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

Abstract

This invention provides an information processing system, information processing method, and information processing program for accurately and efficiently determining the arrangement of particles during simulations of materials. [Solution] The method involves an information processing device performing a process to acquire material information relating to a substance, assigning each of the acquired candidate nuclear arrangements to one of at least one first qubit states, performing a predetermined first quantum gate operation on the first qubit to generate a superposition state of multiple first qubit states, performing a process to generate a correlated qubit state in which there is a correlation between the first qubit and at least one second qubit representing the electronic state of the substance, and, based on the observation results for the first qubit in the generated correlated qubit state, identifying the arrangement among the candidate nuclear arrangements that has a relatively low lowest energy eigenvalue.

Description

Technical Field

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

Background Art

[0002] Patent Document 1 discloses a molecular dynamics simulation apparatus including: a coordinate information storage unit that stores information on nuclear coordinates and internal coordinates; a potential constant information storage unit that takes different values depending on the coordination state of each atom; a dynamic bond order evaluation unit that calculates the bond order between atoms based on the nuclear coordinates and internal coordinates; a coordination state determination unit that determines the coordination state of atoms based on the bond order; a potential energy calculation unit that calculates the total potential energy based on the nuclear coordinates, 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 performing first-order differential processing on the potential energy; a simulation unit that calculates the amount of movement in a specified short time based on the force applied to the internal degrees of freedom that determine the nuclear coordinates and the direction of the covalent bonds of each atom, updates the coordinate information, and repeatedly performs the bond order calculation, potential energy calculation, and differential calculation a specified number of times based on this, thereby performing a molecular dynamics calculation regarding the time evolution of the nuclear coordinates and internal degree-of-freedom variables; and an output unit that outputs the simulation result.

[0003] By applying the technology described in Patent Document 1, in a molecular dynamics simulation of a large-scale system handling thousands or more atoms, a structural change involving recombination of covalent bonds in a substance having a complex composition with multiple elements mixed therein is efficiently reproduced, while faithfully reproducing the structural energy change depending on the coordination state of each atom.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

[0005] Incidentally, when performing simulations on materials, the arrangement of the particles that make up the material is sometimes important. Therefore, it is desirable to determine the particle arrangement with high accuracy. However, when there are multiple candidate particle arrangements, it is necessary to perform dynamic simulations sequentially for each of the multiple candidate arrangements, which may increase the computation time. [Means for solving the problem]

[0006] According to one aspect of the present invention, an information processing system is provided. This information processing system comprises at least one processor capable of executing a program so as to perform the following steps: The acquisition step involves acquiring material information relating to a substance comprising at least one atomic nucleus and at least one electron. The material information includes a plurality of candidate atomic nucleus arrangements and interactions acting on the atomic nucleus and electron, respectively. The interactions include at least an electron-nucleus interaction acting between the atomic nucleus and the electron. The assignment step involves assigning each of the acquired candidate atomic nucleus arrangements to one of at least one first qubit state. The first qubit state is composed of at least one first qubit and is an observable state by an observation operation on the first qubit. The superposition step involves generating a superposition state of a plurality of first qubit states by performing a predetermined first quantum gate operation on the first qubit. In the interaction step, a second quantum gate operation, including the acquired interaction, is performed on a first qubit representing a superposition state and at least one second qubit representing the electronic state of the material, thereby generating a correlated qubit state in which there is a correlation between the first and second qubits. In the identification step, based on the observations of the first qubit in the generated correlated qubit state, a configuration with a relatively low lowest energy eigenvalue is identified among the candidate configurations of the atomic nucleus.

[0007] Such an information processing system can improve computational efficiency when identifying the appropriate particle arrangement from among multiple candidate arrangements. [Brief explanation of the drawing]

[0008] [Figure 1] This is a diagram showing the configuration of Information Processing System 1. [Figure 2] This is a block diagram showing the hardware configuration of the information processing device 2. [Figure 3] Block diagram showing the hardware configuration of quantum computer 3. [Figure 4] This is a block diagram showing the hardware configuration of user terminal 4. [Figure 5] This is a block diagram showing the functional configuration of processor 23. [Figure 6] This is an activity diagram showing an overview of the information processing performed in Information Processing System 1. [Figure 7] This figure shows an example of a computational quantum circuit (QC1). [Figure 8] This is a diagram illustrating an example of the first quantum gate operation QC11. [Figure 9] This is a diagram illustrating an example of the reference quantum gate operation QC12. [Figure 10] This is a diagram illustrating the computational quantum circuit QC1 based on the stochastic imaginary time evolution method. [Figure 11] This figure shows an example of how to express the contribution exp(-iVΔt) of the interaction V within the unit quantum circuit QC131. [Figure 12] This figure shows an example of a quantum circuit for implementing the real-time evolution operator exp(-iV_enΔt) in the case n_e=4 and n_nucl=3. [Figure 13] This figure shows an example of a search quantum circuit C_PITE for performing imaginary time evolution. [Figure 14] This figure shows an example of a quantum amplitude amplifier circuit Q in the imaginary time evolution method. [Figure 15] This figure shows the simulation results for the first step (i.e., the initial state). [Figure 16] This figure shows the simulation results for step 8. [Figure 17] This figure shows the simulation results for step 14. [Figure 18] This figure shows the simulation results of the weights of each candidate structure immediately after 19 steps have passed. [Figure 19] This is an activity diagram showing an overview of the information processing in this embodiment, which is performed in the information processing system 1. [Figure 20]This is an example of the computational quantum circuit QC1 for VQE. [Figure 21] The differential circuit QC2 for calculating the differential (-2i)·∂|φ(θ)> / ∂θ_k with respect to θ_k is shown. [Figure 22] This is a diagram showing the simulation results of the sum of the weights of the energy eigenstates in each nuclear configuration (Geom 0 to Geom 7). [Figure 23] This is a diagram showing the weights of the energy eigenstates of the ground state (1st lowest), the first excited state (2nd lowest), the second excited state (3rd lowest), and the total sum (Total) of the electron wave function in the optimal configuration (Geom 4). [Figure 24] This is a diagram showing an example of the unit quantum circuit QC131 for performing an information processing method on a qubit system considering only nuclear configurations. [Figure 25] This is a diagram showing an example of the second quantum gate operation QC13 for generating a Gibbs state to perform a finite temperature calculation. [Figure 26] This is a diagram showing an example of the maximum entanglement state generation circuit U_ME. [Figure 27] This is a flowchart showing the flow of the quantum circuit generation process in this embodiment. [Figure 28] This is a diagram showing an example of the input generation circuit QC10 in this embodiment. [Figure 29] This is a diagram showing an example of the quantum circuit representing the virtual Hamiltonian as the second quantum gate operation QC13. [Figure 30] This is a diagram showing an example of the computational quantum circuit QC1 in this embodiment. [Figure 31] This is a diagram showing the relationship between the observed probability of each candidate and the number of steps as a simulation result when the adiabatic time evolution method is adopted as the ground state search method. [Figure 32] This is a diagram showing the components included in the wave function in the final state. [Figure 33] This is a flowchart showing the flow of the fourth information processing. [Figure 34]This is a flowchart of the fifth information processing flow. [Modes for carrying out the invention]

[0009] Embodiments of the present invention will be described below with reference to the drawings. The various features shown in the embodiments below can be combined with each other.

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

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

[0012] Furthermore, a circuit in a broad sense is a circuit realized by combining at least a suitable combination of circuits, circuits, processors, and memory. In other words, it includes application-specific integrated circuits (ASICs), programmable logic devices (for example, simple programmable logic devices (SPLDs), complex programmable logic devices (CPLDs), and field programmable gate arrays (FPGAs)), etc.

[0013] 1. Hardware Configuration This section describes the hardware configuration of the information processing system 1 according to this embodiment. <Information Processing System 1> Figure 1 is a diagram showing the configuration of an information processing system 1. The information processing system 1 comprises 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 communicate with each other via a telecommunications line. In one embodiment, the information processing system 1 consists of one or more devices or components. For example, if it consists only of the information processing device 2, then the information processing system 1 can be the information processing device 2. These components will be described below.

[0014] <Information Processing Device 2> Figure 2 is a block diagram showing the hardware configuration of the information processing device 2. The information processing device 2 comprises a communication unit 21, a storage unit 22, and a processor 23, and these components are electrically connected within the information processing device 2 via a communication bus 20. Each component will be described in more detail.

[0015] <Communications Department 21> The communication unit 21 preferably uses wired communication methods such as USB, IEEE1394, Thunderbolt®, and wired LAN network communication, but may also include wireless LAN network communication, mobile communication such as 3G / LTE / 5G, and Bluetooth® communication as needed. In other words, it is more preferable to implement it as a collection of these multiple communication methods. That is, the information processing device 2 may communicate various information from the outside via the communication unit 21 and the network.

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

[0017] <Processor 23> The processor 23 performs processing and control of the overall operation 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 predetermined programs stored in the memory unit 22. That is, information processing by software stored in the memory unit 22 can be concretely realized by the processor 23, which is an example of hardware, and 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 a single unit, and may be implemented with multiple processors 23 for each function, or a combination thereof.

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

[0019] <Communications Department 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 both) or peripheral devices.

[0020] <Quantum Memory 32> The quantum memory 32 stores various types of information as 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 comprises a plurality of qubits 320. The qubits 320 can be implemented in any way, such as nuclear spins, photons, ions, atoms, quantum dots, or superconducting Josephson elements. The qubits 320 include a computational qubit 321 and auxiliary qubits 322. The computational qubit 321 includes at least one first qubit 321n and at least one second qubit 321e. The first qubit 321n functions as a qubit to represent the arrangement of atomic nuclei contained in a material. The second qubit 321e functions as a qubit to represent the electronic state of a material. In detail, the second qubit 321e functions, for example, as a qubit representing the arrangement of electrons contained in a material. The quantum memory 32 may include a classical memory device.

[0021] <Quantum Processor 33> The quantum processor 33 performs processing and control of the overall operation related to the quantum computer 3. The quantum processor 33 realizes various functions related to the quantum computer 3 by reading a program stored in the quantum memory 32 or a predetermined program input via the communication unit 31. In Figure 3, it is shown as a single quantum processor 33, but in reality, it is not limited to this, and it may be implemented with multiple quantum processors 33 for each function, or a combination thereof.

[0022] The quantum processor 33 is configured to perform various quantum operations on the qubit 320 that can be implemented on a quantum circuit. For example, the quantum circuit is configured to define a set of quantum operations on the qubit 320. These quantum operations include, for example, quantum gate operations and observation operations. Quantum gate operations correspond to unitary operations on the quantum state of the qubit 320. Observation operations correspond to projection operations on the quantum state of the qubit 320.

[0023] <User Terminal 4> Next, the hardware configuration of the user terminal 4 will be described. Figure 4 is a block diagram showing the hardware configuration of the user terminal 4. The user terminal 4 comprises 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 within the user terminal 4 via a communication bus 40. The explanation of the communication unit 41, memory 42, and processor 43 is the same as the explanation of each part in the information processing device 2, so it will be omitted.

[0024] <Display section 44> The display unit 44 may be included in the casing of the user terminal 4 or it may be an external component. The display unit 44 displays a graphical user interface (GUI) screen that can be operated by the user. This is preferably done by using different display devices such as a CRT display, liquid crystal display, organic EL display, and plasma display, depending on the type of user terminal 4.

[0025] <Input section 45> The input unit 45 may be included in the casing of the user terminal 4 or it may be an external component. For example, the input unit 45 may be integrated with the display unit 44 and implemented as a touch panel. If it is a touch panel, the user can input tap operations, swipe operations, etc. Of course, a switch button, mouse, QWERTY keyboard, etc. may be used instead of a touch panel. In other words, the input unit 45 receives operation input made by the user. This input is transmitted as a command signal to the processor 43 via the communication bus 40, and the processor 43 can perform predetermined controls and calculations as needed.

[0026] 2. Functional configuration of processor 23 This section describes the functional configuration of the processor 23 of the information processing device 2 according to this embodiment. Figure 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 a specification unit 235.

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

[0028] <Candidate generation unit 232> The candidate generation unit 232 generates various information related to quantum computation. For example, the candidate generation unit 232 generates candidate arrangements of atomic nuclei based on the information acquired by the acquisition unit 231.

[0029] <Allocation section 233> The assignment unit 233 is configured to be able to assign various types of information, such as candidate arrangements of atomic nuclei, to the state of the qubit 320.

[0030] <Quantum operation unit 234> The quantum operation unit 234 is configured to perform various quantum operations on the qubit 320. The quantum operation unit 234 may be configured to directly perform quantum operations on the qubit 320, or it may be configured to send commands to the quantum processor 33 to perform quantum operations. In this embodiment, the quantum operation unit 234 causes the quantum processor 33 to perform quantum operations by sending various quantum circuits to the quantum processor 33.

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

[0032] 3. Information processing methods This chapter describes the flow of information processing performed in the aforementioned information processing system 1. The information processing described in this chapter may be referred to as the first information processing.

[0033] 3.1. Information Processing Flow Figure 6 is an activity diagram showing an overview of the information processing performed in Information Processing System 1. Note that this information processing may include arbitrary exception handling not shown in the activity diagram. Exception handling includes interrupting the information processing or omitting individual processes. The selections or inputs performed in this information processing may be based on user operation or performed automatically without user operation.

[0034] In this information processing, the quantum processor 33 initializes the qubits 320 as needed. If a qubit 320 has two states, a ground state and an excited state, for example, the quantum processor 33 sets all qubits 320 to the ground state. For the sake of explanation, we may use bracket notation below, denoting the ground state of a single qubit 320 as |0> and the excited state as |1>.

[0035] This information processing method can be used, for example, to determine the optimal arrangement of atomic nuclei in any given substance. While the following explanation uses natural units, other unit systems such as the SI system and the CGS system can also be arbitrarily adopted.

[0036] [Activity A1] First, in Activity A1, the user terminal 4 transmits information about a substance to the processor 23. This information includes information that can identify the substance, such as the substance's name. This information may also include the substance information IF1 described later. This information may be entered by the user or automatically entered by the user terminal 4.

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

[0038] <Substance information IF1> Material information IF1 is information about a substance containing at least one atomic nucleus and at least one electron. Material information IF1 includes candidate arrangements of multiple atomic nuclei and interactions V acting on each of the atomic nuclei and electrons. Material information IF1 may also include the charge Z of each of the multiple atomic nuclei. In this embodiment, material information IF1 includes information about the reference position R_ν0 of the atomic nuclei. The acquisition unit 231 then acquires candidate arrangements of atomic nuclei, which are generated based on the reference position R_ν0 of the atomic nuclei by a candidate generation process described later.

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

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

[0041] The interaction V includes at least an electron-nucleus interaction V_en. In this embodiment, the interaction V further includes an electron-nucleus interaction V_ee and an internuclear 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 the sake of explanation, let's assume that the charge and position of the ν-th 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), where d is the distance between the paired particles. For example, in the case of Coulomb interaction, V(d) = 1 / d. Also, let's assume that each electron is subject to an external potential V_ext. This external potential V_ext is given by, for example, an electric field, a magnetic field, heat, or disturbances.

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

number

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

[0045] [Activity A3] Next, the process proceeds to activity A3, where the candidate generation unit 232 performs the acquired candidate generation process. This causes the candidate generation unit 232 to generate multiple candidate nucleus arrangements. For example, the candidate generation unit 232 generates multiple candidate nucleus arrangements by adding a predetermined displacement ΔR to the acquired reference position R_ν0. More specifically, the candidate generation unit 232 generates multiple candidate nucleus arrangements from the reference position R_ν0 by combining the displacement ΔR_ν (ν=0,1,..., n_nucl-1) of the ν-th nucleus from the reference position R_ν0. Subsequently, the acquisition unit 231 acquires the generated candidate nucleus arrangements.

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

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

number

[0048] This allows the nucleus position operator to represent discrete displacements from a reference position R_ν0. n_qn is the number of first qubits 321n used to generate candidate nucleus arrangements for one degree of freedom. n_qn first qubits 321n constitute a quantum state |j_νx>_n_qn, which is represented by the Kronecker product of 2^{n_qn} independent qubit states. Each of these independent quantum states is also called a computational basis. These computational bases become eigenstates of the position operator R_νx, as shown in equation 2. n_qn is a parameter that gives the resolution of the search and is not necessarily directly related to the actual size of the target molecule. Since the spatial degrees of freedom of the molecular system in this embodiment are 3, 3 × n_qn first qubits 321n are used to represent candidate nucleus arrangements in the molecular system. Therefore, the number of computational bases to represent the position of a single nucleus is 2^{3n_qn}.

[0049] For each of these computational bases, at least one of the obtained candidate nucleus arrangements is assigned through the process described below. Therefore, the state |j_ν>_3n_qn for each of these computational bases corresponds to the first qubit state. For the sake of explanation, the first qubit state corresponding to the Jth candidate nucleus arrangement may be denoted as |J>_{3n_{nucl}}_{n_qn} or simply |J>.

[0050] The Hamiltonian H shown in Equation 1 includes a set of nucleus position coordinates {R_ν} as a parameter. 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 nucleus position operator.

number

[0051] The above generalization also defines V_en~, E_nn~, and V_ext~ for the electron-nucleus interaction V_en, internuclear interaction energy E_nn, and external potential V_ext contained in the original Hamiltonian H, where the positions of the nuclei contained in each are replaced as operators. For the sake of explanation, the tilde symbols (~) in V_en~, E_nn~, and V_ext~ may be omitted below.

[0052] [Activity A4] Next, the process proceeds to activity A4, in which the assignment unit 233 performs the assignment process. In this process, the assignment unit 233 assigns each of the acquired candidate nuclear arrangements to one of at least one first qubit state |J> (i.e., a computational basis). The first qubit state consists of at least one first qubit 321n and is an observable state by an observation operation on the first qubit. In this embodiment, the assignment unit 233 assigns each of the candidate nuclear arrangements, described as classical point charges, to one of at least one first qubit state. In this embodiment, the assignment unit 233 assigns one candidate nuclear arrangement to each of a plurality of computational basis states. The first qubit 321n functions as a computational qubit 321 representing the nuclear arrangement. The processing of activity A4 corresponds to the processing including the assignment 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 Hamiltonian H described above, and generates a computational quantum circuit QC1 that defines a series of quantum operations to be performed on the qubit 320. The computational quantum circuit QC1 in this embodiment is generated as a command to cause the quantum computer 3 to perform the quantum operations.

[0054] <Computational quantum circuit QC1> Here, we will describe an example of a computational quantum circuit QC1. Figure 7 shows an example of a computational quantum circuit QC1.

[0055] Computational quantum circuit QC1 defines a series of quantum operations for optimizing the structure of a target system (in other words, matter). Specifically, it consists of gate operations and measurements on a first qubit 321n representing the nuclear arrangement and a second qubit 321e representing the multi-electron wave function. More specifically, 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 detail, 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 qubit 321n and the second qubit 321e, and then perform the observation operation QC14 on the first qubit 321n. In Figures 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 the reference circuit U_ref.

[0056] <First quantum gate operation QC11> Figure 8 is a diagram illustrating an example of a first quantum gate operation QC11. By acting on the first qubit 321n, it generates a superposition state of multiple first qubit states. In this embodiment, the first quantum gate operation QC11, by acting on an initialized first qubit 321n, generates a superposition state of first qubit states |J>, each candidate for optimal nuclear arrangement assigned an appropriate estimated weight w_{guess,J}. The process of generating such a first quantum gate operation QC11 corresponds to the superposition step in this embodiment. The estimated weight w_{guess,J} may be set equally for all J as equal weights, or it 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 superposition step, which is a process of generating a superposition state of multiple first qubit states |J> by performing a predetermined first quantum gate operation QC11 on the first qubit 321n. 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> Figure 9 is a diagram illustrating an example of a reference quantum gate operation QC12. The reference quantum gate operation QC12 is performed on a qubit 320 that includes a generated superposition state. A superposition state of the reference electron state is generated for each candidate arrangement of atomic nuclei included in the superposition state. In this embodiment, the reference quantum gate operation QC12 is performed on the superposition state of multiple first qubit states |J> produced by the first quantum gate operation QC11 and the quantum state of the second qubit 321e that represents the electronic state of the material. Through this, the appropriate reference electron state associated with each candidate arrangement of atomic nuclei is generated via the reference quantum gate operation QC12. The process of generating such a reference quantum gate operation QC12 is an example of the electron arrangement step in 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 the electron arrangement step.

[0058] <Second quantum gate operation QC13> The second quantum gate operation QC13 involves an acquired interaction V with a first qubit representing a superposition state and a second qubit 321e. More specifically, the second quantum gate operation QC13 corresponds to a Hamiltonian H (in this embodiment, a generalized Hamiltonian H~) including the acquired interaction V. In this embodiment, the second quantum gate operation QC13 is performed on a qubit that includes a superposition state of a reference electronic state generated through the reference quantum gate operation QC12. More specifically, the second quantum gate operation QC13 generates a second qubit state that, as a result of the interaction, represents an electronic state that can converge to the ground state in the nuclear arrangement represented by the superposition state. The second quantum gate operation QC13 is also configured to search for the combination of nuclear displacements ΔR_ν(opt) that results in the lowest ground state energy based on the generalized Hamiltonian H shown in Equation 3. This generates a correlated qubit state in which the first qubit 321n and the second qubit 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 reduce the energy of matter in a quantum state represented by the first qubit 321n and the second qubit 321e. For example, the second quantum gate operation QC13 is configured to execute a predetermined ground state calculation method based on the first quantization form. The specific form of the ground state calculation method may be the variational eigenvalue solver (VQE), or any other method such as cubitization. In this embodiment, the stochastic imaginary time evolution method is adopted as the ground state calculation method. The process of reducing energy by the second quantum gate operation QC13 can also be called an energy minimization process. This energy minimization process includes at least one quantum gate operation. In this embodiment, in order to use the stochastic imaginary time evolution method, the energy minimization process includes an observation operation of auxiliary bit 322. A method for implementing such a ground state calculation method as a quantum circuit will be described later.

[0060] <Observation Operation QC14> As shown in Figure 7, the observation operation QC14 is an operation that observes multiple first qubits 321n. This projects the multiple first qubits 321n onto one of several first qubit states (i.e., computational ground states) to which candidate nuclear arrangements are assigned. The observation operation QC14 is also called a projection operation. At this time, the probability of observing a particular first qubit state increases as the energy of the ground state corresponding to the Hamiltonian H~ decreases. Therefore, among the superposition states of multiple first qubit states included in the correlated qubit state, the first qubit state with the lowest ground state energy is observed most frequently. In other words, the nuclear arrangement assigned to the first qubit state that is observed relatively frequently via the correlated qubit state is suggested to be the arrangement with the relatively low ground state energy among the candidate nuclear arrangements. A ground state search is performed through such observation operations.

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

number

[0062] K is a notation that combines 3n_e integers (each value being between 0 and 2^n_qe) that specify the positional eigenstates of a multi-electron system. Similarly, J is a notation that combines 3n_nucl integers (each value being between 0 and 2^n_qn).

[0063] The normalization conditions are given by equation 5.

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[0064] The weight w_J of the configuration state of the Jth atomic nucleus is given by equation 6. For the sake of explanation, the configuration of the Jth atomic nucleus will sometimes simply be referred to as nuclear configuration J.

number

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

number

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

number

[0067] Number 4 can be written as shown in number 9 using number 8.

number

[0068] For a multi-qubit state |Ψ> in equation 9, the probability distribution of the nuclear configuration J obtained by measuring 3nnuclear displacement qubits (i.e., the first qubit 321n) is found to be the same as the weight w_J of the nuclear configuration J. Therefore, when a sufficient number of steps are taken to search for the ground state (in this embodiment, stochastic imaginary time evolution or VQE), the J(opt) that gives the maximum value of the distribution of w_J for the resulting multi-qubit state |Ψ> corresponds to the optimal nuclear configuration ΔR_νμ (ν=0,1,...,nnuclear-1,μ=x,y,z).

[0069] In this way, the processor 23 generates a computational quantum circuit QC1 to identify the optimal nuclear arrangement based on the acquired information.

[0070] [Activity A6] As shown in Figure 6, the process then proceeds to activity A6, where processor 23 sends the generated computational quantum circuit QC1 to quantum computer 3. The quantum processor 33 then acquires the computational quantum circuit QC1.

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

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

[0073] The information processing system 1 repeats the processing of activities A7 and A8 until predetermined termination conditions are met. As a result, the calculation results from the quantum computer 3 are stored in the information processing device 2. The termination conditions can be arbitrarily set, such as whether the number of repeating steps has reached a predetermined value or whether the user has performed a termination operation. Furthermore, the acquisition unit 231 constructs a computational quantum circuit QC1 with predetermined parameters updated based on the "observation results transmitted by the quantum processor 33" and transmits it to the quantum processor 33. This enables the execution of calculations with higher accuracy.

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

[0075] [Activity A10] Next, the process proceeds to activity A10, where the identification unit 235 performs a process to identify a relatively low-energy configuration among the candidate nucleus configurations based on the observation results for the first qubit 321n in the generated correlated qubit state. Specifically, based on the observation results, the identification unit 235 identifies the nucleus configuration that has the lowest ground-state energy eigenvalue among the candidate nucleus configurations. For example, the identification unit 235 identifies the candidate nucleus configuration assigned to the first qubit state with the highest observed frequency as a relatively low-energy configuration among the nucleus configurations (specifically, the nucleus configuration that has the lowest ground-state energy eigenvalue). The processing in activity A10 is an example of the identification step in this embodiment. Note that 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 the identification step.

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

[0077] 3.2. An example of the second quantum gate operation QC13 This chapter will explain the details of the second quantum gate operation QC13 generated in the information processing method described in the previous chapter, 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] Figure 10 is a diagram illustrating the 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, auxiliary bits 322 are also used to implement the stochastic imaginary time evolution method on the quantum circuit. In this embodiment, one auxiliary bit 322 is denoted 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 detail, the second quantum gate operation QC13 is configured to repeatedly act on the unit quantum circuit QC131 on the computational qubit 321 and the auxiliary bit 322 for 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 auxiliary bit 322. In detail, the unit quantum circuit QC131 is configured to perform the search quantum circuit C_PITE on the first qubit 321n and the second qubit 321e, and then perform the observation operation on auxiliary bit 322.

[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. For convenience of explanation in this chapter, 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) whose generator is Hamiltonian H. This configures the search quantum circuit C_PITE to be able to perform an imaginary time evolution method based on the first quantization form. Δt is the step size during real-time evolution.

[0082] FIG. 11 is a diagram showing an example of the expression of the contribution exp(−iVΔt) of the interaction V within the unit quantum circuit QC131. As shown in FIG. 11, among the real-time evolution operators exp(−iHΔt), the interaction part exp(−iVΔt) is expressed as exp(−i(V_ee + V_en + V_nn)Δt). The nuclear interaction V_nn acts only on the first qubit 321n, and the electron interaction V_ee acts only on the second qubit 321e. Therefore, these interaction parts are implemented as quantum gate operations acting only on the first qubit 321n and quantum gate operations acting only on the second qubit 321e, as in the right circuit of FIG. 6.

[0083] Since the number of combinations of two out of the electrons contained in the target molecule is proportional to n_e^2, the circuit implementation depth of exp(−iV_eeΔt) is O(n_e^2). Similarly, it can be seen that the circuit implementation depth of exp(−iV_nnΔt) is O(n_nucl^2). For almost all molecules targeted for practical calculations, n_nucl << n_e. Also, the circuit implementation of exp(−iV_eeΔt) is independent of the presence or absence of atomic nuclei. In view of these circumstances, the exp(−iV_enΔt) part 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) mainly comes from exp(−iV_eeΔt).

[0084] Next, we will explain the input-output correspondence for each 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. The implementation method for each gate is arbitrary, as long as it follows the correspondence below. For each gate, the functional form of the interaction V can be expressed as a polynomial using existing techniques such as Non-Patent Literature 1: PJ Ollitrault, G. Mazzola, and I. Tavernelli, "Nonadiabatic molecular quantum dynamics with quantum computers", Phys. Rev. Lett. 125, 260511 (2020). or Non-Patent Literature 2: G. Benenti and G. Strini, "Quantum simulation of the single-particle schroedinger equation", American Journal of Physics 76, 657 (2008), and this function system can be implemented in a circuit using phase gates.

[0085] The position eigenvalue of a single electron is denoted as r^(k_x,k_y,k_z) using three integers k_x, k_y, and k_z (each between 0 and 2^n_qe-1). The eigenstate corresponding to this position eigenvalue is denoted as |k_x,k_y,k_z>. The phase gate U_ee^(pair) acting on an electron pair is defined as shown in equation 10 using the second qubit 321e.

number

[0086] The real-time evolution operator exp(-iV_eeΔt), derived from the electron-electron interaction V_ee, can be written as shown 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) using n_e(n_e-1) / 2 U_ee^(pair) gates.

number

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

number

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

number

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

number

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

number

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

number

[0092] The real-time evolution operator exp(-iV_enΔt) can be implemented in a circuit with depth O(n_e^1 n_nucl^0) with respect to n_e and n_nucl by using equation 16. Figure 12 shows 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] A phase gate U_ext acting on a single electron is defined as shown in equation 17.

number

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

number

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

[0096] The above explanation describes a method of generating candidate structures by displacing all n_nuclei. If we optimize the positions of some of the n_nuclei (e.g., n_nucle' nuclei) and not the positions of the other n_nuclei-n_nuclei' nuclei (e.g., by fixing the positions of the other nuclei), the potentials resulting from the latter can be absorbed into the definition of the external potential v_ext. Thus, the above method can be applied to n_nucle' nuclei.

[0097] 3.3. An example of the search quantum circuit C_PITE Here, we will describe 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. Figure 13 is a diagram showing an example of the search quantum circuit C_PITE for performing imaginary time evolution. In Figure 13, the real time evolution operator exp(-iHΔt) is denoted as U_{RTE}. The search quantum circuit C_PITE is configured to sequentially perform Hadamard gate operations H and W gate operations on auxiliary bit 322, then use auxiliary bit 322 as the control bit to perform a controlled NOT gate operation, and then perform a rotation gate operation R_z(-2θ_0) and the Hermitian conjugate operation of the W gate on auxiliary bit 322. For the controlled NOT gate operation, auxiliary bit 322 is set as the control bit and computational qubit 321 is set as the target bit. The controlled NOT gate operation is configured such that, depending on the state of auxiliary bit 322, it is determined whether to apply a forward real-time evolution operator U_{RTE} or a retrograde real-time evolution operator U^†_{RTE} to the computational qubit 321. 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 act on a |ψ>*|0> state (where * represents the Kronecker product) consisting of the state |ψ> of computational qubit 321 and the state |0> of auxiliary bit 322. This allows for the probabilistic acquisition of states obtained by applying the imaginary time evolution operator exp(-HΔτ), which uses a general Hermitian operator H as a generator, to such a multi-qubit system. Such a quantum circuit C_PITE is configured to be polynomial expandable with respect to the time step Δτ as a parameter. Δτ is the step size of the imaginary time evolution method. The polynomial expansion may be limited to the first order of Δτ, or it may include higher-order terms of the second order or higher.

[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 within the search quantum circuit C_PITE.

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

number

[0101] The quantum circuit U_PITE is configured to operate on a multi-qubit state that includes a 321-system computational qubit and a 322-system auxiliary qubit. The quantum circuit U_PITE is configured to operate sequentially on the multi-qubit state with a reference circuit U_ref acting on it, and a quantum circuit C_PITE that implements the real-time evolution operator exp(-iκΘ) using the Hermitian operator Θ as a generator. In detail, the quantum circuit U_PITE can be expressed as shown in Equation 15 using the product of the reference circuit U_ref and the quantum circuit C_PITE.

number

[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 qubits, but does not change the states of the other qubits. The reflection operator S_φ for which the specific state |φ> is |0...0> is called zero reflection S_0.

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

[0104] 3.4.1 Simulation results for electronic molecular systems This section describes the simulation results when the above information processing method is applied to a one-electron molecular system. In this simulation, the material targeted for structural optimization is a molecular system consisting of a single electron and two atomic nuclei. Furthermore, in this simulation, the above information processing was performed on a classical computer using the quantum computation simulation procedure shown in Figure 6.

[0105] To simplify the problem setting, we assumed that space is one-dimensional. The numerical values ​​of the physical quantities that appear below are at the atomic level. We treated electrons as having a charge of -1 and both atomic nuclei as having a charge of +1. We fixed the position of one of the atomic nuclei and divided the distance from there to the other into eight divisions from 1.5 to 3. As the initial electronic state for each atomic nucleus configuration, we defined the initial electronic state as an electron wave function whose amplitude increases with increasing depth of the electrostatic potential due to the atomic nucleus. Such initial electronic states are represented as the second qubit state using the second qubit 321e.

[0106] As the ground state search method, we adopted stochastic imaginary time evolution.

[0107] Figure 15 shows the simulation results for the first step (i.e., the initial state). Figure 16 shows the simulation results for the eighth step. Figure 17 shows the simulation results for the fourteenth step.

[0108] The labels on the horizontal axis in Figures 15 to 17 (Geom 0 to Geom 7) indicate candidate arrangements of atomic nuclei.

[0109] In Figures 15 to 17, bar graphs B1 to B5 show the weights of each energy eigenstate from the ground state (1st lowest) to the 4th excited state (5th lowest), and bar graph B0 shows the sum (Total) of these energy eigenstate weights.

[0110] The line graph L1 in Figures 15-17 shows 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 eigenvalues ​​of the ground state and is the optimal nuclear configuration.

[0111] As shown in Figure 15, the first quantum gate operation QC11 in this simulation assigns equal weights to all candidate nucleus configurations in the initial state. Therefore, the weights of the energy eigenstates included in the initial electron wave function were all equal.

[0112] As shown in Figures 16 and 17, as the ground state search was repeated, the weight of the optimal configuration (i.e., the configuration of the nucleus that yields the lowest energy eigenvalue in the ground state) was the largest with each step, and the weight of the candidate configurations of the nucleus decreased as the deviation from the optimal configuration increased.

[0113] These results indicate that by observing the first qubit state after the ground state search, the probability of observing the optimal configuration (i.e., the configuration of the nuclei with the lowest energy eigenvalue in the ground state) among multiple candidate nucleus configurations is maximized. This result suggests that the optimal molecular structure corresponding to these internuclear distances, namely Geom 4 with the lowest ground state energy, can be obtained through observation of the first qubit state using the above information processing. Therefore, it has been shown that by employing this information processing method, the most stable nucleus configuration can be identified for the Hamiltonian H including the acquired interaction V.

[0114] 3.5. Simulation results for multi-electron molecular systems This section describes 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 electron-electron interactions into consideration. In this simulation as well, the quantum computation simulation performed using the information processing procedure shown in Figure 6 was executed on a classical computer.

[0115] The position of one of the atomic nuclei was fixed, and the distance from that point to the other was divided into eight segments. Each segment was assigned an equal weight to a corresponding candidate structure (Geom0 to Geom7), and the steps were advanced accordingly.

[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 eigenvalues ​​of the ground state and is the optimal nuclear configuration. Bar graph B1 in Figure 18 shows the weights of the energy eigenstates 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 4th excited state (5th lowest).

[0117] Among the multiple candidate arrangements of atomic nuclei, it can be seen that the probability of observing the optimal arrangement (Geom 2 in this case) is maximized. From this, it can be seen that this information processing also gives correct results when electron-electron interactions are present.

[0118] 4. Other examples of information processing methods

[0119] This chapter describes an example of information processing when the computational quantum circuit QC1 is updatable based on predetermined parameters. Specifically, it describes another example of information processing when the variational eigenvalue solver method (hereinafter referred to as VQE) is adopted as the ground state calculation method. Note that explanations of the information processing in this chapter that are common to the information processing in previous chapters may be omitted by assigning the same component number. 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 Figure 19 is an activity diagram showing an overview of the information processing in this embodiment, which is performed in the information processing system 1. Note that this information processing may include arbitrary exception handling not shown in the activity diagram. Exception handling includes interrupting the information processing or omitting individual processes. The selections or inputs performed in this information processing may be based on user operation or performed automatically without user operation.

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

[0122] Next, activities A6 to A8 are processed, and observation results are obtained through quantum computation based on the computational quantum circuit QC1 generated in activity A15. If the termination condition is not met, the process 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. As a result, the computational quantum circuit QC1 is regenerated appropriately to reflect the observation results, thereby increasing the likelihood that the observed state will reach the ground state.

[0124] On the other hand, if the termination conditions are met, activities A9 to A10 are performed to identify the optimal arrangement of atomic nuclei.

[0125] 4.2. An example of a computational quantum circuit QC1 in VQE This section describes 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.

[0126] <Welding state> Figure 20 shows an example of a computational quantum circuit QC1 for VQE. In this section, the computational quantum circuit QC1 for VQE will simply be referred to as the computational quantum circuit QC1. The computational quantum circuit QC1 consists of rotation gate operations (R_y and R_z gate operations) and a 2-qubit gate operation (controlled Z gate) characterized by N_p arbitrary real number parameters θ={θ_1,...,θ_N_p}. 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 qubits 321n. This results in a superposition of the first qubit states composed of the first qubits 321n. Therefore, the rotation gate operation on the computational qubit 321 includes the function of the first quantum gate operation QC11.

[0128] On the other hand, the computational quantum circuit QC1 is configured to perform a rotation gate operation on the second qubit 321e. The parameters of these rotation gate operations are explicitly or implicitly correlated with the state of the first qubit. Therefore, the rotation gate operation on the second qubit 321e includes the function of 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 of d units of a minimum unit (i.e., a unit quantum circuit QC131) configured to perform a rotation gate operation after a two-qubit gate operation. The two-qubit gate operation in this embodiment is a controlled Z gate operation. This controlled Z gate operation can represent the interaction between particles.

[0130] The computational quantum circuit QC1 for VQE shown in Figure 20 is just one example. Any quantum circuit can be used for the computational quantum circuit QC1 for VQE, as long as it is a quantum circuit constructed from parameterized gate operations. For example, the computational quantum circuit QC1 may be constructed based on physical considerations, such as a unitarily 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 to minimize the energy (or cost function). Here, the parameter update process is performed by the information processing device 2. In this chapter, the variational imaginary time evolution method is used as the 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 such as: 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, an imaginary time dependency is given to the parameters 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 by Equation 21 is solved.

number

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

number

number

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

[0134] Number 23 can be calculated from the sum of the results obtained by dividing the Hamiltonian H into a kinetic term T and a potential term V. First, let's discuss the potential term V. Since the potential term V can be represented by a diagonal matrix with respect to the computational basis, it can be calculated from the square of the absolute value of the coefficients obtained by repeatedly measuring each of the computational quantum circuit QC1 and the differential circuit QC2 with respect to the computational basis. Next, let's discuss the kinetic term T. The kinetic term T can be represented by a diagonal matrix in momentum space. Therefore, the processor 23 first transforms the wave function into momentum space by applying a quantum Fourier transform to 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 with respect to the computational basis for the kinetic term T. As a result, the acquisition unit 231 can obtain the square of the absolute value of the coefficients. From these squared absolute values, the processor 23 can calculate a number related to the kinetic term T.

[0135] Since the imaginary time derivative of the parameter can be obtained from equation 21, all that remains is to determine the parameter in the next step from equation 24, for example, by following Euler's method. Here, Δτ is the imaginary time step size.

number

[0136] In this chapter, variational imaginary time evolution was described as an optimization algorithm, but this is merely one example. Other optimization algorithms may also be used.

[0137] This section describes a method for calculating the ground state of the Hamiltonian H using a single computational quantum circuit QC1, but this is merely one example. The ground state may also be calculated as a post-processing step using the information processing device 2 from the calculation results obtained using multiple computational quantum circuits QC1.

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

[0139] Figure 22 shows the simulation results of the sum of the energy eigenstate weights for each nucleus configuration (Geom 0 to Geom 7). The horizontal axis of Figure 22 corresponds to the number of steps in the imaginary time evolution. The vertical axis of Figure 22 corresponds to the sum of the energy eigenstate weights. As shown in Figure 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] Figure 23 shows the weights of the ground state (1st lowest), first excited state (2nd lowest), second excited state (3rd lowest), and total energy eigenstates of the electron wave function in the optimal configuration (Geom 4). The horizontal axis of Figure 23 corresponds to the number of steps in imaginary time evolution. The vertical axis of Figure 23 corresponds to the weights of the energy eigenstates. In Figure 23, D0 shows the plot of the total, D1 shows the plot of the ground state (1st lowest), D2 shows the plot of the first excited state (2nd lowest), and D3 shows the plot of the second excited state (3rd lowest). As shown in Figure 23, it can be seen that as the number of steps in 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 ground state is amplified by the computational quantum circuit QC1 (particularly the second quantum gate operation QC13).

[0141] 5. Others The above-mentioned information processing system 1 may be further improved in the following ways.

[0142] The substance does not have to be a single molecule; it may be a system of multiple molecules, a metal containing metal atoms or ions, or a metal oxide, etc. Furthermore, the substance may be a single molecule or amorphous material without a periodic or quasi-periodic structure, or a polycrystalline or single crystal material with a periodic structure, or a combination of these. In other words, it is sufficient if the substance contains at least one atomic nucleus and at least one electron. Moreover, if we do not consider electron interactions, the substance is sufficient if it contains at least one atomic nucleus.

[0143] In detail, the above information processing method optimizes both the nuclear configuration and the multi-electron state in parallel, but it is also applicable to 3n_nucln_qn qubit systems that consider only the nuclear configuration. Figure 24 shows an example of a unit quantum circuit QC131 for performing the information processing method on a qubit system that considers only the nuclear configuration. The second quantum gate operation QC13 shown in Figure 24 is composed of the part of the second quantum gate operation QC13 shown in Figure 5 that does not relate to the second qubit 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 internuclear interaction V_nn needs to be implemented on the unit quantum circuit QC131. This makes it possible to perform 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, but any particle can be used. For example, if a substance is composed of multiple molecules, each molecule can be treated as a single particle, and after setting such interparticle interactions Vpp (e.g., hydrogen bonds, Coulomb bonds, van der Waals bonds, etc.), the above information processing method can be executed. In this case, the operator corresponding to energy is not limited to the Hamiltonian, but can be any operator corresponding to energy as appropriate depending on the system of interest, such as the Gibbs free energy.

[0145] In other words, the material information IF1 is information about a material containing at least one particle, and it is sufficient to include candidate arrangements of multiple particles and interactions acting on the particles. In this case, the interaction V is sufficient to include at least inter-particle interactions Vpp acting between particles. In this case, the acquisition unit 231 performs the process of acquiring the material information IF1, similar to the activity A2 described above. The assignment unit 233 assigns each of the acquired candidate particle arrangements to one of at least one first qubit states, similar to the activity A4 described above. The first qubit state is composed of at least one first qubit and is an observable state by an observation operation on the first qubit. The quantum operation unit 234 performs the process of generating a superposition state of multiple first qubit states by performing a predetermined first quantum gate operation QC11 on the first qubit 321n. The quantum operation unit 234 performs a second quantum gate operation QC13, which includes the acquired interaction V, on the first qubit 321n representing a superposition state, thereby generating a correlated qubit state in which the first qubits 321n are correlated. As a result, a computational quantum circuit QC1 is generated through a process similar to that of activity A5, and this computational quantum circuit QC1 is executed by the quantum processor 33. Then, the identification unit 235, similar to activity A10 described above, performs a process to identify a relatively low-energy arrangement among the candidate particle arrangements based on the observation results for the first qubit 321n in the generated correlated qubit state.

[0146] The number of particle types can be one type (atomic nucleus only), two types (atomic nucleus 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 considering their kinetic energy at all. However, it is similarly applicable when atomic nuclei are quantum mechanical particles. For example, the allocation unit 233 can represent the multi-nucleus wave function (separate from nuclear displacement) using 3n_{qn}n_{nucl} first qubits 321n, just as it represents the multi-electron wave function using 3n_{qe}n_{e} second qubits 321e. In this case, the motion part exp(-iTΔt) of the real-time evolution operator can include contributions from both electrons and nuclei. Both the motion part of the electrons and the motion part of the nuclei can be implemented on a quantum circuit by utilizing the quantum Fourier transform. In this way, the ground state of a purely quantum mechanical system consisting of electrons and nuclei can be obtained by 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 stochastic imaginary time evolution while treating both electrons and atomic nuclei as quantum mechanical particles. In this case, the energy obtained should be the electron state and atomic nucleus configuration that have the lowest free energy at a finite temperature.

[0149] The following describes in detail a variation of the information processing method for determining the arrangement of atomic nuclei at a finite temperature. Figure 25 shows an example of a second quantum gate operation QC13 that generates a Gibbs state for finite temperature calculations. In this variation, qubit 320 further includes environment bit 323. Environment bit 323 is used to represent the interaction with the environment, indicating that it is a finite temperature.

[0150] The multi-electron, multi-nucleus wavefunction is represented 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 (specifically the unit quantum circuit QC131) that generates the Gibbs state includes the search quantum circuit C_PITE, the observation operation of the auxiliary bit 322, and further includes the maximum entanglement state generator circuit U_ME. The maximum entanglement state generator circuit U_ME is configured to act on the computational qubits 321 representing the target system, such as a molecular system (i.e., the first qubit 321n and the second qubit 321e), and the environment bit 323. The computational qubits 321 representing the target system are denoted as "System," and the environment bit 323 is denoted as "Environment."

[0151] <Maximum Entanglement State Generation Circuit U_ME> Figure 26 shows an example of the maximum entanglement state generation circuit U_ME. The maximum entanglement state generation circuit U_ME is configured to apply an Hadamard gate H to the computational qubit 321 and auxiliary bit 322, and then apply a controlled NOT gate with the computational qubit 321 as the control bit and the environment bit 323 as the target bit. The search quantum circuit C_PITE for quantum mechanical systems consisting of electrons and atomic nuclei can be constructed 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 Boltzmann's constant and T is temperature), the n computational qubits 321 for the system of interest change to the Gibbs state exp(-H_en / (k_B T)) when the state of auxiliary qubit 322 is observed as |0>. H_en is the Hamiltonian of the system of interest. Furthermore, it is possible to derive a relationship between the probability of obtaining such an observation and the partition function Z of the system of interest. Therefore, Z can be calculated from the number of times |0> is obtained out of many measurements of auxiliary qubit 322. From this result and the well-known thermodynamic relation for free energy F, exp(-F / (k_B T))=Z, the free energy can be calculated. By comparing the free energies of the candidate configurations, the optimal nuclear configuration can be identified.

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

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

[0156] The above-described information processing system 1 may be implemented by a program that causes a computer to function as information processing system 1. This program may be available for download from a server, or it may be executed and distributed on a cloud computer, or it may be stored on a non-volatile or volatile storage medium and distributed in that manner.

[0157] In the above embodiment, the unit quantum circuit QC131 was implemented with the Hamiltonian H~ explicitly including the nuclear coordinate R_ν, but it can be similarly implemented even when the Hamiltonian H does not explicitly consider the presence of the atomic nucleus.

[0158] The processor 23 does not necessarily have to actually execute the quantum computation performed by the computational quantum circuit QC1 using the quantum computer 3. For example, the processor 23 may convert the quantum computation algorithm defined by the generated computational quantum circuit QC1 into a computation algorithm that can be executed by a classical computer, and then have the classical computer execute that computation algorithm. For example, the processor 23 may convert the quantum operation represented by the computational quantum circuit QC1 into a computation algorithm that can be executed by a classical computer by replacing it with a matrix calculation problem.

[0159] Some of the processing performed by processor 23 may be converted into a computation algorithm that can be executed by a quantum computer, and then the quantum computer 3 may be instructed to execute that computation algorithm.

[0160] Quantum computer 3 may also function as a quantum measuring device. For example, in this case, the computational quantum circuit 5 is represented by a unitary operation for initial state generation and free-time evolution.

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

[0162] The above-described information processing system 1 can be applied to various information processing related to quantum computing, such as quantum measurement and quantum communication.

[0163] The embodiments described above are not limited to the information processing system 1, but may also 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 and second information processing described above. For the sake of explanation, components or processes of the third information processing that are common to the first information processing may be omitted from the explanation below. The following processes can also be used as appropriate in the second information processing. The flow of the third information processing is the same as the flow of the first information processing shown in Figure 6. Therefore, the differences between the first and third information processing in each activity will be explained here. 6.1. Systems to which the third information processing method is applied First, let's describe the system to which the third information processing method applies. This system is defined, for example, by various pieces of information contained in material information IF1. Note that this is merely an example, and the third information processing method can be applied to any system.

[0165] In this embodiment, the system consists of a total of (N_{el} + N_{ion}) particles, each containing N_{el} electrons and N_{ion} atomic nuclei. For the sake of explanation, in this embodiment, the charge of each atomic nucleus is assumed to be equal. Therefore, in this embodiment, atomic 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, based on Equation 1 as follows.

number

[0166] However, N_{el} corresponds to n_{e} in equation 1. N_{ion} corresponds to n_{nucl} in equation 1. i and j are indices representing individual electrons in the system, and correspond to l and l' in equation 1. I and J are indices representing individual nuclei in the system, and correspond to ν and ν' 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 momentum energy term of the electron, and is denoted as T_{el} below. The second term represents the electron-electron interaction and is expressed by the interaction operator v_{ee}. Below, the second term is denoted as V_{ee}. The third term represents the electron-nucleus interaction and is expressed by the interaction operator v_{ej}. Below, the third term is denoted as V_{ei}. The fourth term represents the internuclear interaction and is expressed by the interaction operator v_{ii}. Below, the fourth term is denoted as V_{ii}. These interaction operators include the nuclear charge Z as a parameter as appropriate.

[0168] Note that the indices i, j, I, and J are attached to the momentum operator and position operator in the equation, 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 generation unit 232 generates candidate nucleus arrangements in a candidate generation process using the same method as the first information processing, and assigns these candidate arrangements to the first qubit 321n through an assignment process. The resulting qubit state can be expressed, for example, as follows.

number

[0170] |Ψ> represents the qubit state of the entire system, consisting of Nel electrons and Nion nuclei. |ψel({RI)> represents a partial qubit state (i.e., the second qubit state) consisting of Nel electrons. |{RI> represents a partial qubit state (i.e., the first qubit state) consisting of Nion nuclei. In this embodiment, for the sake of explanation, nion first qubits 321n are used to represent the states of Nion nuclei, and nel second qubits 321e are used to represent the states of Nel electrons. Thus, the first qubits 321n can represent 2^(nion) states of nuclei, and the second qubits 321e can represent 2^(nel) states of electrons.

[0171] 6.2. About the Quantum Circuit Generation Process Next, we will describe the quantum circuit generation process (Activity A5) performed in the third information processing step. Figure 27 is a flowchart showing the flow of the quantum circuit generation process in this embodiment.

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

number

[0173] Of the initial Hamiltonian H_{initial} described above, the operators T_{el} and J_x*I_{el} (* corresponds to the Kronecker product) that act on the electronic state (i.e., the second qubit 321e) represent the Hamiltonian of the electron in free space, and X_l that acts on the nucleus (i.e., the first qubit 321n) represents the X gate operation on the l-th first qubit 321n. I_{el} and I_{ion} are identity operators that act only on the electronic and nuclear portions of the computational qubit 321, respectively.

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

number

[0175] |Ψ_{init}> is also called the input state that is input to the second quantum gate operation QC13. |ψ_{init}> is the ground state of the Hamiltonian for the entire N_{el} electron system when interparticle interactions are ignored and only the kinetic energy T_{el} between electrons is considered. |+> is also an example of a state in which the |0> state and |1> state of each atomic nucleus constituting the system are superimposed. In this embodiment, |+> is a state in which the |0> state and |1> state of each atomic nucleus are superimposed with equal weights. The weights of each state when superimposing the |0> state and |1> state of each atomic nucleus are arbitrary. Hereafter, for the sake of explanation, the ground state of the initial Hamiltonian H_{initial} will be referred to as the initial ground state.

[0176] Next, in step S3, the processor 23 generates an 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, identifying the initial Hamiltonian H_{initial} and the input generation circuit QC10 corresponding to its ground state based on calculation results performed in the past.

[0177] Figure 28 shows an example of the input generation circuit QC10 in this embodiment. The input generation circuit QC10 is configured to perform an Adamard gate operation on each of the first qubit 321n and the second qubit 321e. |ψ_{init}> is obtained by performing an Adamard operation on each of the second qubits 321e in the |0> state. Similarly, the |+> state is obtained by performing an Adamard operation on each of the first qubits 321n in the |0> state. Therefore, by inputting the initial state |000...00> of the computation qubit 321 to the input generation circuit QC10, the input state |ψ_{init}> can be converted to the ground state of the initial Hamiltonian H_{initial}.

[0178] The input generation circuit QC10 is an example of the first quantum gate operation QC11 and also an example of the reference quantum gate operation QC12. For example, a series of Hadamard gate operations acting on the first qubit 321n in the input generation circuit QC10 corresponds to the first quantum gate operation QC11, which superimposes the states of the first qubit 321n. Furthermore, a series of Hadamard gate operations acting on the second qubit 321e can generate a superposition state of the reference electron states for each candidate arrangement of atomic nuclei included in the superposition state, and therefore this 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 computational qubit 321, which is in its initial state, the qubit of computational qubit 321 takes on an eigenstate (including the ground state) of the pre-set 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 321n and the second qubit 321e such that both the first qubit state and the second qubit state are eigenstates of the initial Hamiltonian H_{initial}.

[0180] The form of the initial Hamiltonian H_{initial} is not limited to this and can be arbitrary, but it is preferable that its ground state is analytically computable, 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] As shown in Figure 27, after the processing in step S3, the process proceeds to step S4, in which the processor 23 generates a second quantum gate operation QC13 based on the Hamiltonian of the acquired system (see number 26 above). The second quantum gate operation QC13 in this embodiment is constructed to define the adiabatic time evolution of the generated input state |Ψ_{init}>.

[0182] Subsequently, processor 23 sets up 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 the initial Hamiltonian H_{initial} to the final Hamiltonian H_{final} using at least one real-time evolution operator. The virtual Hamiltonian H(t) can be expressed, for example, by the following equation.

number

[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 internuclear 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 time-dependent parameters 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, with increasing t.

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

number

[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, with respect to the time evolution of the qubit state |Ψ>, using the time width Δt which represents the unit of that time evolution:

number

[0186] R_x^{*n_{ion}}(θ_k) (where * represents the Kronecker product) is a rotation gate operation that rotates each state of the first qubit 321n by a rotation angle θ_k around the x-axis. For the sake of explanation, the operator that represents the time evolution by the virtual Hamiltonian will be called the virtual time evolution operator. Note that the expressions for each interaction are not limited to those above. For example, by applying arbitrary mathematical transformations to the above expressions, such as sign inversion, constant multiplication, or addition / subtraction of constants to each coefficient A_i and parameter θ_k, it is possible to adopt expressions equivalent to the above expressions. The qubit state |Ψ(nΔt)> that has evolved n × Δt from the initial state |Ψ(0)> by such a virtual time evolution operator can be expressed, for example, in the range of a first-order Suzuki-Trotter expansion as follows.

number

[0187] Note that the expression in equation 32 may use, for example, a higher-order Suzuki-Trotter expansion, and is arbitrary as long as it represents the virtual time evolution exactly or approximately.

[0188] Figure 29 shows 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 according to an integer k (k=1,2,...) corresponding to the number of iterations, so the second quantum gate operation QC13 corresponding to k is sometimes denoted as QC13k. Each state of the first qubit 321n becomes a |+> state, taking a state in which each first qubit state is superimposed. As this second quantum gate operation QC13 is performed from k=n to k=1, the overall qubit state of the final computation qubit 321 reaches the final state |Ψ(nΔt)> represented by number 32.

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

[0190] Subsequently, 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. Figure 30 shows 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 the initialized first qubit 321n and second qubit 321e, respectively. As a result, the computational qubit 321 becomes the ground state of the initial Hamiltonian H_{initial} or a state close to it.

[0192] Furthermore, the computational quantum circuit QC1 is configured to perform a 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 a time width Δt, reaching the final state |Ψ(nΔt)>.

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

[0194] Furthermore, the system to which the third information processing is applied is not limited to systems containing multiple types of particles, such as atomic nuclei and electrons, but can also include systems containing only one type of particle, such as systems containing only atomic nuclei. For example, when the above third information processing is performed 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 that acts on the first qubit 321n, as in the input generation circuit QC10 in the system containing electrons. Also, the second quantum gate operation QC13 only needs to include U_{ii}^(k) and R_x^{*n_{ion}}(θ_k), as in the second quantum gate operation QC13 in the system containing electrons.

[0195] 6.3. Simulation results when the adiabatic time evolution method is adopted This section describes the simulation results when the adiabatic time evolution method is adopted as the ground state search method. In other words, this section explains the simulation results using the computational quantum circuit QC1 based on the third information processing method described above. It should be noted that these simulation results are merely one example to demonstrate the usefulness of this information processing method and do not limit the interpretation of the technical ideas related to the information processing described above.

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

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

Equation

[0198] However, x represents the coordinate corresponding to the position of the particle in a one-dimensional coordinate system with the midpoint of the two atomic nuclei as 0 and the direction towards each atomic nucleus as the x-axis.

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

[0200] Next, the allocation unit 233 allocates the generated candidates for the atomic nucleus arrangement to the qubit state of the first qubit 321n. In this embodiment, in order to represent four candidates for the atomic nucleus arrangement, two first qubits 321n are used. Specifically, the allocation unit 233 allocates candidates for the atomic nucleus arrangement to each of the first qubit states such that the arrangement with d = 2 indicates |00>, the arrangement with d = 4 indicates |01>, the arrangement with d = 6 indicates |10>, and the arrangement with d = 8 indicates |11>.

[0201] Next, the processor 23 performs a third information processing based on this information to generate a computational quantum circuit QC1. By having a classical computer simulate the calculations performed by the computational quantum circuit QC1 thus generated, the simulation results described below are obtained. In this embodiment, the total number of steps n is 10000, and the elapsed time t_f during the adiabatic time evolution from the starting state to the final state is Δt*10000.

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

[0203] As shown in Figure 31, the probability of observing d=2 increases with each step. Furthermore, as shown in Figure 32, the probability of observing d=2 in the final state is more than nine times higher than the probability of observing other states. This suggests that the nucleus configuration resulting in d=2 is the most stable structure.

[0204] Furthermore, when the ground state energy E_gs of each candidate was calculated using a conventional classical algorithm, the results were 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. Therefore, it was shown 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}. Hereafter, 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 the initial Hamiltonian H_{initial}. The details of step S11 are the same as in step S1.

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

[0208] Next, in step S13, the processor 23 sets a virtual state |Ψ_{QAOA}> based on the Hamiltonian H_{final} of the system (see Equation 25). The virtual state |Ψ_{QAOA}> is set based on the final state |Ψ(nΔt)>=|Ψ(t_f)> (see Equation 32) obtained when the virtual Hamiltonian H(t) described above 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}> is obtained by making the quantities related to the time width Δt contained in each component corresponding to each energy term of |Ψ(nΔt)> (for example, each component represented by Equation 31) unknown variables (parameterization). In this embodiment, the virtual state |Ψ_{QAOA}> is expressed as follows using the unknown variables α_k, β_k, γ_k, δ_k, θ_k.

number

[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 represents the rotation angle with the above x-axis as the axis of rotation. |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 unknown variable α_k, β_k, γ_k, δ_k, θ_k. This quantum circuit is defined by the operator that acts on the initial state |Ψ(0)> in the above equation 34. Here, multiple sets of each unknown variable {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. This energy expectation value E is expressed as follows:

number

[0212] H(t_f) is the time at which each coefficient A_i in the virtual Hamiltonian H(t) becomes 1. In other words, the above energy expectation value E is the energy expectation value of the virtual state for the final state of the virtual Hamiltonian due to time evolution.

[0213] Next, at step S16, the processor 23 identifies the unknown variables α_k, β_k, γ_k, δ_k, θ_k for which the above energy expectation value is minimized. Thereby, the processor 23, as a parameter determination unit, determines the parameters by minimizing the energy expectation value of the virtual state with respect to 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 reduces to identifying each unknown variable α_k, β_k, γ_k, δ_k, θ_k such that the above energy expectation value E is minimized. When the energy expectation value E for each set of multiple sets of unknown variables has been calculated, the processor 23 determines the change amount of the unknown variables α_k, β_k, γ_k, δ_k, 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, θ_k after calculating the change amount. When the change amount of the energy expectation value thereby becomes less than or equal to a predetermined error tolerance value, the virtual state |Ψ_{QAOA}> represented by the final set of unknown variables α_k, β_k, γ_k, δ_k, θ_k indicates the most stable state (the most stable structure) of the substance. By observing the state of the first qubit 321n among such virtual states |Ψ_{QAOA}>, the most stable nuclear arrangement can be obtained. Note that the identification of the most stable state may be calculated as an optimization problem by a classical computer or may be appropriately calculated using a quantum computer. Also, the method for minimizing the above energy expectation value E is arbitrary, and for example, various methods used for classical variational problems may be used.

[0214] Note that the initial Hamiltonian H_{initial} is not limited to the form represented 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 represented as follows.

Equation

[0215] Given such an initial Hamiltonian H_{initial}, the processor 23 should set a virtual Hamiltonian H(t) as follows:

number

[0216] Coefficients A_5 and A_6, like A_1, A_2, A_3, and A_4 above, are coefficients that represent the contribution of each energy.

[0217] In this case, |ψ_{init}>, expressed in equation 28, is the ground state of the Hamiltonian for the entire N_{el} electron system, considering the kinetic energy T_{el} between electrons and the initial Hamiltonian V_{init}.

[0218] Furthermore, the quantum circuit for generating |ψ_{init}> does not necessarily have to be defined to perform Hadamard gate operations on the first qubit 321n and the second qubit 321e, and the initial Hamiltonian H_{initial} can be appropriately determined according to the number of electrons in the system.

[0219] 7. Regarding the method of generating the computational basis This chapter describes another example of how to generate the computational basis assigned to the computational qubit 321 when performing each of the above information processing operations, along with the flow of the information processing. In this embodiment, the particles are atomic nuclei constituting matter and are classical point particles, but are not limited to these and may be any interacting particles such as electrons, quasiparticles, aggregates, etc. Hereinafter, for the sake 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 or second information processing (i.e., from obtaining material information IF1 to executing the assignment process).

[0220] 7.1. Regarding the fifth information processing flow This section describes the fifth information processing flow. Figure 34 is a flowchart of the fifth information processing flow.

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

[0222] The classification information is information for distinguishing different types of particles, and in this embodiment, it includes atomic species of particles that make up a substance, such as hydrogen atoms, oxygen atoms, and carbon atoms. However, the classification is not limited to this and may include classification by any state, such as the valence of an ion or isotope. For example, the classification may represent the types 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, but may also be information for distinguishing composite particles such as micelles. Classification information can also be said to be information that represents the classification of particles.

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

[0224] Next, in step S23, the assignment unit 233 assigns the state of the computational qubit 321 to each of the generated computational basis. This configures the computational basis so that it can represent, by type, which candidate arrangement the particle is placed in.

[0225] For example, if the classification is information that distinguishes four types of atomic species S, the qubit state |Ψ> of the computational qubit 321 can be expressed as follows using the qubit states |S_l> of the partial computational qubit 321 that correspond to the ground state of each atomic species S_l (l=1,2,3,4).

number

[0226] Each computational basis corresponds to the state of the L partial computational qubits 321 assigned to each atomic species S_l, where the state is either |0> or |1>. For example, the computational basis corresponding to the state where atomic species S_l is located at the m-th lattice point out of L lattice points is assigned to a qubit state such that the state of the m-th computational qubit 321 out of the L computational qubits 321 corresponding to atomic species S_l is |1>. In other words, the assignment unit 233 assigns at least one computational qubit to each specific position for each particle classification. With this configuration, the state of a complex system containing a mixture of particles of multiple classifications can be represented with fewer computational qubits 321.

[0227] The configuration of the computational basis is arbitrary and is not limited to being represented by at least k × L computational qubits 321. In other words, the allocation unit 233 assigns a group of computational qubits, each containing at least one computational qubit, to each specific location. The group of computational qubits is composed of computational qubits 321 and can represent at least two different states in total. In other words, the group of computational qubits is configured such that at least a first state and a second state are observable states. The first state indicates the presence of a particle at the corresponding specific location. The second state indicates the absence of a particle at the corresponding specific location. Below, we will describe the case where the group of computational qubits is composed of a single computational qubit 321. In this case, the first state corresponds, for example, to the qubit state of a certain computational qubit 321 being |1>, and the second state corresponds to the qubit state of the said computational qubit 321 being |0>. With such a configuration, the state of a particle present at a specific location is represented as the state of the computational qubit 321, thus improving the interpretability of the quantum computation.

[0228] In this embodiment, in the next step S24, the acquisition unit 231 further acquires information regarding the interactions between particles placed at candidate placements (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 at the i-th lattice point and a particle at the j-th lattice point can be expressed by J_{ij}. The origin of the interaction can be arbitrary, such as interatomic forces, Coulomb forces, weak forces, or strong forces. The interactions also include three-body or more interactions, such as empirical potentials.

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

number

[0230] However, S is a set of atomic species, for example, S={H,C,O,N}. J_{ij} is a constant representing the magnitude of the interaction, for example, the value of the interaction potential, with reference to distance and atomic species. k_1~k_N_{grid} are subscripts representing the qubits assigned to atom k. N_k is the number of atoms corresponding to classification k (i.e., the k-th atomic species). N_{grid} is the total number of candidate arrangements, equal to N_d^3. N_k may be manually entered by the user or estimated by the processor 23, etc., based on various measurement results for the material. P_k is a penalty factor for 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 by 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-hand side of the above equation is an example of the first factor, representing a two-body interaction. The second term on the right-hand side is an example of the second factor, where P_k is a positive constant.

[0231] Thus, it is preferable that the objective function H_{int} be expressed in the form of an Ising-type function or a QUBO (Quadratic Unconstrained Binary Optimization) function. Therefore, in this embodiment, in step S26, the processor 23 determines whether or not the objective function H_{int} is in the form of a QUBO function. The method of determination is arbitrary, but for example, it can be determined based on whether or not the Hamiltonian form contains terms of order three or higher.

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

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

[0234] Subsequently, the fifth information processing is completed, and the processor 23 generates a computational quantum circuit QC1 based on the set Hamiltonian and performs a computation using the quantum computer 3. The computational 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 described above. As a result, the quantum operation unit 234 performs a first quantum operation on the computational qubit 321 based on the computational quantum circuit QC1 to generate a first superposition state in which states corresponding to the computational basis are superimposed. This state can be implemented, for example, by an Hadamard gate operation that sets the individual qubit states of the first qubit 321n to the |+> 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 that reflects at least the interactions acting between particles on 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 to identify a relatively low-energy arrangement among the candidate particle arrangements based on the observation results for the computational qubit 321 in the generated second superposition state. The specific manner of this identification process is the same as that performed in the first information processing, etc.

[0237] According to the fifth information processing method described above, for example, the quantum circuit used to identify the optimal configuration in a non-degenerate system can be simplified. Therefore, it becomes easier to identify the optimal configuration in a non-degenerate system.

[0238] 7.2. Variations of Information Processing in Section 5 The fifth information processing method is not limited to those described above, and can be implemented by appropriately combining the following variations, for example.

[0239] In the fifth information processing described above, the processor 23 generated a computational basis represented by k × L computational qubits 321, but is not limited to this. For example, if n is an integer of 2 or more, the processor 23 may generate a computational basis consisting of n × k × L computational qubits, thereby configuring the computational basis to represent the case where multiple particles exist in the same candidate arrangement. In other words, the first qubit states may be configured so that states other than |0> and |1> are assigned to a single lattice point. For example, if three atoms can be placed in a single lattice point, the assignment unit 233 may assign two first qubits 321n to that lattice point. For example, the assignment unit 233 can assign the first qubit states to the ground states corresponding to each number of nuclei: |00> when the number of nuclei at the lattice point is 0, |01> when the number of nuclei at the lattice point is 1, |10> when the number of nuclei at the lattice point is 2, and |11> when the number of nuclei at the lattice point is 3. In other words, the computational qubit group includes 2 or more computational qubits 321, and is configured so that at least one qubit state different from the first and second states is observable. Each qubit state is associated with the number of particles present at a corresponding specific location. With this configuration, for example, in a boson system, the state in which multiple particles exist at the same specific location can be assigned to the state of a computational qubit, thereby improving the interpretability of quantum computations 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-field interactions can be expressed as an m-th degree expression in the binary variable x_i. Therefore, it may also be written in the form of HUBO (binary optimization without higher-order constraints) as follows.

number

[0241] The second factor is not limited to the form 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., but may be variable as in the following form.

number

[0242] This means that the value of the second factor increases when the ratio of the number of particles in classification k_1 to the number of particles in classification k_2 does not match C_{k_1} / C_{k_2}, so the ratio of the number of particles in each classification can be incorporated 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 factor to C_{k_1}=2 and C_{k_2}=1, where classification k_1 represents Si and classification k_2 represents O.

[0243] Furthermore, if the atomic species contains positive or negative ions, the processor 23 may set a penalty factor (second factor) representing the neutrality condition of the substance by obtaining information on the valency. This penalty factor can be expressed in the same form as number 41 above. For example, when determining the arrangement of atomic nuclei in sodium chloride NaCl, Na + Ion valence (+1) and Cl - The second factor should be set to C_{k_1}=C_{k_2}=1 so that it balances with the ion's valence (-1). Furthermore, if the aggregate of atomic nuclei is ionized (for example, a carboxylic acid in an aqueous solution), and the valence of the entire aggregate is Q, then the processor 23 should set the second factor to the following form.

number

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

[0245] The second factor may contain at least one of the forms described above, or it may contain multiple forms, for example. Such a second factor can be generalized using the following expression.

number

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

[0247] Furthermore, the target space is not limited to 3-dimensional real space, but may also be a space based on coordinates other than real space coordinates, such as spin space or wave number space. Also, the dimension of the target space is not limited to 3, but may be a lower-dimensional space such as 1 or 2, or a hyperspace of 4 dimensions or more. In other words, the target space is arbitrary as long as it is a space that can be mathematically described as a field, such as the presence or absence or state of particles. To put it another way, the fifth information processing described above is not limited to candidate particle arrangements (i.e., candidate position states), but can be applied to any candidate state. In short, the acquisition unit 231 acquires state information relating to L candidate states in a given state space, and classification information relating to k types of classifications of N particles. Each particle takes one of the candidate states. The processor 23, as a basis generation unit, generates a computational basis represented by at least k × L computational qubits based on the acquired state information. The computational qubit 321 includes at least L position qubits corresponding to each of the candidate states set for each of the k classifications, thereby configuring the computational basis to represent, for each classification, which of the candidate states a particle can take. For example, the state information indicates the candidate states that each of the N particles can take. More specifically, the state information indicates, for example, the coordinates in state space for the states that each of the N particles can take. The position information in the description of the fourth process above can be considered an example of the state information described above.

[0248] Furthermore, each of the above information processing methods can constitute a technical concept on its own. For example, the fifth information processing method can be used for any information processing that can be handled using quantum algorithms, other than processing for obtaining calculation results related to physical phenomena such as nuclear arrangement, such as calculation results for combinatorial optimization problems or the traveling salesman problem.

[0249] Some of the processing performed by processor 23 may be converted into a computation algorithm that can be executed by a quantum computer, and then the quantum computer 3 may be instructed to execute that computation algorithm.

[0250] Quantum computer 3 may also function as a quantum measuring device. For example, in this case, the computational quantum circuit 5 is represented by a unitary operation for initial state generation and free-time evolution.

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

[0252] The above-described information processing system 1 can be applied to various information processing related to quantum computing, such as quantum measurement and quantum communication.

[0253] The embodiments described above are not limited to the information processing system 1, but may also 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 preceding information processing methods and programs are not limited to those executed for ground state calculations. They may also be used to obtain low-energy states other than the ground state, under realistic information processing constraints such as computation time and hardware configuration. For example, if the preceding information processing of a system constituting a crystal as the ground state results in the output of a metastable amorphous structure, the preceding information processing methods and programs may be executed as a method to obtain the amorphous structure. In other words, the information processing system 1 may, in a specific step, perform a process to identify a configuration among candidate nuclear arrangements in which the energy eigenvalue of a predetermined level is relatively low, based on the observation result for the first qubit in the generated correlated qubit state, instead of the lowest energy eigenvalue. Such a configuration makes it easier to identify various nuclear arrangements, such as metastable structures.

[0255] The above-mentioned information processing system 1, etc., may be provided in any of the following embodiments.

[0256] (1) An information processing system comprising at least one processor capable of executing a program such that the following steps are performed, wherein the acquisition step is to perform a process to acquire material information relating to a substance comprising at least one atomic nucleus and at least one electron, wherein the material information comprises a plurality of candidate arrangements of the atomic nucleus and interactions acting on the atomic nucleus and the electron, respectively, wherein the interactions include at least an electron-nucleus interaction acting between the atomic nucleus and the electron, and the assignment step is to perform a process to assign each of the acquired candidate arrangements of the atomic nucleus to one of at least one first qubit states, wherein the first qubit state is composed of at least one first qubit, and by an observation operation on the first qubit The state is observable, and in the superposition step, a process is performed to generate a superposition state of multiple first qubit states by performing a predetermined first quantum gate operation on the first qubit, and in the interaction step, a process is performed to generate a correlated qubit state in which there is a correlation between the first qubit and the second qubit by performing a second quantum gate operation including the acquired interaction on the first qubit representing the superposition state and at least one second qubit representing the electronic state of the material, and in the identification step, a process is performed to identify the arrangement among the candidate arrangements of the atomic nucleus that has a relatively low lowest energy eigenvalue based on the observation result for the first qubit in the generated correlated qubit state.

[0257] In this configuration, multiple candidate nuclear arrangements are represented by the first qubit. Then, through a first quantum gate operation, the first qubit can represent a superposition state of the multiple candidate nuclear arrangements. The electronic state represented by the second qubit interacts with this superposition state through a second quantum gate operation, allowing the first and second qubits to represent the electronic state of each candidate nuclear arrangement under different environments. At this point, the observation probability of the nuclear arrangement represented by the first qubit is higher for states with lower overall system energy, represented by the first and second qubits. Therefore, through the second quantum gate operation, nuclear arrangements with relatively low overall system energy become more easily observable from the first qubit. Thus, relatively low-energy nuclear arrangements are identified. Here, by acting on the electronic state with respect to the superposition state of multiple candidate nuclear arrangements, a state similar to that generated by acting on the electronic state for each of the multiple nuclear arrangements individually can be produced. Therefore, the calculations can be performed more efficiently compared to performing calculations for each of the multiple candidate nuclear configurations.

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

[0259] With this configuration, as the electronic state converges to the ground state, the energy of the entire system containing that electronic state decreases. Therefore, it becomes easier to identify relatively lower-energy configurations among the arrangements of atomic nuclei.

[0260] (3) In the information processing system described in (1) or (2) above, the electron configuration step further involves performing a reference quantum gate operation on the qubit including the generated superposition state to generate a superposition state of reference electron states for each candidate arrangement of the atomic nuclei included in the superposition state, and the interaction step involves performing the second quantum gate operation on the qubit including the generated superposition state of reference electron states.

[0261] With this configuration, by setting an appropriate reference electronic state when realizing the energy state of matter through a second quantum gate operation, the computation time required to identify a lower energy configuration can be reduced.

[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 perform a predetermined ground state calculation method based on the first quantization form.

[0263] With this configuration, performing calculations based on the first quantization form makes it easier to obtain a more intuitively understandable picture of the nuclear arrangement compared to, for example, calculations based on the second quantization form, thus simplifying the interpretation of the calculation results.

[0264] (5) In an information processing system described in any one of (1) to (4) above, the assignment step involves assigning each of the candidate arrangements of the atomic nuclei, which are described as classical point charges, to one of the first qubit states.

[0265] This configuration allows for a reduction in the number of first qubits required to represent the arrangement of atomic nuclei compared to cases where the arrangement of atomic nuclei is described including quantum fluctuations.

[0266] (6) In an information processing system described in any one of (1) to (4) above, the material information includes information relating to the reference position of the atomic nuclei, and the candidate generation step further involves generating a plurality of candidate arrangements of the atomic nuclei by adding a predetermined displacement to the acquired reference position.

[0267] This configuration reduces the effort required to input each candidate arrangement of multiple atomic nuclei.

[0268] (7) In an information processing system described in any one of (1) to (6) above, the interaction further includes an electron-electron interaction.

[0269] In this configuration, electron-electron interactions contribute more to the overall energy of the system than electron-nucleus interactions. This results in a larger energy difference between the states generated by the second quantum gate operation, making it easier to identify the configuration of lower-energy nuclei.

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

[0271] This configuration reduces 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 described in any one of (1) to (8) above, the first quantum gate operation includes at least an Adamard gate operation.

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

[0274] (10) In an information processing system according to any one of (1) to (9) above, the first quantum gate operation is configured to act on the computational qubit, which includes the first qubit and the second qubit, such that the computational qubit takes on an eigenstate of a predetermined initial Hamiltonian, and the second quantum gate operation is a gate operation corresponding to a virtual Hamiltonian that evolves in time almost adiabatically from the initial Hamiltonian to the interaction using at least one real-time evolution operator.

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

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

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

[0278] (12) In the information processing system described in any one of (1) to (11) above, the specific step involves performing a process to identify, based on the observation result for the first qubit in the generated correlated qubit state, an arrangement among the candidate arrangements of the atomic nucleus in which the energy eigenvalue of a predetermined level is relatively low, instead of the lowest energy eigenvalue.

[0279] This configuration makes it easier to identify various nuclear arrangements, such as metastable structures.

[0280] (13) An information processing system comprising at least one processor capable of executing a program such that the following steps are performed, wherein the acquisition step is to perform a process to acquire material information relating to a substance comprising at least one particle, wherein the material information comprises a plurality of candidate arrangements of the particle and interactions acting on the particle, wherein the interactions include at least interparticle interactions acting between the particles, and the assignment step is to assign each of the acquired candidate arrangements of the particle to one of at least one first qubit state, wherein the first qubit state is composed of at least one first qubit and observation of the first qubit The operation is observable, and in the superposition step, a process is performed to generate a superposition state of multiple first qubit states by performing a predetermined first quantum gate operation on the first qubit, in the interaction step, a process is performed to generate correlated qubit states where the first qubits are correlated with each other by performing a second quantum gate operation including the acquired interaction on the first qubit representing the superposition state, and in the identification step, a process is performed to identify a relatively low-energy arrangement among the candidate arrangements of the particle based on the observation results for the first qubit in the generated correlated qubit state.

[0281] In this configuration, multiple candidate particle arrangements are represented by the first qubit. A first quantum gate operation allows the first qubit to represent a superposition state of these candidate particle arrangements. The observation probability of the particle arrangement represented by the first qubit is higher for states with lower overall system energy, as represented by the first qubit. Therefore, by performing a second quantum gate operation that relatively lowers the energy, particle arrangements with relatively low overall system energy become more easily observable from the first qubit. Thus, relatively low-energy arrangements among the particle arrangements are identified. Consequently, this method allows for more efficient calculations compared to individually calculating the energy for each of the multiple candidate particle arrangements.

[0282] (14) An information processing system comprising at least one processor capable of executing a program such that the following steps are performed: an acquisition step, which acquires positional information relating to L candidate arrangements in a given space and classification information relating to k types of classifications of N particles arranged in the candidate arrangements; and a basis generation step, which generates a computational basis represented by at least k × L computational qubits based on the acquired positional information, wherein the computational qubits include at least L positional qubits corresponding to each of the candidate arrangements, set for each of the k types of classifications, so that the computational basis can represent which candidate arrangement the particles are arranged in for each classification.

[0283] This configuration allows for a reduction in 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 the interaction between the particles arranged in the candidate arrangement and information regarding the number of particles for each classification, wherein the interaction is determined by at least the positional relationship between the particles and the classification of the particles, and the generation step further generates an objective function based on the computational basis and the interaction, wherein the objective function includes a first factor and a second factor, the first factor corresponding to the Hamiltonian of the system consisting of the particles, and the second factor is configured to output a larger value when the first number representing the number of particles of a certain classification represented by the computational qubit is different from the second number representing the number of particles acquired, compared to when the first number matches the second number.

[0285] With this configuration, when estimating the optimal arrangement of particles in a system of particles, the possibility that a computational basis with a different number of particles than that of the assumed system will be calculated as the optimal arrangement can be reduced.

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

[0287] This configuration allows us to treat cases where the number of particles is less than or more than the assumed system as equivalent, thereby suppressing computational bias.

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

[0289] This configuration makes it possible to perform quantum computations using a quantum annealing machine.

[0290] (18) In an information processing system described in any one of (15) to (17) above, the superposition step involves performing a first quantum operation on the computational qubit to generate a first superposition state in which the states corresponding to the computational basis are superimposed; the interaction step involves performing a second quantum operation on the first superposition state corresponding to the objective function to generate a second superposition state in which at least the interactions acting between the particles are reflected in the first superposition state; and the identification step involves identifying a relatively low-energy arrangement among the candidate arrangements of the particles based on the observation results on the computational qubit in the generated second superposition state.

[0291] This configuration allows for more efficient calculations compared to performing energy calculations individually for each of the multiple candidate particle configurations.

[0292] (19) In the information processing system described in any one of (14) to (18) above, the particle is an atomic nucleus that constitutes matter.

[0293] This configuration makes it easier to simulate materials.

[0294] (20) In the information processing system described in any one of (14) to (19) above, the particle is a classical point particle.

[0295] This configuration allows for a reduction in the number of computational qubits required compared to using a particle picture that extends into quantum space.

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

[0297] With this configuration, candidate arrangements for each atomic species can be represented by at least L position qubits, thus suppressing the 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, the basis generation step generates a computation basis consisting of n × k × L computation qubits, where n is an integer of 2 or more, and the computation basis is configured to further represent the case in which 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 such that the following steps are performed: an acquisition step, which acquires state information relating to L candidate states in a state space and classification information relating to k classifications of N particles, where each of the particles takes one of the candidate states; and a basis generation step, which generates a computation basis represented by at least k × L computation qubits based on the acquired state information, where the computation qubits include at least L position qubits corresponding to each of the candidate states, set for each of the k classifications, so that the computation basis can represent which state of which candidate state a particle takes for each classification.

[0301] This configuration allows for a reduction in 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 such that the following steps are performed: an acquisition step in which information is acquired about a plurality of specific locations which are locations in a space in which a particle can be placed; and an assignment step in which a group of computational qubits, each of which includes at least one computational qubit, is assigned to each of the specific locations, wherein the group of computational qubits is configured such that at least a first state and a second state are observable states, the first state indicating that the particle is present at the corresponding specific location, and the second state indicating that the particle is not present at the corresponding specific location.

[0303] With this configuration, the state of a particle at a specific location is represented as the state of a computational qubit, 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 the classification of the particles, and the assignment step further assigns at least one computational qubit to each of the specific positions for each classification of the particles.

[0305] This configuration allows for the representation of the state of a complex system containing a mixture of particles from multiple classifications using fewer computational qubits.

[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] This configuration allows for the representation of the state of a complex system containing multiple atomic species using fewer computational qubits.

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

[0309] With this configuration, for example, in a boson system, the state in which multiple particles exist at the same specific location can be assigned to the state of a computational qubit, thereby improving the interpretability of quantum computations for a wider variety of systems.

[0310] (28) An information processing method comprising each step of an 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 perform each step of the information processing system described in any one of (1) to (27) above. Of course, this is not always the case.

[0312] Finally, various embodiments of the present invention have been described, but these are presented as examples and are not intended to limit the scope of the invention. These novel embodiments can be implemented in a variety of other forms, and various omissions, substitutions, and modifications can be made without departing from the spirit of the invention. These embodiments and their variations are included in the scope and spirit of the invention, as well as in the claims and their equivalents. [Explanation of Symbols]

[0313] 1: Information Processing System 2: Information Processing Device 3:Quantum computer 4: User terminal 5: Computational quantum circuit 20: Communications bus 21: Communications Department 22: Storage section 23: Processor 231: Acquisition Department 232: Candidate generation section 233: Allocation section 234:Quantum operation section 235: Specific part 30: Communications bus 31: Communications Department 32: Quantum Memory 320: Quantum bit 321: Computational qubit 321n: First qubit 321e: Second qubit 322: Auxiliary bit 323: Environment bit 33: Quantum Processor 40: Communications bus 41: Communications Department 42: Memory 43: Processor 44: Display section 45: Input section B1: Bar graph C_PITE: Search quantum circuit L1: Line graph Q: Quantum amplitude amplifier circuit QC1: Computational 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, The system comprises at least one processor capable of executing a program so that each of the following steps is performed, In the acquisition step, a process is performed to acquire material information relating to a substance containing at least one atomic nucleus and at least one electron, where, The material information includes a plurality of candidate arrangements of the atomic nuclei and interactions acting on the atomic nuclei and electrons, respectively. The interaction includes at least an electron-nucleus interaction acting between the atomic nucleus and the electron, In the assignment step, each of the acquired candidate arrangements of the atomic nuclei is assigned to one of at least one first qubit states, where the first qubit state is composed of at least one first qubit and is an observable state by an observation operation on the first qubit. In the superposition step, a process is performed to generate a superposition state of multiple first qubit states by performing a predetermined first quantum gate operation on the first qubit. In the interaction step, a second quantum gate operation including the acquired interaction is performed on the first qubit representing the superposition state and at least one second qubit representing the electronic state of the material, thereby generating a correlated qubit state in which there is a correlation between the first qubit and the second qubit. In a specific step, based on the observation results for the first qubit in the generated correlated qubit state, a process is performed to identify the arrangement among the candidate arrangements of the atomic nucleus that has the lowest energy eigenvalue relatively low.

2. In the information processing system described in claim 1, The interaction step involves performing the second quantum gate operation to generate a second qubit state that, as a result of the interaction, represents an electronic state that can converge to the ground state in the arrangement of the atomic nuclei represented by the superposition state.

3. In the information processing system according to claim 1 or claim 2, Furthermore, in the electron configuration step, a process is performed to generate a superposition state of the reference electron states for each candidate arrangement of the atomic nuclei included in the superposition state by performing a reference quantum gate operation on the qubit including the generated superposition state. The interaction step involves performing the second quantum gate operation on the qubit, which includes the superposition state of the generated reference electron state.

4. In the information processing system according to any one of claims 1 to 3, The second quantum gate operation is configured to enable a predetermined ground state calculation method based on the first quantization form.

5. In the information processing system according to any one of claims 1 to 4, The assignment step involves assigning each of the candidate arrangements of the atomic nuclei, which are described as classical point charges, to one of the first qubit states.

6. In the information processing system according to any one of claims 1 to 4, The material information includes information relating to the reference position of the atomic nucleus, Furthermore, the candidate generation step involves generating a plurality of candidate arrangements of the atomic nuclei by applying a predetermined displacement to the acquired reference position.

7. In the information processing system according to any one of claims 1 to 6, The aforementioned interaction further includes electron-electron interactions.

8. In the information processing system according to any one of claims 1 to 7, The aforementioned substance is composed of at least one molecular system.

9. In the information processing system according to any one of claims 1 to 8, The first quantum gate operation includes at least an Hadamard gate operation.

10. In the information processing system according to any one of claims 1 to 9, The first quantum gate operation is configured to act on a computational qubit, including the first qubit and the second qubit, such that the computational qubit takes on an eigenstate of a predetermined initial Hamiltonian. The second quantum gate operation is a gate operation that corresponds to a virtual Hamiltonian that evolves almost adiabatically in time from the initial Hamiltonian to the interaction using at least one real-time evolution operator.

11. In the information processing system according to claim 10, Furthermore, in the parameter determination step, a virtual state is generated by applying the virtual Hamiltonian, which includes the time width of the time evolution as a parameter, to the superposition state of the first qubit state. The parameters are determined by minimizing the energy expectation value of the virtual state for the final state of the virtual Hamiltonian as it evolves over time.

12. In the information processing system according to any one of claims 1 to 11, In the aforementioned specific step, based on the observation results for the first qubit in the generated correlated qubit state, a process is performed to identify, among the candidate arrangements of the atomic nucleus, an arrangement in which the energy eigenvalue of a predetermined level is relatively low, instead of the lowest energy eigenvalue.

13. An information processing system, The system comprises at least one processor capable of executing a program so that each of the following steps is performed, In the acquisition step, a process is performed to acquire material information about a substance containing at least one particle, and here, The material information includes a plurality of candidate arrangements of the particles and interactions acting on the particles, The interaction includes at least interparticle interactions acting between the particles, In the assignment step, each of the acquired candidate particle arrangements is assigned to one of at least one first qubit state, where the first qubit state is composed of at least one first qubit and is observable by an observation operation on the first qubit. In the superposition step, a process is performed to generate a superposition state of multiple first qubit states by performing a predetermined first quantum gate operation on the first qubit. In the interaction step, a second quantum gate operation including the acquired interaction is performed on the first qubit representing the superposition state to generate correlated qubit states that are correlated between the first qubits. In a specific step, based on the observation results for the first qubit in the generated correlated qubit state, a process is performed to identify a relatively low-energy arrangement among the candidate arrangements of the particle.

14. An information processing system, The system comprises at least one processor capable of executing a program so that each of the following steps is performed, In the acquisition step, positional information relating to L candidate arrangements in a given space and classification information relating to k types of classifications of N particles to be placed in the candidate arrangements are acquired. In the basis generation step, a computational basis is generated based on the acquired positional information, which is represented by at least k × L computational qubits, where the computational qubits include at least L positional qubits corresponding to each of the candidate arrangements set for each of the k classifications, so that the computational basis is configured to represent which of the candidate arrangements the particle is placed in for each classification.

15. In the information processing system described in claim 14, In the acquisition step, further information is obtained regarding the interactions between the particles arranged in the candidate arrangement, and information regarding the number of particles for each classification, where the interactions are determined by at least the positional relationship between the particles and the classification of the particles. Furthermore, in the generation step, an objective function is generated based on the computational basis and the interaction, where, The aforementioned objective function includes a first factor and a second factor, The first factor corresponds to the Hamiltonian of the system consisting of the particles, The second factor is configured to output a larger value when the first number representing the number of particles of a certain classification represented by the computational qubit is different from the second number representing the number of particles obtained, compared to when the first number matches the second number.

16. In the information processing system described in claim 15, The second factor is expressed as an even function of the difference between the first number and the second number.

17. In the information processing system according to claim 15 or claim 16, The aforementioned objective function is expressed as an Ising-type function or in QUBO format.

18. In the information processing system according to any one of claims 15 to 17, In the superposition step, a first quantum operation is performed on the computational qubit to generate a first superposition state in which the states corresponding to the computational basis are superimposed. In the interaction step, a second quantum operation corresponding to the objective function is performed on the first superposition state to generate a second superposition state that reflects at least the interactions acting between the particles on the first superposition state. In a specific step, based on the observation results for the computational qubit in the generated second superposition state, a process is performed to identify a relatively low-energy arrangement among the candidate arrangements of the particle.

19. In the information processing system according to any one of claims 14 to 18, The aforementioned particles are atomic nuclei that make up matter.

20. In the information processing system according to any one of claims 14 to 19, The aforementioned particle is a classical point particle.

21. In the information processing system according to any one of claims 14 to 20, The aforementioned classification includes the atomic species of the particles.

22. In the information processing system according to any one of claims 14 to 21, In the basis generation step, if n is an integer of 2 or more, a computational basis consisting of n × k × L computational qubits is generated, thereby configuring the computational basis to represent the case in which multiple particles exist in the same candidate arrangement.

23. An information processing system, The system comprises at least one processor capable of executing a program so that each of the following steps is performed, In the acquisition step, state information relating to L candidate states in a given state space and classification information relating to k types of classifications of N particles are acquired, where each of the particles takes one of the candidate states. In the basis generation step, a computational basis is generated based on the acquired state information, which is represented by at least k × L computational qubits, where the computational qubits include at least L positional qubits corresponding to each of the candidate states set for each of the k classifications, so that the computational basis is configured to represent, for each classification, which of the candidate states the particle will take.

24. An information processing system, The system comprises at least one processor capable of executing a program so that each of the following steps is performed, In the acquisition step, information about multiple specific locations where particles can be placed in a given space is acquired. In the allocation step, a group of computational qubits, each of which contains at least one computational qubit, is allocated to each of the specified locations, where, The computational qubit group is configured such that at least the first and second states are observable states. The first state indicates that the particle is present at the corresponding specific location. The second state indicates that the particle is not present at the corresponding specific location.

25. In the information processing system described in claim 24, In the acquisition step, classification information representing the classification of the particles is further acquired. The assignment step further involves assigning at least one computational qubit to each of the specific positions for each classification of the particle.

26. In the information processing system described in claim 25, The classification of the particles includes at least the atomic species of the particles.

27. In the information processing system according to any one of claims 24 to 26, The computational qubit group includes two or more computational qubits, and is configured such that at least one qubit state different from the first state and the second state is observable. Each of the aforementioned qubit states is associated with the number of particles present at the corresponding specific location.

28. Information processing method, A method comprising each step of the information processing system described in any one of claims 1 to 27.

29. It is an information processing program, A device that causes at least one computer to perform each step of the information processing system described in any one of claims 1 to 27.

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