference quantum gate operation QC12, and the second quantum gate operation QC13 to at least the first quantum bit 321n and the second quantum bit 321e, and then execute the observation operation QC14 on the first quantum bit 321n. In FIGS. 7 to 16, the first quantum gate operation QC11 is also denoted as U_guess, and the reference quantum gate operation QC12 is also denoted as reference circuit U_ref.

[0056] <First Quantum Gate Operation QC11> FIG. 8 is a diagram illustrating an example of the first quantum gate operation QC11. By acting on the first quantum bit 321n, a superposition state of multiple first quantum bit states is generated. In this embodiment, the first quantum gate operation QC11 acts on the initialized first quantum bit 321n to generate a superposition state of first quantum bit states |J> in which appropriate estimated weights w_{guess, J} are assigned to each candidate for the optimal nucleus configuration. The process of generating such a first quantum gate operation QC11 corresponds to the superposition step of this embodiment. The estimated weights w_{guess, J} may be set equal for all J as an equal weight ratio, or may be set to different values ​​for each J based on other simulation results. The process of generating such a first quantum gate operation QC11 is an example of a process of generating a superposition state of a plurality of first quantum bit states |J> by performing a predetermined first quantum gate operation QC11 on the first quantum bit 321n, i.e., a superposition step. The process of having the quantum computer 3 perform a quantum operation based on such a first quantum gate operation QC11 is also an example of a superposition step.

[0057] <Reference Quantum Gate Operation QC12> FIG. 9 is a diagram illustrating an example of the reference quantum gate operation QC12. The reference quantum gate operation QC12 is performed on the quantum bit 320 including the generated superposition state. A superposition state of reference electronic states is generated for each candidate nucleus configuration included in the superposition state. In this embodiment, the reference quantum gate operation QC12 is performed on the superposition state of multiple first quantum bit states |J> generated by the first quantum gate operation QC11 and the quantum state of the second quantum bit 321e representing the electronic state of the material. As a result, an appropriate reference electronic state associated with each candidate nucleus configuration is generated through the reference quantum gate operation QC12. The process of generating such a reference quantum gate operation QC12 is an example of an electron configuration step of this embodiment. The process of having the quantum computer 3 perform a quantum operation based on such a reference quantum gate operation QC12 is also an example of an electron configuration step.

[0058] <Second Quantum Gate Operation QC13> The second quantum gate operation QC13 includes the obtained interaction V for the first quantum bit representing the superposition state and the second quantum bit 321e. Specifically, the second quantum gate operation QC13 corresponds to a Hamiltonian H (in this embodiment, a generalized Hamiltonian H∼) including the obtained interaction V. In this embodiment, the second quantum gate operation QC13 is performed on a quantum bit including a superposition state of the reference electronic state generated through the reference quantum gate operation QC12. Specifically, the second quantum gate operation QC13 generates a second quantum bit state representing an electronic state that can converge to a ground state in the arrangement of nuclei represented by the superposition state as a result of the interaction. Furthermore, the second quantum gate operation QC13 is configured to search for a combination of nuclear displacements ΔR_ν(opt) that results in the lowest energy of the ground state based on the generalized Hamiltonian H shown in Equation 3. This generates a correlated quantum bit state in which the first quantum bit 321n and the second quantum bit 321e are correlated. The process of generating such a second quantum gate operation QC13 is an example of an interaction step. Furthermore, the process of causing the quantum computer 3 to perform a quantum operation based on such a second quantum gate operation QC13 is also an example of an interaction step.

[0059] The second quantum gate operation QC13 is configured to lower the energy of matter in a quantum state represented by the first quantum bit 321n and the second quantum bit 321e. For example, the second quantum gate operation QC13 is configured to execute a predetermined ground state calculation method based on the first quantization format. A specific aspect of the ground state calculation method may be a variational eigenvalue solver method (VQE) or any other method, such as a cubitization method. In this embodiment, a stochastic imaginary time evolution method is employed as the ground state calculation method. The process of lowering the energy by the second quantum gate operation QC13 can also be referred to as an energy minimization process. The energy minimization process includes at least one quantum gate operation. In this embodiment, since the stochastic imaginary time evolution method is used, the energy minimization process includes an observation operation of the auxiliary bit 322. A method of implementing such a ground state calculation method as a quantum circuit will be described later.

[0060] <Observation Operation QC14> As shown in FIG. 7 , the observation operation QC14 is an operation of observing the multiple first quantum bits 321n. As a result, the multiple first quantum bits 321n are projected onto one of the multiple first quantum bit states (i.e., computational bases) to which candidate nucleus configurations are assigned. The observation operation QC14 is also referred to as a projection operation. At this time, the probability of observing a specific first quantum bit state increases as the energy of the ground state corresponding to the Hamiltonian H~ decreases. Therefore, among the superposition states of the multiple first quantum bit states included in the correlated quantum bit state, the first quantum bit state with the lowest ground state energy is most likely to be observed. In other words, it is suggested that the nucleus configurations assigned to the first quantum bit states observed relatively frequently via the correlated quantum bit states are configurations with relatively low ground state energy among the multiple candidate nucleus configurations. A ground state search is performed through such observation operations.

[0061] Here, the theoretical background of the above ground state search will be explained. As described above, n_qe second quantum bits 321e are assigned to each direction of each electron in order to express the multi-electron wave function in real space. In this case, the normalized multi-qubit state |Ψ> to be optimized is composed of 3(n_{e}n_{qe}+n_{nucl}n_{qn}) computation quantum bits 321. The above multi-qubit state |Ψ> can be written as shown in Equation 4 by the Kronecker product of the first quantum bit state |J> and the second quantum bit state |K> using the expansion coefficients c_K,J.

[0062] K is a notation that collectively represents 3n_e integers (each value is 0 or greater and less than 2^n_qe) that specify the position eigenstates of a multi-electron system. J is a notation that collectively represents 3n_nucl integers (each value is 0 or greater and less than 2^n_qn).

[0063] The normalization condition is given by Equation 5.

[0064] The weight w_J of the state of the Jth atomic nucleus configuration is given by Equation 6. Hereinafter, for convenience of explanation, the Jth atomic nucleus configuration may be simply referred to as atomic nucleus configuration J.

[0065] The expansion coefficient c_K[J] is defined by Equation 7.

[0066] The normalized multi-electron state |ψ[J]> associated with a nuclear configuration specified by a fixed J can be written as in Equation 8.

[0067] Using Equation 8, Equation 4 can be written as shown in Equation 9.

[0068] It can be seen that for the multi-qubit state |Ψ> in Equation 9, the probability distribution of the nuclear configuration J obtained by measuring 3n_{nucl}n_{qn} nuclear displacement quantum bits (i.e., first quantum bits 321n) is the weight w_J of the nuclear configuration J itself. Therefore, when a ground state search (in this embodiment, stochastic imaginary time evolution or VQE) is performed a sufficient number of steps, J(opt) that gives the maximum value of the distribution of w_J possessed by the resulting multi-qubit state |Ψ> corresponds to the optimal nuclear configuration ΔR_νμ (ν=0, 1, ..., n_{nucl-1}, μ=x, y, z).

[0069] In this way, the processor 23 generates a computational quantum circuit QC1 for identifying the optimal atomic nucleus configuration based on the acquired information.

[0070] 6, the process then proceeds to activity A6, where the processor 23 transmits the generated computation quantum circuit QC1 to the quantum computer 3. As a result, the quantum processor 33 acquires the computation quantum circuit QC1.

[0071] [Activity A7] Next, processing proceeds to activity A7, in which the quantum processor 33 performs a quantum operation on the quantum bit 320 based on the acquired computational quantum circuit QC1. As a result, the quantum processor 33 generates a correlated quantum bit state from the initialized first quantum bit 321 n and second quantum bit 321 e, and observes the first quantum bit 321 n in the correlated quantum bit state. The quantum processor 33 then transmits the observation result (i.e., which first quantum bit state was observed) to the information processing device 2.

[0072] [Activity A8] Next, in activity A8, the acquisition unit 231 acquires the observation results sent by the quantum processor 33.

[0073] The information processing system 1 repeats the processing of activity A7 and activity A8 until a predetermined termination condition is met. As a result, the calculation results from the quantum computer 3 are accumulated in the information processing device 2. The termination condition can be set arbitrarily, such as whether or not the number of repetition steps has reached a predetermined value, or whether or not a termination operation has been performed by the user. Furthermore, the acquisition unit 231 constructs a computational quantum circuit QC1 in which predetermined parameters have been updated based on the "observation results transmitted by the quantum processor 33," and transmits the circuit to the quantum processor 33. This enables calculations to be performed with higher accuracy.

[0074] [Activity A9] On the other hand, if the termination condition is satisfied, the process proceeds to activity A9, where the processor 23 aggregates the observation results obtained by the processing of each activity A8. Here, the observation probability of each first quantum bit state depends on the weight w_J of the nucleus configuration J described above. Therefore, the aggregated observation results correspond to the weight w_J of the nucleus configuration J.

[0075] [Activity A10] Next, the process proceeds to activity A10, where the identification unit 235 performs a process of identifying a relatively low-energy configuration among candidate nucleus configurations based on the observation results of the first quantum bit 321n in the generated correlated quantum bit state. Specifically, the identification unit 235 identifies, based on the observation results, a nucleus configuration among the candidate nucleus configurations that has the lowest ground-state energy eigenvalue. For example, the identification unit 235 identifies the candidate nucleus configuration assigned to the most frequently observed first quantum bit state as a relatively low-energy configuration among the nucleus configurations (specifically, the nucleus configuration with the lowest ground-state energy eigenvalue). The process of activity A10 is an example of an identification step in this embodiment. The process in which the processor 23 causes the quantum computer 3 to perform the identification and obtains the identification result is also an example of an identification step.

[0076] [Activity A11] Next, the process proceeds to activity A11, where the processor 43 displays the arrangement of atomic nuclei on the display unit 44. At this time, the processor 43 may display any information, such as the calculation conditions and calculation results of the quantum computer 3.

[0077] 3.2. An example of the second quantum gate operation QC13 In this chapter, the details of the second quantum gate operation QC13 generated in the information processing method described in the previous chapter will be described using stochastic imaginary time evolution as an example. Note that the second quantum gate operation QC13 described in this chapter is merely an example and is not limited to this.

[0078] 10 is a diagram for explaining a computational quantum circuit QC1 based on the stochastic imaginary time evolution method. The first quantum gate operation QC11 and the reference quantum gate operation QC12 are the same as those described in the previous chapter. In this embodiment, an auxiliary bit 322 is further used to implement the stochastic imaginary time evolution method on the quantum circuit. In this embodiment, one auxiliary bit 322 is represented as "Ancilla," but the number of auxiliary bits 322 may be two or more.

[0079] The second quantum gate operation QC13 includes at least one unit quantum circuit QC131. In particular, the second quantum gate operation QC13 is configured to operate the unit quantum circuit QC131 on the computation qubit 321 and the ancillary bit 322 repeatedly a predetermined number of times (e.g., n_{steps} times).

[0080] <Unit Quantum Circuit QC131> The unit quantum circuit QC131 includes a search quantum circuit C_PITE and an observation operation on the auxiliary bit 322. In detail, the unit quantum circuit QC131 is configured to perform an observation operation on the auxiliary bit 322 after causing the search quantum circuit C_PITE to act on the first quantum bit 321 n and the second quantum bit 321 e.

[0081] <Search Quantum Circuit C_PITE> The search quantum circuit C_PITE is a circuit that advances the imaginary time evolution by one step based on the Hamiltonian H~ of the target system defined by Equation 3. In this chapter, for convenience of explanation, the Hamiltonian H~ will be simply referred to as Hamiltonian H. The search quantum circuit C_PITE includes a real time evolution operator exp(-iHΔt) with the Hamiltonian H as a generator. This configures the search quantum circuit C_PITE to be able to execute the imaginary time evolution method based on the first quantization form. Δt is the step size during real time evolution.

[0082] 11 is a diagram showing an example of an expression of the contribution exp(-iVΔt) of the interaction V in the unit quantum circuit QC131. As shown in FIG. 11, the interaction portion exp(-iVΔt) of the real-time evolution operator exp(-iHΔt) is expressed as exp(-i(V_ee + V_en + V_nn)Δt). The inter-nuclear interaction V_nn acts only on the first quantum bit 321n, and the inter-electron interaction V_ee acts only on the second quantum bit 321e. Therefore, these interaction portions are implemented as a quantum gate operation that acts only on the first quantum bit 321n and a quantum gate operation that acts only on the second quantum bit 321e, as shown in the right circuit of FIG. 6.

[0083] Because the number of combinations of two electrons contained in the target molecule is proportional to n_e^2, the depth of the circuit implementation of exp(-iV_eeΔt) is O(n_e^2). Similarly, the depth of the circuit implementation of exp(-iV_nnΔt) is O(n_nucl^2). For almost all molecules that are the subject of practical calculations, n_nucl<<n_e. Furthermore, the circuit implementation of exp(-iV_eeΔt) is independent of the presence or absence of a nucleus. Given these circumstances, the exp(-iV_enΔt) portion of exp(-iVΔt) does not affect the overall depth of the search quantum circuit C_PITE. Therefore, the contribution to the depth of the circuit implementing exp(-i(V_ee + V_en + V_nn)Δt) is primarily from exp(-iV_eeΔt).

[0084] Next, the correspondence between inputs and outputs of the gates exp(-iV_eeΔt), exp(-iV_nnΔt), exp(-iV_enΔt), and exp(-iV_extΔt) included in the above-mentioned search quantum circuit C_PITE will be explained. As long as the correspondence below is followed, any method for implementing each gate can be used. Each gate can be implemented, for example, as described in Non-Patent Document 1: P. J. Ollitrault, G. Mazzola, and I. Tavernelli, "Nonadiabatic molecular quantum dynamics with quantum computers", Phys. Rev. Lett. 125, 260511 (2020). or Non-Patent Document 2: G. Using existing techniques such as G. Benenti and G. Strini, "Quantum simulation of the single-particle schroedinger equation", American Journal of Physics 76, 657 (2008), the functional form of the interaction V can be expressed as a polynomial, and the function system can be implemented as a circuit using a phase gate.

[0085] The position eigenvalue of a single electron is expressed as r^(k_x, k_y, k_z) using three integers k_x, k_y, k_z (each of which is equal to or greater than 0 and equal to or less than 2^n_qe-1). The eigenstate corresponding to the position eigenvalue is expressed as |k_x, k_y, k_z>. The phase gate U_ee^(pair) acting on the electron pair is defined as in Equation 10 using the second quantum bit 321e.

[0086] The real-time evolution operator exp(-iV_eeΔt) derived from the electron-electron interaction V_ee can be written as in Equation 11 by using the phase gate U_ee^(pair). This means that exp(-iV_eeΔt) can be implemented with a circuit depth of O(n_e^2) from n_e(n_e-1) / 2 U_ee^(pair) gates.

[0087] As described above, the displacement of the v-th atom is expressed as 3n_qn quantum bit states |j_νx, j_νy, j_νz>_3n_qn. The phase gate U_nn^(ν,ν') acting on the 6n_qn quantum bit states representing the displacement of the v-th and v'th atoms is defined as in Equation 12.

[0088] The real-time evolution operator exp(-iV_nnΔt) derived from the internuclear interaction V_nn can be written as in Equation 13 by using the phase gate U_nn^(ν,ν'). This means that exp(-iV_nnΔt) can be implemented with n_nucl(n_nucl-1) / 2 U_nn^(ν,ν') gates with a circuit depth of O(n_nucl^2).

[0089] The phase gate U_en^(ν) acting on a single electron and the ν-th nucleus is defined as in Equation 14.

[0090] The real-time evolution operator exp(-iV_enΔt) derived from the electron-nucleus interaction V_en can be written as shown in Equation 15 by using the phase gate U_en^(ν).

[0091] The real-time evolution operator exp(-iV_enΔt) derived from the electron-nucleus interaction V_en can also be written as in Equation 16. This means that the real-time evolution operator exp(-iV_enΔt) can be implemented from n_en n_nucl U_en^(ν) gates.

[0092] The real-time evolution operator exp(-iV_enΔt) can be implemented by a circuit of depth O(n_e^1 n_nucl^0) with respect to n_e and n_nucl by using Formula 16. Fig. 12 is a diagram showing an example of a quantum circuit for implementing the real-time evolution operator exp(-iV_enΔt) when n_e=4 and n_nucl=3.

[0093] The phase gate U_ext acting on a single electron is defined as in Equation 17.

[0094] The real-time evolution operator exp(-iV_extΔt) derived from the external potential can be written as in Equation 18 using the phase gate U_ext.

[0095] This means that exp(-iV_extΔt) can be implemented from n_e U_ext gates with a circuit depth of O(1).

[0096] The above explanation was about a method for generating candidate structures by displacing all n_nucl nuclei. If the positions of some specific nuclei (e.g., n_nucl') of the n_nucl nuclei are targeted for optimization, and the positions of the other n_nucl-n_nucl' nuclei are not targeted for optimization (e.g., when the positions of the other nuclei are fixed), the potential due to the latter can be absorbed into the definition of the external potential v_ext. This allows the above method to be applied to n_nucl' nuclei.

[0097] 3.3. Example of Search Quantum Circuit C_PITE Here, an example of the configuration of the search quantum circuit C_PITE when the imaginary time evolution method is adopted as the ground state calculation method will be described. FIG. 13 is a diagram showing an example of a search quantum circuit C_PITE for performing imaginary time evolution. In FIG. 13, the real time evolution operator exp(-iHΔt) is denoted as U_{RTE}. The search quantum circuit C_PITE is configured to sequentially perform a Hadamard gate operation H and a W gate operation on the auxiliary bit 322, then perform a controlled NOT gate operation using the auxiliary bit 322 as a control bit, and then perform a rotation gate operation R_z(-2θ_0) and a Hermitian conjugate operation of the W gate on the auxiliary bit 322. The controlled NOT gate operation sets the auxiliary bit 322 as the control bit and the computation quantum bit 321 as the target bit. The controlled NOT gate operation is configured to determine whether to act a forward real-time evolution operator U_{RTE} or a backward real-time evolution operator U^†_{RTE} on the computation quantum bit 321, depending on the state of the auxiliary bit 322. Note that the specific configuration of the search quantum circuit C_PITE is not limited to this and is arbitrary.

[0098] Such a search quantum circuit C_PITE is configured to operate on a |ψ>*|0> state (* indicates a Kronecker product) composed of the state |ψ> of the computation quantum bit 321 and the state |0> of the ancillary bit 322. As a result, a state in which an imaginary time evolution operator exp(-HΔτ) with a general Hermitian operator H as a generator is applied to such a multi-qubit system is probabilistically obtained. Such a quantum circuit C_PITE is configured to be capable of polynomial expansion with the time step Δτ as a parameter. Note that Δτ is the step width of the imaginary time evolution method. The polynomial expansion may be an expansion up to the first order range of Δτ, or an expansion including higher-order terms of second or higher order.

[0099] The real-time evolution operator exp(-iHΔt) can be approximately expressed by a combination of the kinetic energy contribution exp(-iTΔt) and the interaction V contribution exp(-iVΔt). In this embodiment, as shown in Equation 3, the Hamiltonian H explicitly includes the nuclear coordinates R_ν. Therefore, the interaction V contribution exp(-iVΔt) needs to be implemented in the search quantum circuit C_PITE.

[0100] <Quantum Amplitude Amplification Circuit Q> When the second quantum gate operation QC13 includes an observation operation of the ancillary bit 322, the second quantum gate operation QC13 may further include a quantum amplitude amplification circuit Q. FIG. 14 is a diagram showing an example of a quantum amplitude amplification circuit Q in the imaginary time evolution method. The quantum amplitude amplification circuit Q is a quantum circuit that can improve the probability that the ancillary bit 322 is observed as a predetermined state. The amplitude amplification operator Q applies an oracle S_χ and then applies a zero reflection S_0 sandwiched between U_PITE and U_PITE^†. Specifically, the amplitude amplification operator Q is defined by Equation 19.

[0101] The quantum circuit U_PITE is configured to operate on a multi-qubit state including a computation qubit 321 system and an ancillary bit 322 system. The quantum circuit U_PITE is configured to operate, in order, on a reference circuit U_ref that operates on the multi-qubit state and a quantum circuit C_PITE that implements a real-time evolution operator exp(-iκΘ) with the Hermitian operator Θ as a generator. In detail, the quantum circuit U_PITE is expressed as shown in Equation 15 using the product of the reference circuit U_ref and the quantum circuit C_PITE.

[0102] <Zero Reflection S_0> The reflection operator S_φ is an operation that inverts the sign of a specific state |φ> among the states of N quantum bits, but does not change other states. The reflection operator S_φ in which the specific state |φ> is |0...0> is called zero reflection S_0.

[0103] <Oracle S_χ> The oracle S_χ performs an operation to invert the sign of the state orthogonal to the state to be amplified. The zero reflection S_0 can be implemented as a quantum circuit that does not depend on the algorithm combined with quantum amplitude amplification. The oracle S_χ can be appropriately implemented as a quantum circuit that corresponds to such an algorithm (in this embodiment, the imaginary time evolution method).

[0104] 3.4. Simulation Results for a One-Electron Molecular System This section describes the simulation results when the above information processing method is applied to a one-electron molecular system. In this simulation, the substance to be optimized is a molecular system consisting of a single electron and two atomic nuclei. In addition, in this simulation, the above information processing was performed on a classical computer using quantum computing simulation according to the procedure shown in Figure 6.

[0105] To simplify the problem setting, space is assumed to be one-dimensional. The numerical values ​​of physical quantities shown below are in atomic units. An electron is treated as having a charge of -1, and both nuclei are treated as having a charge of +1. The position of one of the nuclei is fixed, and the distance from it to the other is divided into eight parts ranging from 1.5 to 3. The initial electronic state for each nucleus arrangement is an electronic wave function whose amplitude increases the deeper the electrostatic potential of the nuclei. This initial electronic state is expressed as a second quantum bit state using the second quantum bit 321e.

[0106] The ground state search method used is stochastic imaginary time evolution.

[0107] Fig. 15 is a diagram showing the simulation results of the first step (i.e., the initial state), Fig. 16 is a diagram showing the simulation results of the eighth step, and Fig. 17 is a diagram showing the simulation results of the fourteenth step.

[0108] The labels on the horizontal axis in FIGS. 15 to 17 (Geom 0 to Geom 7) indicate candidates for the arrangement of atomic nuclei.

[0109] Bar graphs B1 to B5 in Figures 15 to 17 show the weights of each energy eigenstate from the ground state (1st lowest) to the fourth excited state (5th lowest), and bar graph B0 shows the sum (Total) of the weights of these energy eigenstates.

[0110] 15 to 17 are graphs showing the energy eigenvalues ​​of the ground state. As shown in line graph L1, the fifth nuclear configuration from the left (Geom 4) has the lowest total energy eigenvalue of the ground state and is the optimal nuclear configuration.

[0111] 15, the first quantum gate operation QC11 in this simulation assigns equal weights to all candidate nuclear configurations in the initial state, so that the weights of the energy eigenstates included in the initial electron wave function are all equal.

[0112] As shown in Figures 16 and 17, as the ground state search was repeated and the steps progressed, the weight of the optimal configuration (i.e., the configuration of the nuclei with the lowest energy eigenvalue of the ground state) was the largest, and as the deviation from the optimal configuration increased, the weight of the candidate nuclear configuration decreased.

[0113] These results indicate that by observing the first quantum bit state after the ground state search, the probability of observing the optimal configuration (i.e., the nuclear configuration with the lowest ground state energy eigenvalue) is maximized among multiple candidate nuclear configurations. This result suggests that the above information processing can obtain the optimal molecular structure corresponding to these internuclear distances, i.e., Geom 4 with the lowest ground state energy, through observation of the first quantum bit state. Therefore, it was shown that by employing this information processing method, it is possible to identify the most stable nuclear configuration for the Hamiltonian H including the obtained interaction V.

[0114] 3.5. Simulation Results for a Multi-Electron Molecular System In this section, we explain the simulation results when the above information processing method is applied to a molecular system consisting of two electrons and two atomic nuclei. Unlike the simulation in the previous section, this simulation takes into account the interactions between electrons. In this simulation, quantum computing simulation using the information processing procedure shown in Figure 6 was also performed on a classical computer.

[0115] The position of one of the nuclei was fixed, and the distance from there to the other was divided into eight parts, and the corresponding candidate structures (Geom0 to Geom7) were given equal weights as steps were taken.

[0116] Figure 18 shows the simulation results of the weights of each candidate structure immediately after 19 steps have passed. Line graph L1 in Figure 18 shows the energy eigenvalues ​​of the ground state. As shown in line graph L1, the third nuclear configuration from the left (Geom 2) has the lowest total energy eigenvalue of the ground state and is the optimal nuclear configuration. Bar graph B1 in Figure 18 shows the weight of the energy eigenstate of the ground state (1st lowest), and bar graph B0 shows the sum (Total) of the weights of each energy eigenstate from the ground state (1st lowest) to the fourth excited state (5th lowest).

[0117] It can be seen that the probability of observing the optimal configuration (Geom 2 in this case) is the highest among multiple candidate configurations of atomic nuclei. This shows that this information processing gives correct results even when there is an electron-electron interaction.

[0118] 4. Other examples of information processing methods

[0119] This chapter describes an example of information processing in which the computational quantum circuit QC1 can be updated based on predetermined parameters. Specifically, another example of information processing in which the variational eigensolver method (hereinafter referred to as VQE) is used as the ground state calculation method is described. Note that, among the information processing in this chapter, descriptions of commonalities with the information processing in previous chapters may be omitted by assigning the same component numbers. The information processing described in this chapter may be referred to as the second information processing to distinguish it from the first information processing.

[0120] 4.1. Information Processing Flow FIG. 19 is an activity diagram showing an overview of information processing in this embodiment executed in the information processing system 1. Note that the information processing may include any exception handling not shown in the activity diagram. Exception handling includes interruption of the information processing or omission of each process. Selection or input performed in the information processing may be based on a user operation or may be performed automatically without relying on a user operation.

[0121] The information processing of this embodiment differs from the information processing of the previous chapter in that the circuit generation process in activity A15 can be performed based on the observation results from activity A8. Specifically, after the information processing system 1 performs the processes of activities A1 to A4, it executes the quantum circuit generation process in activity A15. At this time, the processor 23 further generates a computational quantum circuit QC1 based on predetermined parameters. Specifically, the processor 23 sets the quantum gate operation included in the computational quantum circuit QC1 according to certain parameters. The parameters include, for example, the rotation angle (phase angle) of the rotation gate operation. Note that, in the case of the first activity A15, the processor 23 may generate the computational quantum circuit QC1 based on the initial values ​​of predetermined parameters. Details of the computational quantum circuit QC1 and the parameters will be described later.

[0122] Next, the processing of activities A6 to A8 is performed, and the observation results are obtained by quantum computation based on the computational quantum circuit QC1 generated in activity A15. If the termination condition is not met, the processing returns to activity A15.

[0123] At this time, the processor 23 calculates the parameters used to generate the computational quantum circuit QC1 in activity A15 based on the observation results obtained in activity A8. This allows the computational quantum circuit QC1 to be regenerated appropriately reflecting the observation results, thereby increasing the likelihood that the observed state will reach the ground state.

[0124] On the other hand, if the termination condition is met, the processing of activities A9 and A10 is carried out to identify the optimal arrangement of atomic nuclei.

[0125] 4.2. An Example of a Computational Quantum Circuit QC1 in VQE In this section, an example of a method for generating a computational quantum circuit QC1 when VQE is adopted as the ground state calculation method used in the information processing described in the previous section will be described.

[0126] <Hypothetical State> Figure 20 is an example of a computational quantum circuit QC1 for VQE. In this section, the computational quantum circuit QC1 for VQE is simply referred to as the computational quantum circuit QC1. The computational quantum circuit QC1 is composed of rotation gate operations (R_y and R_z gate operations) characterized by N_p arbitrary real number parameters θ = {θ_1, ... , θ_N_p} and a two-qubit gate operation (controlled Z gate). The N_p arbitrary real number parameters θ = {θ_1, ... , θ_N_p} correspond to predetermined parameters for generating the computational quantum circuit QC1 in the above information processing.

[0127] Specifically, the computational quantum circuit QC1 is configured to first perform a rotation gate operation on each of the first quantum bits 321n. This results in a superposition of first quantum bit states formed by the first quantum bits 321n. Therefore, the rotation gate operation on the computational quantum bits 321n includes the function of a first quantum gate operation QC11.

[0128] Meanwhile, the computational quantum circuit QC1 is configured to perform rotation gate operations on the second qubit 321e. The parameters of these rotation gate operations are explicitly or implicitly correlated with the first qubit state. Thus, the rotation gate operations on the second qubit 321e include a function as a reference quantum gate operation QC12.

[0129] Next, the computational quantum circuit QC1 is configured to perform a second quantum gate operation QC13. The second quantum gate operation QC13 can be constructed by repeating an arbitrary number d of minimum units (i.e., unit quantum circuits QC131) configured to perform a two-qubit gate operation followed by a rotation gate operation. The two-qubit gate operation in this embodiment is a controlled Z gate operation. The controlled Z gate operation can represent an interaction between each particle.

[0130] The computational quantum circuit QC1 for VQE shown in Figure 20 is an example. The computational quantum circuit QC1 for VQE can be any quantum circuit constructed from parameterized gate operations. For example, the computational quantum circuit QC1 may be constructed based on physical considerations, such as a unitary coupled cluster hypothetical state.

[0131] <Optimization Algorithm> In the VQE method, the acquisition unit 231 acquires the ground state by updating the parameters included in the computational quantum circuit QC1 so as to minimize the energy (or cost function). Here, the processing for updating the parameters is performed by the information processing device 2. In this chapter, the variational imaginary time evolution method is used as a method for updating the parameters included in the computational quantum circuit QC1. The variational imaginary time evolution method can be constructed based on non-patent literature: S. McArdle, et al., "Variational ansatz-based quantum simulation of imaginary time evolution", npj Quantum Information, 5, 75 (2019). In the variational imaginary time evolution method, parameters are given imaginary time dependency θ(τ), and the parameters are determined so that the time evolution in the imaginary time direction is reproduced with each step. To determine the parameters in the next step, the linear equation given in Equation 21 is solved.

[0132] Here, the matrix M and the vector C are given by Equations 22 and 23, respectively.

[0133] Figure 21 shows a differentiation circuit QC2 for calculating the differential (-2i)∂|φ(θ)> / ∂θ_k with respect to θ_k. The parameter differentiation of the computational quantum circuit QC1 included in equation 22 can be calculated using the differentiation circuit QC2. A unitary operation that depends on θ_1,...,θ_{k-1} is denoted as U(θ_1,...,θ_{k-1}). The same applies to U(θ_{k-1},...,θ_{N_p}). The R_σ gate (σ = x, y, z) is a rotation gate operation.

[0134] Equation 23 can be calculated by dividing the Hamiltonian H into a kinetic term T and a potential term V and adding up the results of calculating each term. First, the potential term V will be described. The potential term V can be expressed as a diagonal matrix in the computational base, and therefore can be calculated from the absolute squared values ​​of the coefficients obtained by repeatedly measuring each of the computational quantum circuit QC1 and the differential circuit QC2 in the computational base. Next, the kinetic term T will be described. The kinetic term T can be expressed as a diagonal matrix in momentum space. Therefore, the processor 23 first converts the wave function into momentum space by performing a quantum Fourier transform on the computational quantum circuit QC1 and the differential circuit QC2. Then, similar to the calculation of the potential term V, the processor 23 also repeatedly measures each of the computational quantum circuit QC1 and the differential circuit QC2 in the computational base for the kinetic term T. This allows the acquisition unit 231 to acquire the absolute squared values ​​of the coefficients. The processor 23 can calculate a number related to the kinetic term T from the absolute squared values.

[0135] Since the imaginary time derivative of the parameter can be obtained from Equation 21, the parameter in the next step can be determined from Equation 24 according to, for example, Euler's method. Here, Δτ is the imaginary time step width.

[0136] In this chapter, we have explained the variational imaginary time evolution method as an optimization algorithm, but this is only one example. Other optimization algorithms may also be used.

[0137] In this section, a method for calculating the ground state of the Hamiltonian H using one computational quantum circuit QC1 has been described, but this is merely an example. The ground state may be calculated by the information processing device 2 as post-processing from the calculation results using multiple computational quantum circuits QC1.

[0138] 4.3 Simulation based on VQE This section describes the simulation results when VQE is used as the ground state search method. The calculation conditions are the same as those in the examples of Figures 15 to 17. Specifically, the state generated by the computational quantum circuit QC1, which is characterized by parameters generated by random numbers, was used as the initial state.

[0139] FIG. 22 shows the simulation results of the sum of the weights of the energy eigenstates in each nuclear configuration (Geom 0 to Geom 7). The horizontal axis of FIG. 22 corresponds to the number of steps in the imaginary time evolution. The vertical axis of FIG. 22 corresponds to the sum of the weights of the energy eigenstates. As shown in FIG. 22, it can be seen that the weight of the optimal configuration (Geom 4) is amplified as the number of steps in the imaginary time evolution increases.

[0140] FIG. 23 shows the weights of the energy eigenstates of the ground state (1st lowest), first excited state (2nd lowest), second excited state (3rd lowest), and total (Total) of the electronic wave function in the optimal configuration (Geom 4). The horizontal axis of FIG. 23 corresponds to the number of steps in the imaginary time evolution. The vertical axis of FIG. 23 corresponds to the weights of the energy eigenstates. In FIG. 23, D0 indicates the plot of the total (Total), D1 indicates the plot of the ground state (1st lowest), D2 indicates the plot of the first excited state (2nd lowest), and D3 indicates the plot of the second excited state (3rd lowest). As shown in FIG. 23, it can be seen that as the number of steps in the imaginary time evolution increases, the ratio of the weight of the ground state (1st lowest) to the total weight increases compared to the ratio of the weights of the other states. This suggests that the weight of the basis state is amplified by the computational quantum circuit QC1 (particularly the second quantum gate operation QC13).

[0141] 5. Others The information processing system 1 may be further improved in the following manner.

[0142] The substance does not have to be a single molecule, but may be a system consisting of multiple molecules, a metal containing metal atoms or ions, a metal oxide, or the like. Furthermore, the substance may be a single molecule, an amorphous substance that does not have a periodic or quasi-periodic structure, a polycrystalline or single-crystalline substance that has a periodic structure, or a combination of these. In other words, any substance containing at least one atomic nucleus and at least one electron is sufficient. Furthermore, if electron interactions are not taken into consideration, any substance containing at least one atomic nucleus is sufficient.

[0143] In particular, the above-described information processing method is a method for optimizing both the nuclear configuration and the multi-electron state in parallel, but it can also be applied to a 3n_nucln_qn quantum bit system that considers only the nuclear configuration. FIG. 24 is a diagram showing an example of a unit quantum circuit QC131 for performing the information processing method on a quantum bit system that considers only the nuclear configuration. The second quantum gate operation QC13 shown in FIG. 24 is composed of the second quantum gate operation QC13 shown in FIG. 5 except for the part related to the second quantum bit 321e. In this case, of the time evolution operators based on the interaction V, only the time evolution operator exp(-iV_nnΔt) based on the nuclear interaction V_nn needs to be implemented on the unit quantum circuit QC131. This allows structural optimization of a system consisting only of classical point charges. The circuit depth in this case is O(n_nucl^2).

[0144] Furthermore, by appropriately setting the interaction V, the particles are not limited to atomic nuclei or electrons, and any particles can be used. For example, if a substance is composed of multiple molecules, the molecule is treated as a single particle, and the inter-particle interaction Vpp (e.g., hydrogen bond, Coulomb bond, van der Waals bond, etc.) is set, and then the above information processing method is executed. In this case, the operator corresponding to energy is not limited to Hamiltonian, and any operator corresponding to energy appropriately depending on the system to be focused on, such as Gibbs energy, can be used.

[0145] That is, the substance information IF1 is information about a substance containing at least one particle, and may include multiple particle configuration candidates and interactions acting on the particles. In this case, the interaction V may include at least the inter-particle interaction Vpp acting between particles. In this case, the acquisition unit 231 performs a process of acquiring the substance information IF1, similar to the above-described activity A2. The assignment unit 233 assigns each of the acquired particle configuration candidates to at least one first quantum bit state, similar to the above-described activity A4. The first quantum bit state is composed of at least one first quantum bit and is a state that can be observed by an observation operation on the first quantum bit. The quantum operation unit 234 performs a process of generating a superposition state of multiple first quantum bit states by performing a predetermined first quantum gate operation QC11 on the first quantum bit 321n. The quantum operation unit 234 performs a process of generating a correlated quantum bit state in which the first quantum bits 321n are correlated with each other by performing a second quantum gate operation QC13, including the obtained interaction V, on the first quantum bit 321n representing the superposition state. As a result, a computational quantum circuit QC1 is generated through a process similar to that of activity A5, and the computational quantum circuit QC1 is executed by the quantum processor 33. Then, similar to activity A10 described above, the identification unit 235 performs a process of identifying a configuration with relatively low energy from among candidate particle configurations, based on the observation results for the first quantum bit 321n in the generated correlated quantum bit state.

[0146] The number of particle types may be one type (atomic nuclei only), two types (atomic nuclei and electrons), or three or more types including other particles. In other words, the number of particle types is arbitrary. Therefore, the above information processing method can be applied to complex biological systems composed of multiple types of molecules.

[0147] In the above information processing method, atomic nuclei are treated as classical point charges, and the ground state is obtained without any consideration of their kinetic energy. However, this method is equally applicable when atomic nuclei are quantum mechanical particles. For example, the allocation unit 233 may express the multi-nuclear wave function (separate from the nuclear displacement) using 3n_{qn}n_{nucl} first quantum bits 321n, in the same way as expressing the multi-electron wave function using 3n_{qe}n_{e} second quantum bits 321e. In this case, the motional part exp(-iTΔt) of the real-time evolution operator may include contributions not only from electrons but also from atomic nuclei. Both the electron motional part and the nuclear motional part can be implemented on a quantum circuit using quantum Fourier transform. In this way, the ground state of a purely quantum mechanical system consisting of electrons and atomic nuclei can be obtained using the stochastic imaginary time evolution method. The lowest energy state obtained in this case is below absolute zero.

[0148] Based on the above information processing method, it is also possible to obtain the lowest energy state at a finite temperature by calculating the stochastic imaginary time evolution while treating both electrons and atomic nuclei as quantum mechanical particles. In this case, it is sufficient to obtain the electronic state and atomic nuclear configuration that give the lowest free energy at a finite temperature.

[0149] A modified example of the information processing method for identifying the configuration of atomic nuclei at a finite temperature will be described in detail below. Fig. 25 is a diagram showing an example of a second quantum gate operation QC13 that generates a Gibbs state for performing finite temperature calculations. In this modification, the quantum bit 320 further includes an environment bit 323. The environment bit 323 is used to represent an interaction with the environment that indicates a finite temperature.

[0150] The multi-electron multi-nuclear wave function is expressed using 3n_{qe}n_{e}+3n_{qn}n_{nucl} computational qubits 321 (hereinafter, for convenience of explanation, referred to as n computational qubits 321). The second quantum gate operation QC13 (more specifically, unit quantum circuit QC131) that generates the Gibbs state includes a search quantum circuit C_PITE, an observation operation of an ancillary bit 322, and further includes a maximally entangled state generation circuit U_ME. The maximally entangled state generation circuit U_ME is configured to act on computational qubits 321 (i.e., first qubit 321n and second qubit 321e) that represent a target system such as a molecular system, and on environment bit 323. The computational qubit 321 that represents the target system is denoted as "System," and the environment bit 323 is denoted as "Environment."

[0151] 26 is a diagram showing an example of a maximally entangled state generation circuit U_ME. The maximally entangled state generation circuit U_ME is configured to operate a Hadamard gate H on a computation quantum bit 321 and an auxiliary bit 322, and then operate a controlled NOT gate with the computation quantum bit 321 as a control bit and the environment bit 323 as a target bit. A search quantum circuit C_PITE for a quantum mechanical system consisting of electrons and atomic nuclei can be configured in a similar manner to the method described above.

[0152] By defining the imaginary time step Δτ as 1 / (2k_B × T), where k_B is the Boltzmann constant and T is temperature, the n computational qubits 321 for the target system change to a Gibbs state exp(−H_en / (k_B T)) when the state of the ancillary bit 322 is observed as |0>. H_en is the Hamiltonian of the target system. Furthermore, it is possible to derive a relationship linking the probability of obtaining such an observation result to the partition function Z of the target system. Therefore, Z can be calculated from the number of times |0> is obtained among multiple measurements of the ancillary bit 322. The free energy can be calculated from this result and the well-known thermodynamic relationship exp(−F / (k_B T)) = Z for the free energy F. By comparing the free energies of each candidate configuration, the optimal nuclear configuration can be identified.

[0153] In the above information processing, the number of quantum bits used to represent the electronic state by dividing each direction of three-dimensional space at equal intervals is defined as n_qe, and the number of quantum bits for nuclear displacement is defined as n_qn, but the number of computational quantum bits 321 assigned to each degree of freedom can be changed arbitrarily. For example, these conditions may be relaxed, and different numbers of quantum bits n_qeμ, n_qnμ (μ = x, y, z) may be used depending on the direction. The multi-qubit state |Ψ> used in this case consists of 3 (n_e(n_qex + n_qey + n_qez) + n_nucl(n_qnx + n_qny + n_qnz)) quantum bits.

[0154] In the above information processing, the candidate generation unit 232 generates multiple candidate arrangements of nuclei from the reference position R_ν0 in activity A3 by combining displacements ΔR_ν (ν=0, 1, ..., n_nucl-1) of the ν-th nucleus from the reference position R_ν0, and the acquisition unit 231 acquires the generated candidate arrangements of nuclei, but this is not limiting. For example, the acquisition unit 231 may acquire multiple candidate arrangements of nuclei prepared in advance by a user. Furthermore, the candidate arrangements of nuclei may include mutually discontinuous arrangements that are difficult to generate by combining displacements ΔR_ν at regular intervals from the reference position R_ν0.

[0155] The acquisition unit 231 may acquire the Hamiltonian H itself including the interaction V in activity A2. In this case, the acquisition unit 231 does not need to generate the Hamiltonian H from the interaction V. Furthermore, the acquisition unit 231 may accept a setting of the Hamiltonian H from the user.

[0156] The information processing system 1 may be realized by a program that causes a computer to function as the information processing system 1. This program may be downloadable from a server, may be executed or distributed on a cloud computer, or may be stored in a non-volatile or volatile storage medium and distributed.

[0157] In the above embodiment, the unit quantum circuit QC131 is implemented such that the Hamiltonian H~ explicitly includes the atomic nucleus coordinates R_ν, but it can also be implemented in a similar manner in a case where the Hamiltonian H does not explicitly take into account the existence of atomic nuclei.

[0158] The processor 23 does not need to actually execute the quantum computation by the computation quantum circuit QC1 using the quantum computer 3. For example, the processor 23 may convert the quantum computation algorithm defined by the generated computation quantum circuit QC1 into a computation algorithm executable by a classical computer, and then cause the classical computer to execute the computation algorithm. For example, the processor 23 may convert the quantum operation expressed by the computation quantum circuit QC1 into a computation algorithm executable by a classical computer by replacing it with a matrix computation problem.

[0159] A part of the processing of the processor 23 may be converted into a calculation algorithm that can be executed by a quantum computer, and then the quantum computer 3 may be made to execute the calculation algorithm.

[0160] The quantum computer 3 may function as a quantum measurement device. For example, in this case, the computational quantum circuit 5 is represented by a unitary operation for generating an initial state and free time evolution.

[0161] The information processing device 2 may be a classical computer, a quantum computer, or a combination thereof.

[0162] The information processing system 1 can be applied to various information processes related to quantum computation, such as quantum measurement and quantum communication.

[0163] The above-described embodiment is not limited to the information processing system 1, and may be an information processing method or an information processing program. The information processing method includes each step of the information processing system 1. The information processing program causes at least one computer to execute each step of the information processing system 1.

[0164] 6. An Example of the First Information Processing (Third Information Processing) When the Adiabatic Time Evolution Method is Used as the Ground State Calculation Method The above-mentioned ground state calculation method may include the so-called adiabatic time evolution method. This section describes an example of the first information processing performed using the adiabatic time evolution method as the ground state calculation method. The information processing described in this chapter may be referred to as the third information processing to distinguish it from the first information processing and the second information processing described above. For convenience of explanation, the following description may omit components or processes common to the first information processing in the third information processing. Note that the following processes may also be used in the second information processing as appropriate. The flow of the third information processing is similar to the flow of the first information processing shown in FIG. 6. Therefore, differences between the first information processing and the third information processing in each activity will be described here. 6.1. A System to which the Third Information Processing is Applied First, a system to which the third information processing is applied will be described. This system is defined by, for example, various pieces of information included in substance information IF1. It should be noted that this system is merely an example, and the third information processing method can be applied to any system.

[0165] In this embodiment, the system is composed of a total of (N_{el}+N_{ion}) particles, including N_{el} electrons and N_{ion} nuclei. In this embodiment, for convenience of explanation, it is assumed that the charge of each nucleus is equal. Therefore, in this embodiment, nuclei and ions are treated almost the same, and particles corresponding to atomic nuclei are expressed as ions. The Hamiltonian H_{final} of the system in this embodiment is set, for example, as follows based on Equation 1:

[0166] Here, N_{el} corresponds to n_{e} in equation 1. N_{ion} corresponds to n_{nucl} in equation 1. i and j are indices indicating individual electrons contained in the system, and correspond to l and l' in equation 1. I and J are indices indicating individual nuclei contained in the system, and correspond to v and v' in equation 1. The nucleus r is the position operator of the electron. R is the position operator of the nucleus. The first term is the kinetic energy term of the electron, and is denoted as T_{el}.

[0167] The first term is the electron momentum energy term, and is hereinafter denoted as T_{el}. The second term represents the electron-electron interaction, and is represented by the interaction operator v_{ee}. In the following, the second term is denoted as V_{ee}. The third term represents the electron-nucleus interaction, and is represented by the interaction operator v_{ej}. In the following, the third term is denoted as V_{ei}. The fourth term represents the nuclear interaction, and is represented by the interaction operator v_{ii}. In the following, the fourth term is denoted as V_{ii}. These interaction operators appropriately include the nuclear charge Z as a parameter.

[0168] The indices i, j, I, and J are assigned to the momentum operator and the position operator in the formula, respectively. Also, the i in the third term v_{ei} and the fourth term v_{ii} is a symbol indicating an atomic nucleus, and is different from the i used as an index to identify a particle.

[0169] Based on this system, the candidate generator 232 generates candidates for the arrangement of atomic nuclei in a candidate generation process using a method similar to the first information processing, and assigns the candidate arrangement to the first quantum bit 321 n in an assignment process. The quantum bit state expressed as a result of the assignment is expressed, for example, as follows:

[0170] |Ψ> indicates the quantum bit state of the entire system composed of N_{el} electrons and N_{ion} nuclei. |ψ_{el}({R_I})> indicates a partial quantum bit state (i.e., the second quantum bit state) composed of N_{el} electrons. |{R_I}> indicates a partial quantum bit state (i.e., the first quantum bit state) composed of N_{ion} nuclei. In this embodiment, for convenience of explanation, n_{ion} first quantum bits 321n are used to represent the states of N_{ion} nuclei, and n_{el} second quantum bits 321e are used to represent the states of N_{el} electrons. As a result, the first quantum bit 321n can represent 2^(n_{ion}) different states of the nuclei, and the second quantum bit 321e can represent 2^(n_{el}) different states of the electrons.

[0171] 6.2 Quantum Circuit Generation Processing Next, the quantum circuit generation processing (activity A5) performed in the third information processing will be described. Fig. 27 is a flowchart showing the flow of the quantum circuit generation processing in this embodiment.

[0172] First, in step S1, the processor 23 sets an initial Hamiltonian H_{initial}. The initial Hamiltonian H_{initial} may be set automatically based on the acquired Hamiltonian H_{final} of the system, may be set independently of the Hamiltonian H_{final} of the system, or may be set arbitrarily by the user. The initial Hamiltonian H_{initial} in this embodiment is expressed, for example, by the following mathematical formula:

[0173] In the initial Hamiltonian H_{initial}, the operators T_{el} and J_x*I_{el} (* corresponds to the Kronecker product) acting on the electronic state (i.e., second quantum bit 321e) represent the Hamiltonian of an electron in free space, and X_l acting on the nucleus (i.e., first quantum bit 321n) represents an X-gate operation on the l-th first quantum bit 321n. I_{el} and I_{ion} are identity operators acting only on the electronic part and the nuclear part of computation quantum bit 321, respectively.

[0174] Next, in step S2, the processor 23 sets a ground state corresponding to the set initial Hamiltonian H_{initial}. The ground state |Ψ_{init}> of the above-mentioned initial Hamiltonian H_{initial} is expressed, for example, as follows:

[0175] |Ψ_{init}> is also referred to as the input state input to the second quantum gate operation QC13. |ψ_{init}> is the ground state of the Hamiltonian of the entire N_{el} electron system when ignoring interactions between particles and considering only the kinetic energy T_{el} between electrons. |+> is also an example of a state in which the |0> state and the |1> state of each nucleus constituting the system are superimposed. In this embodiment, |+> is a state in which the |0> state and the |1> state of each nucleus are superimposed with equal weighting. Note that the weight of each state when superimposing the |0> state and the |1> state of each nucleus is arbitrary. Hereinafter, for convenience of explanation, the ground state of the initial Hamiltonian H_{initial} may be referred to as the initial ground state.

[0176] Next, in step S3, the processor 23 generates the input generation circuit QC10 based on the ground state corresponding to the initial Hamiltonian H_{initial}. The method for generating the input generation circuit QC10 is arbitrary, but the processor 23 may generate the input generation circuit QC10 by, for example, specifying the initial Hamiltonian H_{initial} and the input generation circuit QC10 corresponding to its ground state based on the results of calculations performed in the past.

[0177] 28 is a diagram illustrating an example of an input generation circuit QC10 according to this embodiment. The input generation circuit QC10 is configured to perform Hadamard gate operations on each of the first quantum bit 321n and the second quantum bit 321e. |ψ_{init}> is obtained by performing a Hadamard operation on each of the second quantum bits 321e in the |0> state. Furthermore, the |+> state is obtained by performing a Hadamard operation on each of the first quantum bits 321n in the |0> state. Therefore, by inputting the initial state |000...00> of the computation quantum bit 321 into the input generation circuit QC10, the input state |ψ_{init}> can be converted into the basis state of the initial Hamiltonian H_{init}.

[0178] The input generation circuit QC10 is an example of a first quantum gate operation QC11 and also an example of a reference quantum gate operation QC12. For example, in the input generation circuit QC10, a series of Hadamard gate operations acting on the first quantum bit 321n corresponds to the first quantum gate operation QC11 that superposes the state of the first quantum bit 321n. Furthermore, a series of Hadamard gate operations acting on the second quantum bit 321e can generate a superposition state of reference electronic states for each candidate atomic nucleus configuration included in the superposition state, and therefore the series of Hadamard gate operations corresponds to the reference quantum gate operation QC12.

[0179] In this way, by performing the first quantum gate operation QC11 (input generation circuit QC10) on the computation qubit 321 that is in the initial state, the quantum bit of the computation qubit 321 takes an eigenstate (including the ground state) of the preset initial Hamiltonian H_{initial}. It can also be said that immediately before the second quantum gate operation, the processor 23 assigns states to the first qubit 321 n and the second qubit 321 e so that the first qubit state and the second qubit state are both eigenstates of the initial Hamiltonian H_{initial}.

[0180] The format of the initial Hamiltonian H_{initial} is not limited to this and can be any format, but it is preferable that its ground state be analytically calculable, for example, that an exact solution exists. This reduces the error between the input state input to the computational quantum circuit QC1 and the ground state, thereby improving the accuracy of the calculation results.

[0181] 27, after the processing of step S3, the process proceeds to step S4, where the processor 23 generates a second quantum gate operation QC13 based on the obtained Hamiltonian of the system (see above equation 26). The second quantum gate operation QC13 of this embodiment is constructed so as to define an adiabatic time evolution for the generated input state |Ψ_{init}>.

[0182] Then, the processor 23 sets a second quantum gate operation. In this case, the second quantum gate operation QC13 is a gate operation corresponding to the time evolution of the system by a virtual Hamiltonian H(t) that changes almost adiabatically from an initial Hamiltonian H_{initial} to a target Hamiltonian H_{final} using at least one real-time evolution operator. The virtual Hamiltonian H(t) is expressed, for example, by the following equation:

[0183] The first term on the right-hand side represents the kinetic energy of the electron. The second term on the right-hand side represents the electron-electron interaction. The third term on the right-hand side represents the electron-nucleus interaction. The fourth term on the right-hand side represents the nuclear-nucleus interaction. The fifth term on the right-hand side, together with the first term on the right-hand side, represents the initial Hamiltonian H_{initial}. The coefficients A_i(t) (i = 1, 2, 3, 4) are parameters that depend on time t for introducing each interaction almost adiabatically. The coefficients A_i(t) are 0 in the initial state (i.e., when t = 0) and 1 in the final state (when t = t_f), and are configured to increase, for example, as t increases.

[0184] Here, the time evolution operator of the system due to the contribution of the first term on the right side of Equation 29 is expressed as follows using the Centered Quantum Fourier Transform (hereinafter referred to as CQFT):

[0185] Furthermore, the time evolution operators of the system due to the contributions of the second, third, and fourth terms on the right-hand side of Equation 29 are expressed as follows, using the time width Δt representing the unit of time evolution:

[0186] R_x^{*n_{ion}}(θ_k) (where * denotes the Kronecker product) is a rotation gate operation that rotates each state of the first quantum bit 321n by a rotation angle θ_k around the x-axis. Hereinafter, for convenience of explanation, the operator representing time evolution using the virtual Hamiltonian will be referred to as the virtual time evolution operator. Note that the expressions for each interaction are not limited to those described above. For example, expressions equivalent to the above expressions can be adopted by applying any mathematical transformation to the above expressions, such as sign inversion, constant multiplication, or constant addition / subtraction, to each coefficient A_i or parameter θ_k. The quantum bit state |Ψ(nΔt)> that has evolved in time by n×Δt from the initial state |Ψ(0)> using such a virtual time evolution operator can be expressed, for example, within the scope of a first-order Suzuki-Trotter expansion, as follows:

[0187] The expression of Equation 32 may use, for example, a higher-order Suzuki-Trotter expansion, and may be any expression that expresses the virtual time evolution exactly or approximately.

[0188] 29 is a diagram showing an example of a quantum circuit representing a virtual time evolution operator as the second quantum gate operation QC13. Here, the second quantum gate operation QC13 changes depending on an integer k (k=1, 2, ...) corresponding to the number of iterations, and therefore the second quantum gate operation QC13 corresponding to that k may be denoted as QC13k. Each state of the first quantum bit 321n is a |+> state, in which each first quantum bit state is superposed. By performing such second quantum gate operation QC13 from k=n to k=1, the final quantum bit state of the entire computation quantum bit 321 reaches the final state |Ψ(nΔt)> expressed by Equation 32.

[0189] In the above equation, exp[-iKΔt] is defined as exp[-iKΔt] = U_{kin}. In this way, the processor 23 generates a virtual state by applying a virtual time evolution operator including the time width Δt of the time evolution as a parameter to the superposition state of the first quantum bit state. Note that each coefficient A_i is set to 1 when the end time t_f = nΔt.

[0190] Thereafter, the process proceeds to step S5, where the processor 23 generates a computational quantum circuit QC1 based on the input generation circuit QC10 and the second quantum gate operation QC13. Fig. 30 is a diagram showing an example of the computational quantum circuit QC1 in this embodiment.

[0191] The computational quantum circuit QC1 of this embodiment includes an input generation circuit QC10 and a second quantum gate operation QC13k (k = 0, 1, 2, ..., n). The computational quantum circuit QC1 is configured to first apply the input generation circuit QC10 to each of the initialized first quantum bit 321n and second quantum bit 321e. This causes the computational quantum bit 321 to be in the ground state of the initial Hamiltonian H_{initial} or a state close to this.

[0192] Furthermore, the computational quantum circuit QC1 is configured to apply the second quantum gate operation QC13k sequentially from k = 0 to n after the input generation circuit QC10. As a result, the ground state of the initial Hamiltonian H_{initial} gradually evolves adiabatically over time with a time width Δt, and reaches the final state |Ψ(nΔt)>.

[0193] The computation quantum circuit QC1 is then configured to perform an observation operation QC14 on the first quantum bit 321n, which makes it easier to observe the state of the first quantum bit 321n when the energy of the entire matter represented by the computation quantum bit 321 is low. Thus, the processor 23 can identify the most stable nuclear configuration by aggregating the results of such observations.

[0194] Note that the system to which the third information processing is applied is not limited to a system containing multiple types of particles, such as atomic nuclei and electrons, but may also include a system containing a single type of particle, such as a system containing only atomic nuclei. For example, when performing the third information processing on a system consisting only of atomic nuclei, the generated computational quantum circuit QC1 includes an input generation circuit QC10 and a second quantum gate operation QC13, similar to the system containing electrons described above. In this case, the input generation circuit QC10 only needs to include the gate operation acting on the first quantum bit 321n among the input generation circuits QC10 in the system containing electrons. Furthermore, the second quantum gate operation QC13 only needs to include U_{ii}^(k) and R_x^{*n_{ion}}(θ_k) among the second quantum gate operations QC13 in the system containing electrons.

[0195] 6.3. Simulation Results When the Adiabatic Time Evolution Method is Used This section describes the simulation results when the adiabatic time evolution method is used as the ground state search method. In other words, this section describes the simulation results using the computational quantum circuit QC1 according to the third information processing method. Note that this simulation result is merely an example to demonstrate the usefulness of this information processing, and does not limit the interpretation of the technical concept related to the information processing described above.

[0196] The substance to be calculated in this simulation is a hydrogen molecule (H2), and the substance information IF1 includes the atomic species contained in the hydrogen atom (i.e., two H atoms) and the bond length d of the hydrogen nucleus (an example of the atomic nucleus arrangement). In this embodiment, the bond length d is set to 2. For convenience of calculation in this embodiment, the bond length d is a dimensionless quantity normalized by the Bohr radius.

[0197] In this embodiment, the potential acting on each particle constituting the hydrogen molecule is set as follows.

[0198] Here, x indicates the coordinate corresponding to the position of the particle in a one-dimensional coordinate system in which the midpoint between the two atomic nuclei is set as 0 and the direction toward each atomic nucleus is the x-axis.

[0199] Next, the candidate generator 232 generates candidates for other atomic nucleus configurations for the acquired bond length d. In this embodiment, in addition to d=2, candidates for d=4, 6, and 8 are generated.

[0200] Next, the allocation unit 233 allocates the generated candidate nucleus configurations to the quantum bit states of the first quantum bit 321n. In this embodiment, two first quantum bits 321n are used to represent four candidate nucleus configurations. Specifically, the allocation unit 233 allocates candidate nucleus configurations to each of the first quantum bit states so that the configuration where d = 2 represents |00>, the configuration where d = 4 represents |01>, the configuration where d = 6 represents |10>, and the configuration where d = 8 represents |11>.

[0201] Next, the processor 23 performs a third information processing based on this information to generate a computational quantum circuit QC1. The simulation results described below are obtained by having a classical computer simulate the calculations performed by the computational quantum circuit QC1 generated in this way. In this embodiment, the total number of steps n is 10,000, and the elapsed time t_f during adiabatic time evolution from the start state to the final state is Δt*10,000.

[0202] Figure 31 shows the relationship between the observation probability of each candidate and the number of steps, as a simulation result when the adiabatic time evolution method is used as the ground state search method. Figure 32 shows the components included in the wave function in the final state. The horizontal axis in Figure 32 is a parameter having a dimension representing length, which can be associated with the distance between atomic nuclei. In Figure 32, the region of hydrogen atomic nucleus distances between 0 and less than 15 corresponds to d = 2, the region of 15 and less than 30 corresponds to d = 4, the region of 30 and less than 45 corresponds to d = 6, and the region of 45 and less than 60 corresponds to d = 8.

[0203] As shown in Figure 31, the observation probability of d = 2 increases with increasing number of steps. Also, as shown in Figure 32, the observation probability of d = 2 in the final state is more than nine times that of other states. This suggests that the nuclear configuration with d = 2 is the most stable structure.

[0204] When the ground state energy E_gs of each candidate is calculated using a conventional classical algorithm, E_gs = -0.8107 for d = 2, E_gs = -0.7497 for d = 4, E_gs = -0.6932 for d = 6, and E_gs = -0.6789 for d = 8. This indicates that d = 2 is the most stable state. These results are consistent with the theoretical conclusion that the configuration corresponding to d = 2 is the lowest energy configuration, suggesting the validity of this calculation method.

[0205] 6.4. Information processing for calculating the ground state from the final state (fourth information processing) Next, we will explain the information processing for calculating the ground state of the system from the ground state of the initial Hamiltonian H_{initial} in Equation 32. Hereinafter, this information processing will be referred to as the fourth information processing. Figure 33 is a flowchart showing the flow of the fourth information processing.

[0206] First, in step S11, the processor 23 sets an initial Hamiltonian H_{initial}. Details of step S11 are the same as those of step S1.

[0207] Next, in step S12, the processor 23 sets a ground state corresponding to the initial Hamiltonian H_{initial}. The details of step S12 are the same as those of step S2.

[0208] Next, in step S13, the processor 23 sets a virtual state |Ψ_{QAOA}> based on the Hamiltonian H_{final} (see Equation 25) of the system. The virtual state |Ψ_{QAOA}> is set based on the final state |Ψ(nΔt)>=|Ψ(t_f)> (see Equation 32) when the above-mentioned virtual Hamiltonian H(t) is adiabatically evolved over time from the initial Hamiltonian H_{initial} to the Hamiltonian H_{final} of the system. For example, the virtual state |Ψ_{QAOA}> can be obtained by parameterizing the quantities related to the time width Δt included in each of the components corresponding to each energy term of |Ψ(nΔt)> (for example, each component expressed by Equation 31). In this embodiment, the virtual state |Ψ_{QAOA}> is expressed as follows using the unknown variables α_k, β_k, γ_k, δ_k, and θ_k:

[0209] The unknown variables α_k, β_k, γ_k, δ_k, and θ_k are coefficients that parameterize the contribution of each interaction included in the Hamiltonian H_{final} of the system. α_k is the unknown variable corresponding to U_{kin}. β_k is the unknown variable corresponding to V_{ii}. γ_k is the unknown variable corresponding to V_{ei}. δ_k is the unknown variable corresponding to V_{ee}. θ_k indicates the rotation angle around the x-axis. |Ψ(0)> is the initial state (i.e., the ground state corresponding to the initial Hamiltonian).

[0210] Next, in step S14, the processor 23 generates a computational quantum circuit for generating a virtual state |Ψ_{QAOA}> from the initial state |Ψ(0)> by appropriately setting each of the unknown variables α_k, β_k, γ_k, δ_k, and θ_k. The quantum circuit is defined by the operator acting on the initial state |Ψ(0)> in the above equation 34. Here, multiple sets of unknown variables {α_k, β_k, γ_k, δ_k, θ_k} are set, and a computational quantum circuit corresponding to each set is generated.

[0211] Next, in step S15, the processor 23 calculates the energy expectation value of the virtual state |Ψ_{QAOA}> based on the generated computational quantum circuit. The energy expectation value E is expressed as follows:

[0212] H(t_f) is the time when each coefficient A_i included in the virtual Hamiltonian H(t) becomes 1. In other words, the energy expectation value E is the energy expectation value of a virtual state with respect to the final state of the virtual Hamiltonian due to time evolution.

[0213] Next, in step S16, the processor 23 identifies the unknown variables α_k, β_k, γ_k, δ_k, and θ_k that minimize the energy expectation value. As a result, the processor 23, as a parameter determiner, determines the parameters by minimizing the energy expectation value of the virtual state for the final state of the virtual Hamiltonian due to time evolution. Identifying the most stable state of the substance defined by the substance information IF1 boils down to identifying the unknown variables α_k, β_k, γ_k, δ_k, and θ_k that minimize the energy expectation value E. When the energy expectation values ​​E for each of multiple sets of unknown variables have been calculated, the processor 23 determines changes in the unknown variables α_k, β_k, γ_k, δ_k, and θ_k based on the multiple energy expectation values ​​E, and calculates the energy expectation value E corresponding to the set of unknown variables α_k, β_k, γ_k, δ_k, and θ_k after calculating the changes. When the resulting change in the energy expectation value is equal to or less than a predetermined error tolerance, the virtual state |Ψ_{QAOA}> represented by the final set of unknown variables α_k, β_k, γ_k, δ_k, and θ_k indicates the most stable state (most stable structure) of the material. By observing the state of the first quantum bit 321n in such a virtual state |Ψ_{QAOA}>, the most stable nuclear configuration can be obtained. The identification of the most stable state may be calculated as an optimization problem using a classical computer or may be appropriately calculated using a quantum computer. Furthermore, any method can be used to minimize the energy expectation value E, and may be, for example, any of various methods used for classical variational problems.

[0214] The initial Hamiltonian H_{initial} is not limited to the form expressed by Equation 27, and may further include an initial potential V_{init}. The initial potential V_{init} is a given potential energy, for example, the potential of an electron system. When such an initial potential exists, the initial Hamiltonian H_{initial} is expressed as follows:

[0215] When such an initial Hamiltonian H_{initial} is set, the processor 23 may set the following virtual Hamiltonian H(t).

[0216] The coefficients A_5 and A_6 are coefficients that represent the contribution of each energy, similar to the above-mentioned A_1, A_2, A_3, and A_4.

[0217] In this case, |ψ_{init}> expressed in Equation 28 etc. becomes the ground state of the Hamiltonian of the entire system of N_{el} electrons when the kinetic energy T_{el} between electrons and the initial Hamiltonian V_{init} are taken into consideration.

[0218] Note that the quantum circuit for generating |ψ_{init}> does not have to be specified to perform Hadamard gate operations on each of the first quantum bit 321n and the second quantum bit 321e, and the initial Hamiltonian H_{initial} may be determined appropriately depending on the number of electrons in the system.

[0219] 7. Regarding the Generation of Computational Basis This chapter describes another example of the generation of the computational basis assigned to the computational quantum bit 321 when performing each of the above information processing, along with the flow of the information processing. Note that the particles in this embodiment are atomic nuclei that constitute a substance and are classical point particles, but are not limited to these and may be any interacting particles such as electrons, quasiparticles, or aggregates. Hereinafter, for convenience of explanation, the information processing for generating the computational basis will be referred to as the fifth information processing. The fifth information processing is used, for example, as the processing from activity A2 to activity A4 in the first information processing or the second information processing (i.e., from obtaining substance information IF1 to executing the assignment processing).

[0220] 7.1 Fifth Information Processing Flow This section describes the fifth information processing flow. Fig. 34 is a flowchart showing the fifth information processing flow.

[0221] First, in step S21, the acquisition unit 231 acquires position information regarding L placement candidates in a certain space and classification information regarding k types of classification of N particles to be placed in the placement candidates. The position information indicates, for example, coordinates at which each of the N particles can be placed. The position information is also a position at which a particle can be placed in a certain space, and can also be called a specific position. The specific position is represented, for example, by a single coordinate point at which a particle can exist. In other words, the acquisition unit 231 acquires information regarding multiple specific positions. In particular, the position information indicates coordinates at which each of the N particles can be placed, regardless of classification. The placement candidates are generated, for example, by a method similar to the information processing described above. Hereinafter, for convenience of explanation, the space in which the placement candidates are set is referred to as the target space. Specifically, the placement candidates can be represented as L lattice points by dividing the target space at equal intervals. Each of these lattice points is configured to allow N particles to be placed thereon. In this embodiment, the target space is a three-dimensional real space, and the system representing the substance is configured such that zero or one particle is placed at each lattice point, and multiple particles are not placed at the same position candidate at the same time. Furthermore, the target space has N_d placement candidates (lattice points) per dimension. Therefore, the target space has a total of N_d^3 lattice points as placement candidates. These placement candidates can also be considered the number of divisions of the target space.

[0222] The classification in the classification information is information for distinguishing between different types of particles, and in this embodiment, includes atomic species of particles that make up a substance, such as hydrogen atoms, oxygen atoms, and carbon atoms. Note that the classification is not limited to this, and may include classification based on any state, such as the valence of ions or isotopes. For example, the classification may represent the type of particles that make up an atom, such as electrons, atomic nuclei, and protons. Furthermore, the classification is not limited to representing a single particle, and may be information that distinguishes between composite particles such as micelles. The classification information can also be said to be information that represents the classification of particles.

[0223] Next, in step S22, processor 23, as a basis generator, generates a computational basis represented by at least k×L computational qubits 321 based on the acquired position information. Computational qubits 321 include at least L positional qubits corresponding to each of the placement candidates set for each of k types of classification. In this embodiment, processor 23 generates k×L computational bases, assuming that each of the k types of particles can be placed at a common L candidate positions. In this embodiment, first qubit 321n functions as a positional qubit.

[0224] Next, in step S23, the allocation unit 233 allocates the state of the computation quantum bit 321 to each of the generated computation bases. In this way, the computation bases are configured to be able to express, for each type, in which candidate arrangement the particle is arranged.

[0225] For example, if the classification is information that distinguishes between four types of atomic species S, the quantum bit state |Ψ> of the computation quantum bit 321 is expressed as follows using the quantum bit states |S_l> of the partial computation quantum bits 321 corresponding to the ground states of each atomic species S_l (l = 1, 2, 3, 4):

[0226] Each computational basis is associated with a case where the state of the L partial computational qubits 321 assigned to each atomic species S_l takes |0> or |1>. For example, a computational basis corresponding to a state in which the atomic species S_l is located at the m-th lattice point among the L lattice points is assigned to a qubit state in which the state of the m-th computational qubit 321 among the L computational qubits 321 corresponding to the atomic species S_l is |1>. In other words, the assigning unit 233 assigns at least one computational qubit to each specific position for each particle classification. With this configuration, it is possible to express the state of a complex system in which particles of multiple classifications coexist with a smaller number of computational qubits 321.

[0227] The form of the computation basis is arbitrary and is not limited to one represented by at least k×L computation qubits 321. In other words, the allocation unit 233 allocates a computation qubit group including at least one computation qubit to each specific position. The computation qubit group is composed of computation qubits 321 and can represent at least two different states as a whole. In other words, the computation qubit group is configured so that at least a first state and a second state are observable. The first state indicates that a particle is present at the corresponding specific position. The second state indicates that a particle is not present at the corresponding specific position. The following describes a case where the computation qubit group is composed of a single computation qubit 321. In this case, the first state corresponds to, for example, the quantum bit state of a certain computation qubit 321 being |1>, and the second state corresponds to the quantum bit state of the computation qubit 321 being |0>. With this configuration, the state of a particle present at a specific position is represented as the state of the computation qubit 321, thereby improving the interpretability of quantum computation.

[0228] In the present embodiment, in the next step S24, the acquisition unit 231 further acquires information regarding interactions between particles to be placed at placement candidates (lattice points) and information regarding the number of particles for each classification. The interactions are determined by at least the positional relationship between the particles and the classification of the particles. For example, the interaction between a particle present at the i-th lattice point and a particle present at the j-th lattice point can be expressed by J_{ij}. The origin of the interaction can be any, such as atomic force, Coulomb force, weak force, or strong force. The interactions also include interactions of three or more bodies, such as empirical potentials.

[0229] Next, in step S25, the processor 23 generates an objective function based on the computational basis and the interaction information. The objective function includes a first factor and a second factor. The first factor corresponds to a Hamiltonian of the system of particles. The second factor is configured to output a larger value when a first number representing the number of particles of a certain class represented by the computational qubit is different from a second number representing the number of the particles obtained, compared to when the first number is the same as the second number. For example, the objective function is expressed as H_int as follows:

[0230] Here, S is a set of atomic species, e.g., S = {H, C, O, N}. J_{ij} is a constant representing the magnitude of the interaction, e.g., the value of the interaction potential based on the distance and atomic species. k_1 to k_N_{grid} are subscripts representing the quantum bits assigned to atom k. N_k is the number of atoms corresponding to classification k (i.e., the kth atomic species). N_{grid} is the total number of configuration candidates and is equal to N_d^3. N_k may be manually entered by the user or estimated by the processor 23 or the like based on various measurement results for the material. P_k is a penalty factor specifying the number of atoms corresponding to classification k and takes a positive value. In the above formula, the first number is Σx_{k, l} and the second number is N_k. For example, the second factor is expressed as an even function of the difference between the first number and the second number. In this embodiment, the second factor is expressed by an even function of the difference between the first number and the second number. The first term on the right side of the above equation is an example of the first factor and represents a two-body interaction. The second term on the right side is an example of the second factor, and P_k is a positive constant.

[0231] In this way, it is preferable that the objective function H_{int} be expressed in the form of an Ising function or QUBO (quadratic unconstrained binary optimization). Therefore, in this embodiment, in step S26, the processor 23 determines whether the objective function H_{int} is in the QUBO form. This determination method is arbitrary, but it can be determined, for example, based on whether the form of the Hamiltonian includes a third-order or higher term.

[0232] If the determination result in step S26 is negative, the process proceeds to step S27, where the processor 23 converts the objective function H_{int} into the QUBO format. In particular, if the objective function H_{int} is expressed by an Ising function, there is at least one objective function in the QUBO format that corresponds to the objective function H_{int}. If the objective function cannot be converted into the QUBO format, the processor 23 may notify the user that the objective function cannot be converted into the QUBO format and suspend the information processing. The process then proceeds to step S28. On the other hand, if the determination result in step S26 is positive, there is no need to convert the objective function into the QUBO format again, so the processor 23 skips step S27 and proceeds to step S28.

[0233] In step S28, the processor 23 sets the objective function converted into the QUBO format in this way as the Hamiltonian H in the first information processing or the second information processing. When performing the third information processing, the processor 23 may set the objective function as the virtual Hamiltonian H(t).

[0234] After that, the fifth information processing operation is completed, and the processor 23 generates a computation quantum circuit QC1 based on the set Hamiltonian and executes a calculation using the quantum computer 3. The computation quantum circuit QC1 includes at least a first quantum gate operation QC11 and a second quantum gate operation QC13, similar to the first to third information processing operations. Thus, the quantum operation unit 234 performs a first quantum operation on the computation quantum bit 321 based on the computation quantum circuit QC1, thereby generating a first superposition state in which states corresponding to the computation bases are superposed. This state can be implemented, for example, by a Hadamard gate operation that sets the individual quantum bit state of the first quantum bit 321n to a |+> state.

[0235] Next, the quantum operation unit 234 performs a second quantum operation corresponding to the objective function on the first superposition state based on the computational quantum circuit QC1, thereby generating a second superposition state in which at least the interactions acting between particles are reflected in the first superposition state. The manner in which the second quantum gate operation QC13 is generated is the same as that described in the first information processing, etc.

[0236] Next, the identification unit 235 performs a process of identifying a configuration with a relatively low energy among the candidate particle configurations based on the observation results of the computation quantum bit 321 in the generated second superposition state. The specific aspects of this identification process are the same as those performed in the first information processing, etc.

[0237] According to the fifth information processing, for example, it is possible to simplify the quantum circuit when identifying the optimal arrangement in a non-degenerate system, thereby making it easier to identify the optimal arrangement in a non-degenerate system.

[0238] 7.2. Modifications of the Fifth Information Processing The fifth information processing is not limited to the above-described example, and can be implemented by appropriately combining the following modifications, for example.

[0239] In the fifth information processing, the processor 23 generates a computational basis represented by k×L computational quantum bits 321, but this is not limited to this. For example, the processor 23 may generate a computational basis consisting of n×k×L computational quantum bits, where n is an integer greater than or equal to 2, so that the computational basis can further be configured to represent a case where multiple particles exist in the same configuration candidate. In other words, the first quantum bit state may be configured so that a state other than |0> and |1> is assigned to one lattice point. For example, if three atoms can be placed at one lattice point, the assignment unit 233 may assign two first quantum bits 321n to the lattice point. For example, the assigning unit 233 may assign the basis state to the first quantum bit state according to the number of nuclei arranged at the lattice point so that when the number of nuclei arranged at the lattice point is 0, the state of the two first quantum bits 321n is |00>; when the number of nuclei arranged at the lattice point is 1, the state of the two first quantum bits 321n is |01>; when the number of nuclei arranged at the lattice point is 2, the state of the two first quantum bits 321n is |10>; and when the number of nuclei arranged at the lattice point is 3, the state of the two first quantum bits 321n is |11>. In other words, the computation quantum bit group includes two or more computation quantum bits 321, and is configured so that at least one quantum bit state different from the first state and the second state can be observed. Each quantum bit state corresponds to the number of particles present at the corresponding specific position. With this configuration, it is possible to assign a state in which multiple particles exist at the same specific position, such as in a boson system, to the state of a computational quantum bit, thereby improving the interpretability of quantum computation for a wider variety of systems.

[0240] The first factor is not limited to the form of the first term of H_{int} described above. For example, the contribution of m-body interactions is expressed as an m-th order expression of binary variables x_i. Therefore, it may be written in the form of HUBO (high-order unconstrained binary optimization) as follows:

[0241] The second factor is not limited to the format of the second term of H_{int} described above. For example, the second number included in the second factor does not have to be a fixed value for each classification of atomic species S, etc., and may be variable as in the following format:

[0242] As a result, when the ratio of the number of particles in class k_1 to the number of particles in class k_2 does not match C_{k_1} / C_{k_2}, the value of the second factor increases, and therefore the ratio of the number of particles in each class can be renormalized as a constraint when minimizing the objective function H_{int}. For example, when determining the arrangement of atomic nuclei in silicon dioxide (SiO2), the processor 23 sets the second factors as C_{k_1}=2 and C_{k_2}=1, where class k_1 represents Si and class k_2 represents O.

[0243] Furthermore, when the atomic species includes positive or negative ions, the processor 23 may set a penalty factor (second factor) representing the neutral condition of the substance by acquiring information on the valence. The penalty factor can be expressed in a format similar to that of the above-mentioned formula 41. For example, when determining the arrangement of atomic nuclei in sodium chloride NaCl, Na ＋ Ion valence (+1) and Cl － It is sufficient to set C_{k_1} = C_{k_2} = 1 so that the valence of the ion (-1) is balanced. Furthermore, when an assembly of atomic nuclei is ionized (for example, carboxylic acid in an aqueous solution), if the valence of the entire assembly is Q, the processor 23 sets the second factor in the following format:

[0244] The coefficient C_k is a value set according to the valence of each atomic nucleus (ion). The first term in the above formula represents the sum of the valences of the placed atomic nuclei (ions), and if the value of the first term is different from Q, the value of the second factor increases. Therefore, by introducing such a second factor, the processor 23 can take into account the restriction on the valence of ions in the target space when minimizing the objective function H_{int}.

[0245] The second factor may include at least one of the above forms, and may include more than one of them, and such second factors can be generalized using the following formula:

[0246] m is an index representing the constraint M included in the second factor, such as a charge neutrality condition, a particle number constraint, or a composition ratio constraint. k represents each atomic species S, and the condition associated with k, such as C_{k, m} or M_{k, m}, represents the condition imposed on the kth atomic species. Q_m is a numerical value representing the condition imposed on the entire target space regardless of the type of atomic species, and is a generalization of Q in Equation 42. Note that Q_m can also be set to 0 by appropriately renormalizing it into M_{k, m}. Note that the second factor may be set so as not to be included by setting P_m = 0.

[0247] The target space is not limited to three-dimensional real space, but may be a space based on coordinates other than real space coordinates, such as spin space or wave number space. Furthermore, the dimension of the target space is not limited to three, but may be a lower-dimensional space such as one or two, or a hyperspace of four or more dimensions. That is, the target space may be any space that can be mathematically described as a field, such as the presence or absence and state of particles. In other words, the fifth information processing is not limited to being performed on particle configuration candidates (i.e., positional state candidates), but can be applied to any state candidate. In essence, the acquisition unit 231 acquires state information regarding L state candidates in a certain state space and classification information regarding k types of classification of N particles. Each particle takes one of the state candidates. The processor 23, as a basis generation unit, generates a computational basis represented by at least k × L computational quantum bits based on the acquired state information. The computational qubit 321 includes at least L position qubits corresponding to each of the state candidates set for each of k types of classification, and the computational basis is thereby configured to be able to express, for each classification, which state of each state candidate a particle can take. For example, the state information indicates state candidates that each of the N particles can take. More specifically, the state information indicates, for example, the coordinates in state space of the states that each of the N particles can take. The position information in the above description of the fourth process can also be considered an example of the state information.

[0248] Each of the above information processing methods can independently constitute a technical concept. For example, the fifth information processing method can be used to perform any information processing that can be processed using a quantum algorithm, such as processing other than processing for obtaining calculation results related to physical phenomena such as atomic nucleus configurations, for example, calculation results for combinatorial optimization problems or traveling salesman problems.

[0249] A part of the processing of the processor 23 may be converted into a calculation algorithm that can be executed by a quantum computer, and then the quantum computer 3 may be made to execute the calculation algorithm.

[0250] The quantum computer 3 may function as a quantum measurement device. For example, in this case, the computational quantum circuit 5 is represented by a unitary operation for generating an initial state and free time evolution.

[0251] The information processing device 2 may be a classical computer, a quantum computer, or a combination thereof.

[0252] The information processing system 1 can be applied to various information processes related to quantum computation, such as quantum measurement and quantum communication.

[0253] The above embodiment is not limited to the information processing system 1, and may be an information processing method or an information processing program. The information processing method includes each step of the information processing system 1. The information processing program causes at least one computer to execute each step of the information processing system 1.

[0254] Furthermore, the information processing method and the information processing program are not limited to those executed for ground-state calculations, but may also be used to acquire low-energy states other than the ground state under realistic information processing constraints such as computation time and hardware configuration. For example, when a metastable amorphous structure is output as a result of the information processing on a system that forms a crystal as the ground state, the information processing method and the information processing program may be executed as a technique for acquiring the amorphous structure. In other words, in the identification step, the information processing system 1 may perform a process of identifying, among candidate atomic nucleus configurations, a configuration with a relatively low energy eigenvalue at a predetermined level, instead of the lowest energy eigenvalue, based on the observation results of the first quantum bit in the generated correlated quantum bit state. Such a configuration makes it easier to identify various atomic nucleus configurations, such as metastable structures.

[0255] The information processing system 1 and the like may be provided in the following aspects.

[0256] (1) An information processing system, comprising at least one processor capable of executing a program to perform the following steps: an acquisition step performs processing to acquire substance information related to a substance including at least one atomic nucleus and at least one electron, wherein the substance information includes a plurality of candidates for the arrangement of the atomic nucleus and interactions acting on each of the atomic nucleus and the electron, and the interactions include at least an electron-nucleus interaction acting between the atomic nucleus and the electron; and an assignment step performs processing to assign each of the acquired candidates for the arrangement of the atomic nucleus to one of at least one first quantum bit state, wherein the first quantum bit state is constituted by at least one first quantum bit, and an observation operation on the first quantum bit causes a state to be determined. the superposition step performs a process of generating a superposition state of a plurality of the first quantum bit states by performing a predetermined first quantum gate operation on the first quantum bit; the interaction step performs a process of generating a correlated quantum bit state in which the first quantum bit and the second quantum bit are correlated by performing a second quantum gate operation including the obtained interaction on the first quantum bit representing the superposition state and at least one second quantum bit representing an electronic state of the material; and the identification step performs a process of identifying a configuration having a relatively low minimum energy eigenvalue from among candidate configurations of the atomic nuclei based on an observation result of the first quantum bit in the generated correlated quantum bit state.

[0257] According to this configuration, multiple candidate nuclear configurations are represented by a first quantum bit. At this time, the first quantum bit can represent a superposition state of the multiple candidate nuclear configurations through a first quantum gate operation. The electronic state represented by the second quantum bit interacts with this superposition state through a second quantum gate operation, allowing the first quantum bit and the second quantum bit to represent the electronic state of each candidate nuclear configuration in its respective environment. At this time, the observation probability of the nuclear configuration represented by the first quantum bit is higher the lower the overall energy state of the system represented by the first quantum bit and the second quantum bit. Therefore, through the second quantum gate operation, nuclear configurations with relatively low overall system energy are more likely to be observed by the first quantum bit. Therefore, a configuration with a relatively low energy among the nuclear configurations is identified. Here, by affecting the electronic state on the superposition state of the multiple candidate nuclear configurations, a state similar to that of affecting the electronic state on each of the multiple nuclear configurations can be generated. Therefore, the calculation can be performed more efficiently than when calculation is performed for each of a plurality of candidates for atomic nucleus configuration.

[0258] (2) In the information processing system described in (1) above, in the interaction step, the second quantum gate operation is performed, and as a result of the interaction, a process is performed to generate a second quantum bit state representing an electronic state that can converge to a ground state in the arrangement of the atomic nuclei represented by the superposition state.

[0259] In this configuration, as the electronic state converges to the ground state, the energy of the entire system including that electronic state decreases, making it easier to identify a relatively low-energy configuration among the atomic nuclei.

[0260] (3) In the information processing system described in (1) or (2) above, further, in the electron configuration step, a reference quantum gate operation is performed on the quantum bit including the generated superposition state, thereby generating a superposition state of reference electronic states for each candidate configuration of the atomic nuclei included in the superposition state, and in the interaction step, a second quantum gate operation is performed on the quantum bit including the generated superposition state of the reference electronic states.

[0261] According to this configuration, by setting an appropriate reference electronic state when realizing the energy state of the material by operating the second quantum gate, it is possible to shorten the calculation time required to identify a configuration with low energy.

[0262] (4) In the information processing system described in any one of (1) to (3) above, the second quantum gate operation is configured to be able to execute a predetermined basis state calculation method based on the first quantization format.

[0263] According to this configuration, performing calculations based on the first quantization format makes it easier to obtain an intuitively understandable depiction of the atomic nucleus arrangement compared to, for example, calculations based on the second quantization format, thereby facilitating interpretation of the calculation results.

[0264] (5) In the information processing system described in any one of (1) to (4) above, the assignment step performs a process of assigning each of the candidate arrangements of the atomic nuclei described as classical point charges to one of the first quantum bit states.

[0265] With this configuration, the number of first quantum bits required to express the arrangement of atomic nuclei can be reduced compared to when the arrangement of atomic nuclei is described including quantum fluctuations.

[0266] (6) In the information processing system described in any one of (1) to (4) above, the substance information includes information regarding the reference position of the atomic nuclei, and further, in the candidate generation step, a process is performed to generate candidates for the arrangement of multiple atomic nuclei by adding a predetermined displacement to the acquired reference position.

[0267] This configuration can reduce the time and effort required to input candidates for the arrangement of a plurality of atomic nuclei one by one.

[0268] (7) In the information processing system according to any one of (1) to (6) above, the interactions further include electron-electron interactions.

[0269] In this configuration, the electron-electron interaction contributes more to the overall energy of the system than the electron-nuclear interaction, which increases the energy difference between states generated by the second quantum gate operation, making it easier to identify the configuration of low-energy nuclei.

[0270] (8) In the information processing system according to any one of (1) to (7) above, the substance is composed of at least one molecular system.

[0271] This configuration makes it possible to reduce the computational resources required to predict the shape of molecules such as proteins, which have many degrees of freedom in the arrangement of atomic nuclei.

[0272] (9) In the information processing system according to any one of (1) to (8) above, the first quantum gate operation includes at least a Hadamard gate operation.

[0273] With this configuration, it becomes easier to generate a superposition state of all initial states using simple quantum operations, thereby preventing the calculation result from remaining at a local optimum due to the existence of non-superposed states.

[0274] (10) In the information processing system described in any one of (1) to (9) above, the first quantum gate operation is configured to act on a computation quantum bit including the first quantum bit and the second quantum bit so that the computation quantum bit assumes an eigenstate of a predetermined initial Hamiltonian, and the second quantum gate operation is a gate operation corresponding to a virtual Hamiltonian that evolves approximately adiabatically over time from the initial Hamiltonian to the interaction using at least one real-time evolution operator.

[0275] This configuration simplifies the quantum circuit when identifying the optimal placement, particularly in a non-degenerate system, making it easier to identify the optimal placement in a non-degenerate system.

[0276] (11) In the information processing system described in (10) above, the parameter determination step further comprises generating a virtual state by applying the virtual Hamiltonian, which includes the time width of the time evolution as a parameter, to a superposition state of the first quantum bit state, and determining the parameter by minimizing the energy expectation value of the virtual state with respect to the final state of the virtual Hamiltonian due to time evolution.

[0277] Such a configuration makes it easier to obtain calculation results with the desired accuracy in a short time.

[0278] (12) In the information processing system described in any one of (1) to (11) above, the identifying step performs a process of identifying, from among the candidate arrangements of the atomic nuclei, an arrangement having a relatively low energy eigenvalue at a predetermined level, instead of the lowest energy eigenvalue, based on an observation result for the first quantum bit in the generated correlated quantum bit state.

[0279] Such a configuration makes it easier to identify various atomic nucleus configurations such as metastable structures.

[0280] (13) An information processing system, comprising at least one processor capable of executing a program to perform the following steps: an acquisition step performs processing to acquire substance information about a substance including at least one particle, wherein the substance information includes a plurality of particle configuration candidates and interactions acting on the particle, and the interactions include at least inter-particle interactions acting between the particles; and an assignment step assigns each of the acquired particle configuration candidates to one of at least one first quantum bit state, wherein the first quantum bit state is constituted by at least one first quantum bit, and an observation of the first quantum bit is performed. The superposition step involves performing a predetermined first quantum gate operation on the first quantum bit to generate a superposition state of a plurality of the first quantum bit states, while the interaction step involves performing a second quantum gate operation including the obtained interaction on the first quantum bit representing the superposition state to generate a correlated quantum bit state in which the first quantum bits are correlated with each other, and the identification step involves performing a process of identifying a configuration with a relatively low energy from among candidate configurations of the particle based on the observation results of the first quantum bit in the generated correlated quantum bit state.

[0281] According to this configuration, multiple particle configuration candidates are represented by the first quantum bit. At this time, the first quantum bit can represent a superposition state of the multiple particle configuration candidates by the first quantum gate operation. At this time, the observation probability of the particle configuration represented by the first quantum bit is higher the lower the overall energy of the system represented by the first quantum bit. Therefore, by performing a second quantum gate operation that relatively lowers the energy, particle configurations with relatively low overall system energy are more likely to be observed by the first quantum bit. Therefore, a configuration with relatively low energy is identified among the particle configurations. Therefore, calculations can be performed more efficiently than when calculating the energy individually for each of the multiple particle configuration candidates.

[0282] (14) An information processing system comprising at least one processor capable of executing a program to perform the following steps: in an acquisition step, position information regarding L placement candidates in a space and classification information regarding k types of classification of N particles to be placed in the placement candidates are acquired; in a basis generation step, a computational basis represented by at least k × L computational quantum bits is generated based on the acquired position information, wherein the computational quantum bits include at least L positional quantum bits corresponding to each of the placement candidates set for each of the k types of classification, and thereby the computational basis is configured to be able to express in which of the placement candidates the particles are placed for each of the classifications.

[0283] Such a configuration can reduce the number of computational qubits required to represent the states of multiple particles.

[0284] (15) In the information processing system described in (14) above, the acquisition step further acquires information regarding interactions between the particles to be placed in the placement candidates and information regarding the number of the particles for each classification, wherein the interactions are determined by at least the positional relationships between the particles and the classification of the particles; and the generation step generates an objective function based on the computational basis and the interactions, wherein the objective function includes a first factor and a second factor, wherein the first factor corresponds to a Hamiltonian of a system consisting of the particles, and the second factor is configured to output a larger value when a first number representing the number of particles of a certain classification represented by the computational quantum bit is different from a second number representing the acquired number of particles, compared to when the first number is equal to the second number.

[0285] With this configuration, when estimating the optimal particle arrangement in a system consisting of particles, it is possible to reduce the possibility that a calculation basis in which the number of particles differs from that of the assumed system will be calculated as the optimal arrangement.

[0286] (16) In the information processing system described in (15) above, the second factor is expressed by an even function of the difference between the first number and the second number.

[0287] According to this configuration, the cases where the number of particles is smaller than the assumed system and the cases where the number of particles is larger than the assumed system can be treated equally, so that bias in calculations can be suppressed.

[0288] (17) In the information processing system described in (15) or (16) above, the objective function is expressed in an Ising function or QUBO format.

[0289] With this configuration, it becomes possible to perform quantum computation using a quantum annealing machine.

[0290] (18) In the information processing system described in any one of (15) to (17) above, the superposition step performs a process of generating a first superposition state in which states corresponding to the computational basis are superposed by performing a first quantum operation on the computational quantum bit; the interaction step performs a process of generating a second superposition state in which at least the interaction acting between the particles is reflected in the first superposition state by performing a second quantum operation corresponding to the objective function on the first superposition state; and the identification step performs a process of identifying a configuration with relatively low energy among candidate configurations of the particles based on observation results for the computational quantum bit in the generated second superposition state.

[0291] According to this configuration, calculations can be performed more efficiently than when energy is calculated individually for each of a plurality of particle configuration candidates.

[0292] (19) In the information processing system described in any one of (14) to (18) above, the particles are atomic nuclei that constitute a substance.

[0293] Such a configuration makes it possible to easily simulate the substance.

[0294] (20) In the information processing system according to any one of (14) to (19) above, the particles are classical point particles.

[0295] With this configuration, the number of computational quantum bits required for calculation can be reduced compared to when a particle image extending in quantum space is used.

[0296] (21) In the information processing system according to any one of (14) to (20) above, the classification includes the atomic species of the particles.

[0297] With this configuration, the candidate arrangements for each atomic species can be represented by at least L positional qubits, making it possible to suppress an increase in the number of computational qubits due to an increase in the number of particles.

[0298] (22) In the information processing system described in any one of (14) to (21) above, in the basis generation step, a computational basis consisting of n×k×L computational quantum bits is generated, where n is an integer greater than or equal to 2, and the computational basis is thereby further configured to be able to express a case where multiple particles exist in the same candidate arrangement.

[0299] This configuration makes it easier to identify the optimal particle arrangement in a wider variety of systems.

[0300] (23) An information processing system comprising at least one processor capable of executing a program to perform the following steps: in an acquisition step, state information regarding L state candidates in a state space and classification information regarding k types of classification of N particles are acquired, wherein each of the particles takes one of the state candidates; in a basis generation step, a computational basis represented by at least k×L computational quantum bits is generated based on the acquired state information, wherein the computational quantum bits include at least L positional quantum bits corresponding to each of the state candidates set for each of the k types of classification, thereby configuring the computational basis to be able to express, for each of the classifications, which state of which state candidate the particle takes.

[0301] Such a configuration can reduce the number of computational qubits required to represent the states of multiple particles.

[0302] (24) An information processing system comprising at least one processor capable of executing a program to perform the following steps: an acquisition step acquires information about a plurality of specific positions, which are positions in a space where a particle can be placed; and an allocation step assigns a group of computational qubits including at least one computational qubit to each of the specific positions, wherein the group of computational qubits is configured to have at least a first state and a second state that are observable, the first state indicating that the particle is present at the corresponding specific position, and the second state indicating that the particle is not present at the corresponding specific position.

[0303] According to this configuration, the state of a particle present at a specific position is expressed as the state of a computational quantum bit, thereby improving the interpretability of quantum computation.

[0304] (25) In the information processing system described in (24) above, the acquisition step further acquires classification information representing a classification of the particles, and the allocation step further assigns at least one of the computational quantum bits to each of the specific positions for each classification of the particles.

[0305] With this configuration, it is possible to represent the state of a complex system in which particles of multiple classifications coexist with a smaller number of computational quantum bits.

[0306] (26) In the information processing system described in (25) above, the classification of the particles includes at least the atomic species of the particles.

[0307] With this configuration, the state of a complex system in which multiple atomic species coexist can be expressed with a smaller number of computational quantum bits.

[0308] (27) In the information processing system described in any one of (24) to (26) above, the group of computational quantum bits includes two or more computational quantum bits, and at least one quantum bit state different from the first state and the second state is configured to be observable, and each of the quantum bit states is associated with the number of particles present at the corresponding specific position.

[0309] With this configuration, it is possible to assign a state in which multiple particles exist at the same specific position, such as in a boson system, to the state of a computational quantum bit, thereby improving the interpretability of quantum computation for a wider variety of systems.

[0310] (28) An information processing method, comprising the steps of the information processing system described in any one of (1) to (27) above.

[0311] (29) An information processing program that causes at least one computer to execute each step of the information processing system described in any one of (1) to (27) above. Of course, this is not a limitation.

[0312] Finally, while various embodiments of the present invention have been described, these are presented by way of example only and are not intended to limit the scope of the invention. The novel embodiments may be embodied in various other forms, and various omissions, substitutions, and modifications may be made without departing from the spirit of the invention. Such embodiments and modifications are intended to be included within the scope and spirit of the invention, as well as within the scope of the inventions and their equivalents as defined in the accompanying claims.

[0313] 1: Information processing system, 2: Information processing device, 3: Quantum computer, 4: User terminal, 5: Computational quantum circuit, 20: Communication bus, 21: Communication unit, 22: Memory unit, 23: Processor, 231: Acquisition unit, 232: Candidate generation unit, 233: Allocation unit, 234: Quantum operation unit, 235: Identification unit, 30: Communication bus, 31: Communication unit, 32: Quantum memory, 320: Quantum bit, 321: Computational quantum bit, 321n: First quantum bit, 321e: Second quantum bit, 322: Auxiliary bit, 323: Environmental bit, 33: Quantum processor, 40: Communication bus, 41: Communication unit, 42: Memory, 43: Processor, 44: Display unit, 45: Input unit, B1: Bar graph, C_PITE: Search quantum circuit, L1: Line graph, Q: Quantum amplitude amplifier circuit, QC1: Computation quantum circuit, QC10: Input generation circuit, QC11: First quantum gate operation, QC12: Reference quantum gate operation, QC13: Second quantum gate operation, QC131: Unit quantum circuit, QC14: Observation operation, S_0: Zero reflection, S_φ: Reflection operator, S_χ: Oracle, U_ME: State generation circuit, U_PITE: Quantum circuit, U_ref: Reference circuit

Claims

1. An information processing system, At least one processor capable of executing a program to perform the following steps: In the acquisition step, a process is performed to acquire material information related to a material including at least one atomic nucleus and at least one electron, where the substance information includes a plurality of candidates for the arrangement of the atomic nuclei and interactions acting on each of the atomic nuclei and the electrons; The interaction includes at least an electron-nuclear interaction acting between the nucleus and the electron, In the assignment step, a process is performed to assign each of the acquired candidates for the arrangement of the atomic nuclei to one of at least one first quantum bit state, where the first quantum bit state is a state that is constituted by at least one first quantum bit and is observable by an observation operation on the first quantum bit; In the superposition step, a process of generating a superposition state of a plurality of the first quantum bit states by performing a predetermined first quantum gate operation on the first quantum bit, In the interaction step, a second quantum gate operation including the obtained interaction is performed on the first quantum bit representing the superposition state and at least one second quantum bit representing an electronic state of the substance, thereby performing a process of generating a correlated quantum bit state in which the first quantum bit and the second quantum bit are correlated; The identification step involves performing a process of identifying a configuration having a relatively low minimum energy eigenvalue among candidate configurations of the atomic nuclei based on an observation result for the first quantum bit in the generated correlated quantum bit state.

2. 2. The information processing system according to claim 1, In the interaction step, a process is performed in which the second quantum gate operation is performed to generate a second quantum bit state representing an electronic state that can converge to a ground state in the arrangement of the atomic nuclei represented by the superposition state as a result of the interaction.

3. 2. The information processing system according to claim 1, Furthermore, in the electron configuration step, a reference quantum gate operation is performed on the quantum bit including the generated superposition state, thereby generating a superposition state of a reference electronic state for each candidate of the configuration of each of the atomic nuclei included in the superposition state; In the interaction step, a process of performing the second quantum gate operation on the quantum bit including the generated superposition state of the reference electronic state is performed.

4. 2. The information processing system according to claim 1, The second quantum gate operation is configured to perform a predetermined basis state computation method based on a first quantization format.

5. 2. The information processing system according to claim 1, The assigning step involves a process of assigning each of the candidate configurations of the atomic nuclei described as classical point charges to one of the first quantum bit states.

6. 2. The information processing system according to claim 1, the substance information includes information regarding reference positions of the nuclei; Furthermore, in the candidate generating step, a process is performed to generate candidates for the arrangement of a plurality of the atomic nuclei by adding a predetermined displacement to the acquired reference position.

7. 2. The information processing system according to claim 1, The interaction further includes an electron-electron interaction.

8. 2. The information processing system according to claim 1, The substance is composed of at least one molecular system.

9. 2. The information processing system according to claim 1, The first quantum gate operation includes at least a Hadamard gate operation.

10. 2. The information processing system according to claim 1, the first quantum gate operation is configured to act on a computation qubit including the first qubit and the second qubit such that the computation qubit assumes an eigenstate of a predetermined initial Hamiltonian; The second quantum gate operation is a gate operation corresponding to a virtual Hamiltonian that evolves approximately adiabatically in time from the initial Hamiltonian to the interaction using at least one real-time evolution operator.

11. 11. The information processing system according to claim 10, Furthermore, in the parameter determination step, a virtual state is generated by applying the virtual Hamiltonian including a time width of the time evolution as a parameter to a superposition state of the first quantum bit state; determining the parameters by minimizing an energy expectation value of the virtual state with respect to a final state of the virtual Hamiltonian through time evolution.

12. 2. The information processing system according to claim 1, The identifying step involves performing a process of identifying, from among the candidate configurations of the atomic nuclei, a configuration in which an energy eigenvalue of a predetermined level is relatively low, instead of the lowest energy eigenvalue, based on an observation result for the first quantum bit in the generated correlated quantum bit state.

13. An information processing system, At least one processor capable of executing a program to perform the following steps: The acquisition step includes a process of acquiring substance information related to a substance including at least one particle, the substance information includes a plurality of candidates for the particle arrangement and interactions acting on the particle; The interaction includes at least an inter-particle interaction acting between the particles, In the assignment step, each of the obtained particle configuration candidates is assigned to one of at least one first quantum bit state, where the first quantum bit state is a state that is configured by at least one first quantum bit and is observable by an observation operation on the first quantum bit; In the superposition step, a process of generating a superposition state of a plurality of the first quantum bit states by performing a predetermined first quantum gate operation on the first quantum bit, In the interaction step, a process is performed to generate a correlated quantum bit state in which the first quantum bits are correlated with each other by performing a second quantum gate operation including the obtained interaction on the first quantum bits representing the superposition state; The identification step involves performing a process of identifying a configuration having a relatively low energy among candidate configurations of the particles based on an observation result for the first quantum bit in the generated correlated quantum bit state.

14. An information processing system, At least one processor capable of executing a program to perform the following steps: In the acquisition step, information on a plurality of specific positions, which are positions where particles can be arranged in a certain space, is acquired; In the allocating step, a set of computation qubits including at least one computation qubit is allocated to each of the specific positions, where: The set of computation qubits is configured such that at least a first state and a second state are observable states; the first state indicates the presence of the particle at the corresponding particular location; the second state indicates that the particle is not present at the corresponding particular location; The acquiring step further acquires classification information representing a classification of the particles, The allocating step further comprises allocating at least one of the computational quantum bits to each of the specific positions for each of the particle classifications. thing.

15. In the information processing system according to claim 14, The classification of the particles includes at least the atomic species of the particles.

16. In the information processing system according to claim 14, The computation qubit group includes two or more computation qubits, and is configured to be capable of observing at least one qubit state different from the first state and the second state; Each of the quantum bit states corresponds to the number of particles present at the corresponding specific location.

17. 1. An information processing method, comprising: A method comprising the steps of the information processing system according to any one of claims 1 to 16.

18. An information processing program, A method for causing at least one computer to execute each step of the information processing system according to any one of claims 1 to 16.