Molecular structure optimization system, molecular structure optimization method, molecular structure optimization program, and parametrized quantum circuit

Abstract

To improve calculation efficiency in molecular structure optimization using a parameterized quantum circuit.SOLUTION: A molecular structure optimization system comprises a quantum calculation unit, an update unit, and an optimization unit. The quantum calculation unit calculates a loss function from a coordinate parameter of a molecular to be processed using a quantum circuit with a circuit parameter. The update unit updates the coordinate parameter and the circuit parameter on the basis of the loss function. The optimization unit determines an optimum value of the circuit parameter which minimizes the loss function and an optimum value of the coordinate parameter. The update unit comprises a first update unit and a second update unit. The first update unit fixes the coordinate parameter to a temporary optimum value and estimates the temporary optimum value while changing the circuit parameter according to a Bayesian optimization algorithm. The second update unit fixes the circuit parameter to the temporary optimum value and updates the temporary optimum value while changing the coordinate parameter according to the Bayesian optimization algorithm.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] Embodiments of the present invention relate to a molecular structure optimization system, a molecular structure optimization method, a molecular structure optimization program, and a parametrized quantum circuit. [Background technology]

[0002] In recent years, the development of gate-based quantum computers has progressed significantly, enabling various methods of quantum computing, albeit on a small scale, that utilize quantum properties. These quantum computers, known as NISQs (Noisy Intermediate-Scale Quantum Devices), are considered an important first step toward future quantum computers with error correction capabilities. Research into utilizing NISQs is currently active, and in particular, an algorithm called the Variational Quantum Eigensolver (VQE) (see Non-Patent Document 1), which hybridizes quantum and classical computing, is expected to be applied to quantum chemistry calculations. However, to actually implement this on an NISQ device, a parameterized quantum circuit (PQC) called an ansatz, which corresponds to the trial function of the variational calculus, is prepared. The expectation value of the Hamiltonian sandwiched between the ansatz circuits is calculated on the NISQ device, and the circuit parameters of the ansatz circuit are updated using a classical computer to minimize the expectation value. In other words, VQE requires repeated calculation of expected values ​​and parameter updates, going back and forth between the NISQ device and the classical computer, until the desired expected value becomes sufficiently small. To perform highly accurate VQE calculations, improvements are needed on a wide range of issues, including expressive trial functions and Ansatz functions, high-performance optimizers, efficient sampling methods, error mitigation of noise errors inherent in NISQ devices, and circuit design that takes into account the architecture of the actual device (qubit layout). [Prior art documents] [Chartered documents]

[0003]

Patent Document 1

Non-licensed literature

[0004] [Non-licensed document 1] A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, PJ Love, A. Aspuru-Guzik and JLO'Brien, “A variational eigenvalue solver on a photonic quantum processor,” Nature Communications, 5, article number: 4213, 2014. [Non-licensed document 2] A. Delgado, JM Arrazola, S. Jahangiri, Z. Niu, J. Izaac, C. Roberts, and N. Killoran, “Variational quantum algorithm for molecular geometry optimization” Phys. Rev. A 104, 052402 (2021) [Non-licensed document 3] G. lannelli and K. Jansen, “Noisy Bayesian optimization for variational quantum eigensolvers,” arXiv 2112.00426.

Non-licensed Document 4

[0005] Because VQE can be applied to the minimum eigenvalue problem, it is most promising for application in quantum chemical calculations to calculate the ground state of molecular systems. In recent years, a report has been published (Non-Patent Document 2) demonstrating that molecular structure optimization can be achieved by calculating not only the ground-state energy but also the forces acting on atoms. However, obtaining the ground-state energy using VQE requires repeated iterations between classical and quantum computers to optimize the parameters of the quantum circuit. Therefore, when performing structural optimization using the Hellmann-Feynman force calculated from the gradient of the ground-state energy with respect to the atomic coordinates, a huge number of iterations are required, combining the energy minimization and structural optimization processes. Therefore, reducing the number of VQE iterations is essential for practical molecular structure optimization using quantum computers.

[0006] In a series of studies on reducing the computational cost of VQE, Lannelli & Jansen (Non-Patent Document 3) in 2021 and Rad et al. (Non-Patent Document 4) in 2022 disclosed a method using Bayesian optimization as an optimization method. Non-Patent Documents 3 and 4 reported that when using Bayesian optimization, the optimal value for the total energy can be obtained with fewer parameter updates than with conventional optimization methods, and that variational optimization of NISQ devices can alleviate the Barren Plateaus problem, in which the convergence of parametrized quantum circuits deteriorates with circuit depth. While Bayesian optimization has thus been reported to be effective for variational optimization of energy based on VQE, it is unclear whether it is equally effective for optimizing molecular structures.

[0007] An efficient method for molecular structure optimization using VQE is disclosed in Non-Patent Document 2. According to Non-Patent Document 2, the total energy is optimized in a vector space spanned by circuit parameters and atomic coordinates, and it is reported that efficiency can be improved by sequentially optimizing circuit parameters and atomic coordinates without directly calculating the Hellmann-Feynman forces. However, the optimization method disclosed in Non-Patent Document 2 is based on the conventional gradient method, and cannot be said to be an efficient means.

[0008] The problem to be solved by the present invention is to provide a molecular structure optimization system, a molecular structure optimization method, a molecular structure optimization program, and a parametrized quantum circuit that improve the computational efficiency in molecular structure optimization using a parametrized quantum circuit. [Means for solving the problem]

[0009] A molecular structure optimization system according to an embodiment includes a quantum computing unit, an updating unit, and an optimization unit. The quantum computing unit calculates a loss function from the coordinate parameters of a target molecule using a parameterized quantum circuit defined by circuit parameters. The updating unit updates the coordinate parameters and the circuit parameters based on the loss function. The optimization unit iterates a variational optimization procedure, including the calculation of the loss function by the quantum computing unit and the updating of the coordinate parameters and the circuit parameters by the updating unit, until a stopping condition is satisfied, and determines optimal values ​​of the circuit parameters and the coordinate parameters that minimize or maximize the loss function. The updating unit includes a first updating unit and a second updating unit. The first updating unit fixes a first parameter among the circuit parameters and the coordinate parameters to a first tentative optimal value, while changing a second parameter among the circuit parameters and the coordinate parameters according to a Bayesian optimization algorithm based on the loss function, thereby estimating a second tentative optimal value of the second parameter. The second update unit updates the first tentative optimal value of the first parameter by changing the first parameter based on the loss function in accordance with a Bayesian optimization algorithm while fixing the second parameter at the second tentative optimal value. [Brief explanation of the drawings]

[0010] [Figure 1] Block diagram showing an example of the molecular structure optimization system [Figure 2] Block diagram for molecular structure optimization processing [Figure 3] Schematic diagram of molecular structure optimization processing [Figure 4] Diagram showing the molecular structure optimization process [Figure 5] Schematic diagram of molecular structure optimization processing according to a comparative example [Figure 6] FIG. 10 is a graph showing total energy according to a comparative example. [Figure 7] FIG. 10 is a graph showing the energy error in the most stable structure according to a comparative example. [Figure 8] FIG. 1 is a graph showing total energy according to an embodiment. [Figure 9] FIG. 10 is a graph showing the energy error in the most stable structure according to the embodiment. [Figure 10] FIG. 10 is another graph showing total energy according to the embodiment. [Figure 11] FIG. 10 is another graph showing the energy error in the most stable structure according to the embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0011] Hereinafter, a molecular structure optimization system, a molecular structure optimization method, a molecular structure optimization program, and a parametrized quantum circuit according to this embodiment will be described with reference to the drawings.

[0012] Fig. 1 is a block diagram showing an example of the configuration of a molecular structure optimization system 1 according to this embodiment. As shown in Fig. 1, the molecular structure optimization system 1 includes a classical computer 100 and a quantum computer 200. The classical computer 100 and the quantum computer 200 are connected to each other via wire or wirelessly so that they can communicate information with each other.

[0013] The classical computer 100 is a computer that processes binary classical bits. The classical computer 100 is a computer that has a processing circuit 110, a storage device 120, an input device 130, a communication device 140, and a display device 150. Information communication between the processing circuit 110, the storage device 120, the input device 130, the communication device 140, and the display device 150 is performed via a bus. Therefore, since the processing circuit 110, the storage device 120, the input device 130, the communication device 140, and the display device 150 are connected to other devices via information communication, multiple devices may be collectively referred to as the classical computer 100. Note that the storage device 120, the input device 130, the communication device 140, and the display device 150 are not essential components and can be omitted as appropriate.

[0014] The processing circuit 110 includes a processor such as a CPU (Central Processing Unit) and a memory such as a RAM (Random Access Memory). The processing circuit 110 includes a quantum computing control unit 111, an update unit 112, an optimization unit 113, and a display control unit 114. The processing circuit 110 executes a molecular structure optimization program to realize the functions of the above-mentioned units 111 to 114. The molecular structure optimization program is stored in a non-transitory computer-readable recording medium such as a storage device 120. The molecular structure optimization program may be implemented as a single program that describes all the functions of the above-mentioned units 111 to 114, or may be implemented as multiple modules divided into several functional units. Furthermore, the above-mentioned units 111 to 114 may be implemented using integrated circuits such as an Application Specific Integrated Circuit (ASIC) or an FPGA (Field Programmable Gate Array). In this case, the units may be implemented on a single integrated circuit or individually on multiple integrated circuits.

[0015] The quantum computation control unit 111 controls quantum computation using a parameterized quantum circuit 210 implemented in the quantum computer 200. The quantum computation control unit 111 calculates a loss function from the coordinate parameters of a molecule to be processed, using the parameterized quantum circuit 210 defined by circuit parameters. Specifically, the quantum computation control unit 111 provides the coordinate parameters to the parameterized quantum circuit 210. The coordinate parameters are converted into a loss function by the parameterized quantum circuit 210. The quantum computation control unit 111 obtains the loss function from the parameterized quantum circuit 210.

[0016] The update unit 112 updates the coordinate parameters and the circuit parameters based on the loss function. The update unit 112 includes a first update unit 115 and a second update unit 116. The first update unit 115 estimates a second interim optimal value of a second parameter while fixing a first parameter among the circuit parameters and the coordinate parameters to a first interim optimal value and changing a second parameter among the circuit parameters and the coordinate parameters in accordance with a Bayesian optimization algorithm based on the loss function. The second update unit 116 updates the first interim optimal value of the first parameter while fixing the second parameter to the second interim optimal value and changing the first parameter in accordance with the Bayesian optimization algorithm based on the loss function.

[0017] The optimization unit 113 repeats a variational optimization procedure, including the calculation of the loss function by the quantum computing control unit 111 and the updating of the coordinate parameters and circuit parameters by the update unit 112, until a stopping condition is met, and determines the optimal values ​​of the circuit parameters and the coordinate parameters that minimize or maximize the loss function. By minimizing the loss function, the optimization unit 113 can determine the optimal values ​​of the coordinate parameters when the target molecule has a molecular structure in the ground state. By maximizing the loss function, the optimization unit 113 can determine the optimal values ​​of the coordinate parameters when the target molecule has a molecular structure in the transition state.

[0018] The display control unit 114 displays various information on the display device 150. For example, the display control unit 114 displays coordinate parameters, circuit parameters, loss functions, and the like.

[0019] The storage device 120 is configured by a ROM (Read Only Memory), an HDD (Hard Disk Drive), an SSD (Solid State Drive), an integrated circuit storage device, etc. The storage device 120 stores a molecular structure optimization program and the like.

[0020] The input device 130 inputs various commands from an operator. The input device 130 can be a keyboard, a mouse, various switches, a touchpad, a touch panel display, or the like. An output signal from the input device 130 is supplied to the processing circuit 110. Note that various commands from the operator may be input not through the input device 130 installed in the classical computer 100, but through an input device provided in another classical computer connected via a communication device 140.

[0021] The communication device 140 is an interface for communicating information with an external device such as a quantum computer 200 connected to the classical computer 100 via a wired or wireless connection.

[0022] The display device 150 displays various information under the control of the display control unit 114. As the display device 150, a CRT (Cathode-Ray Tube) display, a liquid crystal display, an organic EL (Electro Luminescence) display, an LED (Light-Emitting Diode) display, a plasma display, or any other display known in the art can be appropriately used. The display device 150 may also be a projector.

[0023] The quantum computer 200 is a computer equipped with a quantum circuit 210 that performs quantum gate operations on multiple quantum bits and performs quantum computations using the quantum circuit 210. The quantum circuit 210 may implement quantum bits and quantum gates using any method, such as a superconducting circuit method, an ion trap method, a quantum dot method, an optical lattice method, or any other method. The quantum computer 200 includes various hardware components for implementing an environment appropriate for the implementation method of the quantum bits and quantum gates. Although not shown in FIG. 1 , the quantum computer 200 may also include a processing circuit for performing various information processing using classical bits, as well as a storage device, an input device, a communication device, a display device, and the like. The quantum computer 200 is an example of a quantum computation unit.

[0024] The quantum computer 200 receives coordinate parameters of a molecule to be processed from the classical computer 100, inputs the coordinate parameters to a parametrized quantum circuit 210 that performs quantum gate operations on multiple quantum bits, and outputs a loss function defined by the coordinate parameters and the circuit parameters. The quantum computer 200 acquires the loss function from the quantum circuit 210. The quantum computer 200 transmits the acquired loss function to the classical computer 100. The quantum computer 200 is an example of a quantum computing unit.

[0025] FIG. 2 is a block diagram of the molecular structure optimization process according to this embodiment. As shown in FIG. 2, the quantum computation control unit 111 inputs a coordinate parameter X to a parameterized quantum circuit 210 controlled by a circuit parameter Θ, and outputs a loss function g(Θ,X). The coordinate parameter X is a vector of the coordinates of atoms included in the target molecule. The parameterized quantum circuit 210 includes a series of quantum gates controlled by the circuit parameter Θ. The quantum gate is assigned a circuit parameter Θ, and performs a quantum gate operation on a quantum bit according to the circuit parameter Θ. The circuit parameter Θ is a rotation angle vector of the quantum gates constituting the parameterized quantum circuit 210. The loss function g(Θ,X) is a Hamiltonian defined by the coordinate parameter X of the target molecule. Because the parameterized quantum circuit 210 is controlled by the circuit parameter Θ, it can be expressed mathematically as U(Θ).

[0026] The parametrized quantum circuit 210 performs a quantum gate operation according to the circuit parameter Θ on a quantum bit in which the coordinate parameter X is encoded, and outputs a loss function g(Θ,X) that represents the energy in a desired quantum state.

[0027] The first updating unit 115 estimates a provisional optimal value of the circuit parameter Θ while fixing the coordinate parameter X, which is a first parameter, at a provisional optimal value and changing the circuit parameter Θ, which is a second parameter, based on a loss function g(Θ, X) in accordance with a Bayesian optimization algorithm. Specifically, the first updating unit 115 fixes the coordinate parameter X to the provisional optimal value Xbest, sets the circuit parameter Θ to a candidate point Θs1, and calculates the loss function g(Θs1, Xbest) using the parametrized quantum circuit 210. Next, the first updating unit 115 estimates the next candidate point Θs2 based on the loss function g(Θs1, Xbest) in accordance with the Bayesian optimization algorithm. Then, the first updating unit 115 fixes the coordinate parameter X to the provisional optimal value Xbest, sets the circuit parameter Θ to a candidate point Θs2, and calculates the loss function g(Θs2, Xbest) using the parametrized quantum circuit 210. Next, the first update unit 115 estimates the next candidate point Θs3 based on the loss function g(Θs2, Xbest) according to the Bayesian optimization algorithm. In this way, the estimation of the candidate point Θsl (l is a natural number equal to or less than N) and the calculation of the loss function g(Θsl, Xbest) are repeated L times. This iterative process is called Bayesian updating. After L iterations, the provisional optimal value Θbest of the circuit parameter Θ that best minimizes or maximizes the loss function g among the L iterations is determined.

[0028] The second updating unit 116 updates the provisional optimal value of the coordinate parameter X by changing the coordinate parameter X based on the loss function g(Θ, X) according to a Bayesian optimization algorithm while fixing the circuit parameter Θ at the provisional optimal value. The second updating unit 116 also repeats the estimation of candidate points Xsm (m is a natural number equal to or less than M) and the calculation of the loss function g(Θbest, Xsm) M times. After the M iterations, it determines the provisional threshold Xbest of the coordinate parameter X that best minimizes or maximizes the loss function g among the M iterations.

[0029] The optimization unit 113 repeats a variational optimization procedure including the calculation of the loss function g(Θ, X) by the quantum computing control unit 111 and the update of the coordinate parameter X and the circuit parameter Θ by the update unit 112 until a stopping condition is satisfied, and determines the optimal value Θopt of the circuit parameter Θ and the optimal value Xopt of the coordinate parameter X that minimize or maximize the loss function. As the variational optimization procedure, for example, the variational quantum eigenvalue method (VQE) is used.

[0030] The molecular structure optimization process according to this embodiment will be described in detail below. In the following description, it is assumed that the molecular structure optimization according to this embodiment solves the problem of minimizing a loss function.

[0031] 3 is a schematic diagram of the molecular structure optimization process according to this embodiment. As shown in FIG. 3, the molecular structure optimization method according to this embodiment optimizes the circuit parameters Θ=(θ0, θ1, θ2, . . . θ) of the parameterized quantum circuit 210. n ) and the coordinate parameters of the molecular structure X = (x0, x1, x2, x n ) in the vector space. Figure 3 shows an example of the energy surface E(Θ,X) expressed by energy contours. The black dots represent the vectors (Θ k ,X k ) and is represented as a point on the energy surface E(Θ,X). The arrows indicate the progression of the optimization steps. Starting from the initial point, which is the initial vector at the start of optimization, the optimization steps are performed sequentially in the order Θ → X → Θ using Bayesian optimization, and the diagram shows how the minimum value opt on the energy surface E(Θ,X) is finally reached.

[0032] Next, we will explain the variational quantum eigenvalue method (VQE). VQE is a variational optimization algorithm that uses quantum circuits and performs calculations using the following steps: Step 1. Embedding the wave function (trial function) into the quantum bit Step 2. Convert the second quantized Hamiltonian to a qubit Hamiltonian Step 3. Calculating the expected value using the NISQ device Step 4. Updating parameters using a classical computer Step 5. Repeat steps 3 and 4 until convergence In VQE, the trial function must be embedded in a quantum bit (qubit) to be calculated on a quantum circuit (Step 1). Specifically, if the quantum bit state "0" is considered to be an unoccupied orbital and the state "1" is considered to be an occupied orbital, the second quantization method, which expresses the quantum state as the occupied state of the spin orbital, can be applied as is. However, it is impossible to calculate the second quantization Hamiltonian directly on a quantum circuit, so the second quantization Hamiltonian must be rewritten using gates that perform quantum bit operations, i.e., Pauli operators (Step 2). A typical method for expressing a Hamiltonian as a linear combination of Pauli operators is the Jordan-Wigner transformation (Jordan, P. and Wigner, E. 1928 “Uber das Paulische Aquivalenzverbot,” Zeitschrift fur Physik 631), and several other transformation methods are known, such as the Bravi-Kitaev transformation (Bravi, S. and Kitaev, A. 2005 “Universal Quantum Computation with ideal Cliffordgates and noisy ancillas,” Phys. Rev. A 022316). Using these transformation methods, the Hamiltonian can be expressed as the following equation (1).

[0033]

number

[0034] In (1), σ l ∈{I,X,Y,Z}, which are the identity operator and the Pauli operators of the X, Y, and Z components, respectively. For example, as shown in equation (2), when a parametrized quantum circuit U(Θ) consisting of unitary operators acts on an initial quantum state, a quantum state ψ(Θ) is obtained.

[0035]

number

[0036] The expectation value can be calculated by inserting the Hamiltonian described in equation (1) above into the quantum state ψ(Θ) as a bra-quette vector (Step 3). Variational optimization of the expectation value is performed via the circuit parameters. The variational optimization is performed by a classical computer (Step 4). In this way, VQE repeatedly switches between the NISQ device and the classical computer, performing iterative calculations until the expectation value becomes sufficiently small (Step 5), and obtaining the ground state energy.

[0037] Next, we will explain molecular structure optimization. By applying VQE to quantum chemical calculations, it is possible to calculate the ground state energy of a molecular system. This allows us to discuss important reactions and compound stability for material development. Furthermore, as reported by Sokolov et al. (I. Sokolov, P. Barkoutsos, L. Moeller, P. Suchsland, G. Mazzola, and I. Tavernelli, “Microcanonical and finite-temperature ab initio molecular dynamics simulations on quantum computers,” Physical Review Research 3, No. 1, 013125 (2021)), the force F acting on atoms can be calculated using the ground state obtained by VQE and the Hellmann-Feynman theorem, as shown in equation (3) below. HF It is possible to calculate

[0038]

number

[0039] where Ψ0 is the ground state whose parameters are optimized by VQE. The Hellmann-Feynman force F HF Using the equations (4) and (5), the Hellmann-Feynman force FHF By displacing the atoms minutely until the σ becomes very small, a stable molecular structure can be obtained.

[0040]

number

[0041] By using equations (4) and (5) in this way, stable and highly accurate VQE calculations can be performed, thereby reducing the number of repeated calculations.

[0042] Next, we explain Bayesian optimization. Bayesian optimization (J. Snoek, L. Hugo, and R. Adams, “Practical Bayesian Optimization of Machine Learning Algorithms,” Advances in Neural Information Processing Systems, No. 25, 2951-2959 (2012)) is a method for searching for input values ​​that maximize or minimize the output value (y value) from a predictive distribution based on prior information (prior∈D). By skillfully utilizing this method, computational and process conditions that maximize or minimize the desired y value can be obtained with as few trials as possible in computationally expensive simulations or complex experimental processes. In Bayesian optimization, a surrogate model, typically Gaussian process regression (GP), is used for the predictive distribution, and the search is performed based on the score of an acquisition function calculated from the expected value and variance of the predictive distribution. When the surrogate model is a GP, the predictive distribution obtained after GP training is a multivariate Gaussian distribution whose variance-covariance matrix is ​​a Gram matrix. When the unknown input value X' is close to X included in D, the prediction variance of X' is small, while the prediction variance for X' that is far from X becomes large. Therefore, Bayesian optimization can perform efficient search by skillfully considering the trade-off relationship between selecting the optimal value (exploitation) and selecting unevaluated points with a large standard deviation (search).

[0043] We will briefly explain the variance-covariance matrix of the predictive distribution in the case of GP. The Gram matrix is ​​given by the following equation (6) using an appropriate positive definite kernel function Ker and X∈D (assuming there are N pieces of data as priors).

[0044]

number

[0045] Now, let us consider the new unknown point X' and the expected value E[X'] and variance Σ[X'] of the unknown point X'. i ,y i ) does not contain noise, and from the analytical properties of the conditional multidimensional Gaussian distribution, they can be analytically calculated according to the following equations (7) and (8), respectively.

[0046]

number

[0047] Rewriting equation (7) using equation (6) gives equation (9), and rewriting equation (8) using equation (6) gives equation (10). Therefore, the expectation and variance of X' can be calculated by the inverse matrix of the N × N Gram matrix created by the original D.

[0048]

number

[0049] If the data in equations (9) and (10) contain noise, the unit matrix I ij can be expanded as shown in the following equations (11) and (12).

[0050]

number

[0051] Noise-free σ n = 0, and similar analysis is possible even when noise is present. A typical function form of the kernel function Ker in equation (6) is the simple and commonly used radial basis function (RBF) shown below in equation (13).

[0052]

number

[0053] Equation (13) includes the hyperparameter β, which is determined during GP training.

[0054] For an unknown input value X', it is possible to determine the candidate point that has the potential to maximize or minimize the y value using the expected value and variance obtained using equations (9), (10), (11), and (12). This candidate point can be determined based on the score value of an evaluation function called an acquisition function. Specifically, X' that shows the highest score value is determined as the next candidate point. There are several definitions of acquisition functions, and here we will explain the representative probability of improvement (PI) and expected improvement (EI), which are also used in the analysis below. First, in PI, when the maximum output value y within D is defined as ybest, the score value is defined as the probability that the predicted value of any X' exceeds ybest. The acquisition function α of PI PI can be calculated according to equation (14).

[0055]

number

[0056] where Ψ normal (x) is the normal distribution function φ normal The cumulative distribution function is obtained by integrating (x) in the range [x:∞] (where x>0). The next candidate point is α PI can be determined as X' that maximizes

[0057] Next, in EI, the expected value of the difference between the predicted value y' and ybest for any X' is defined as the score value. Similarly, the EI acquisition function α EI can be calculated according to the following equation (15).

[0058]

number

[0059] As with PI, the next candidate point is α EI can be determined as X' that maximizes

[0060] 4 is a diagram showing the processing procedure of the molecular structure optimization processing according to this embodiment. As shown in FIG. 4, the first updating unit 115 performs Bayesian update on the circuit parameter Θ L times while fixing the coordinate parameter X at the provisional optimum value Xbest (step S401). The provisional optimum value (initial value) Xbest in the first Bayesian update in step S401 may be set to any value designated by the user or the like. The number of Bayesian updates L may be set to any value equal to or greater than 2.

[0061] The Bayesian update procedure in step S401 is as follows. First, the quantum computing control unit 111 provides the parameterized quantum circuit 210 of the quantum computer 200 with an initial value Xbest of the coordinate parameter X and a candidate point (initial value) Θs1 of the circuit parameter Θ. The initial value Θs1 may be set to an arbitrary value designated by a user or the like, or may be set to a value randomly determined by a random generator or the like. The parameterized quantum circuit 210 performs a quantum gate operation according to the circuit parameter Θs1 on the quantum bit in which the coordinate parameter Xbest is encoded, and outputs a loss function g(Θs1, Xbest) representing the energy in the ground state. The loss function g(Θs1, Xbest) is transferred by the quantum computer 200 to the classical computer 100. The first update unit 115 estimates the next candidate point Θs2 based on the loss function g(Θs1, Xbest) in accordance with the above-mentioned Bayesian optimization algorithm. The quantum computing control unit 111 provides a candidate point Θs2 of the circuit parameter Θ to the parameterized quantum circuit 210 of the quantum computer 200. The parameterized quantum circuit 210 performs a quantum gate operation according to the circuit parameter Θs2 on the quantum bit in which the coordinate parameter Xbest is encoded, and outputs a loss function g(Θs2, Xbest) representing the energy in the ground state. The loss function g(Θs2, Xbest) is transferred by the quantum computer 200 to the classical computer 100. The first update unit 115 estimates the next candidate point Θs3 based on the loss function g(Θs2, Xbest) according to the Bayesian optimization algorithm. In this way, the estimation of the candidate point Θs2 (l is a natural number equal to or less than L) and the calculation of the loss function g(Θs2, Xbest) are repeated L times.

[0062] After step S401 is performed, the first updating unit 115 estimates a provisional optimum value Θbest of the circuit parameter Θ that minimizes the loss function g(Θ,X) (step S402). Specifically, in step S402, the first updating unit 115 identifies the candidate point Θsl that best minimizes the loss function g(Θsl,Xbest) from among the L candidate points Θsl of the circuit parameter Θ obtained by L iterative processes. The identified candidate point Θsl is estimated to be the provisional optimum value Θbest. This completes the Bayesian update for the circuit parameter Θ.

[0063] After step S402, the second updating unit 116 fixes the circuit parameter Θ to the provisional optimum value Θ best estimated in step S402, and performs Bayesian updating on the coordinate parameter X M times (step S403). The number of Bayesian updates M may be set to any value equal to or greater than 2.

[0064] The Bayesian update procedure in step S403 is as follows. First, the quantum computing control unit 111 provides the parameterized quantum circuit 210 of the quantum computer 200 with the initial value Xs1 of the coordinate parameter X and the provisional optimal value Θbest of the circuit parameter Θ estimated in step S402. The provisional threshold Xbest used in step S401 may be used as the initial value Xs1. The parameterized quantum circuit 210 performs a quantum gate operation according to the circuit parameter Θbest on the quantum bit in which the coordinate parameter Xs1 is encoded, and outputs a loss function g(Θbest, Xs1) representing the energy in the ground state. The loss function g(Θbest, Xs1) is transferred by the quantum computer 200 to the classical computer 100. The second update unit 116 estimates the next candidate point Xs2 based on the loss function g(Θbest, Xs1) in accordance with the above-mentioned Bayesian optimization algorithm. The quantum computing control unit 111 provides the candidate point Xs2 of the coordinate parameter X to the parameterized quantum circuit 210 of the quantum computer 200. The parameterized quantum circuit 210 performs a quantum gate operation according to the circuit parameter Θbest on the quantum bit in which the coordinate parameter Xs2 is encoded, and outputs a loss function g(Θbest, Xs2) representing the energy in the ground state. The loss function g(Θbest, Xs2) is transferred by the quantum computer 200 to the classical computer 100. The second update unit 116 estimates the next candidate point Xs3 based on the loss function g(Θbest, Xs2) in accordance with the Bayesian optimization algorithm. In this way, the estimation of the candidate point Xsm (m is a natural number equal to or less than M) and the calculation of the loss function g(Θbest, Xsm) are repeated M times.

[0065] After step S403, the second updating unit 116 estimates a provisional optimal value Xbest of the coordinate parameters X that minimizes the loss function g(Θbest, X) (step S404). Specifically, in step S404, the second updating unit 116 identifies the candidate point Xsm that best minimizes the loss function g(Θbest, Xsm) from among the M candidate points XΘsm of the coordinate parameters X obtained by M iterative processes. The identified candidate point Xsm is estimated to be the provisional threshold Xbest. This completes the Bayesian update for the coordinate parameters X.

[0066] After step S404, the optimization unit 113 determines whether or not to terminate the update (step S405). Specifically, in step S405, the optimization unit 113 determines whether or not a stopping condition for the Bayesian update is satisfied. The stopping condition can be set to any condition, such as the number of iterations of steps S401 to S404 reaching a predetermined number (P times). The predetermined number P may be any natural number equal to or greater than 1, and may be set to any value by the user. If it is determined that the stopping condition is not satisfied, that is, if it is determined that the update should not be terminated (step S405: NO), steps S401 to S405 are repeated.

[0067] The Bayesian update (steps S401 to S402) for the circuit parameter Θ from the second iteration onward may be performed in the same manner as above, except that the provisional optimum value of the coordinate parameter is set to the provisional optimum value Xbest estimated in step S404 in the immediately preceding iteration, and the candidate point Θs1 for the circuit parameter Θ is set to the provisional optimum value Θbest estimated in step S402 in the immediately preceding iteration.

[0068] In this manner, steps S401 to S405 are repeated until it is determined in step S405 that the stopping condition is satisfied. If it is determined in step S405 that the updating is to be terminated (step S405: YES), the optimization unit 113 determines the optimal value Xopt of the coordinate parameter X and the optimal value Θopt of the circuit parameter (step S406). Specifically, in step S406, the optimization unit 113 determines the provisional optimal value Xbest and the provisional optimal value Θbest that best minimize the loss function g from among the P provisional optimal values ​​Xbest and P provisional optimal values ​​Θbest obtained up to this point. The determined provisional optimal values ​​Xbest and Θbest are set as the optimal values ​​Xopt and Θopt. By minimizing the loss function, the optimization unit 113 can determine the optimal values ​​of the coordinate parameters when the target molecule has a molecular structure in the ground state.

[0069] It should be noted that the tendency of the loss function value with respect to the coordinate parameter X is expected to remain qualitatively unchanged, although the absolute value will change in a situation where the circuit parameter Θ is not fully optimized. Therefore, the need to calculate highly accurate provisional thresholds Θbest and Xbest in the Bayesian update for the circuit parameter Θ (steps S401 and S402) and the Bayesian update for the coordinate parameter X (steps S403 and S404) is reduced. This makes it possible to reduce the circuit scale of the quantum circuit 210 without significantly affecting the optimal value Xopt of the coordinate parameter.

[0070] As one example, the optimum value Xopt and the optimum value Θopt determined in step S406 may be displayed in an arbitrary layout on the display device 150 by the display control unit 114. As another example, the optimum value Xopt and the optimum value Θopt may be stored in the storage device 120, or may be transferred to another computer via the communication device 140.

[0071] The optimal value Θopt may be transferred to the quantum computer 200 and set in the parameterized quantum circuit 210. The parameterized quantum circuit 210 in which the optimal value Θopt has been set is able to output a trial wave function, energy, etc. with relatively high accuracy upon receiving the input of the coordinate parameter X without undergoing another Bayesian updating process, optimization process, etc.

[0072] This completes the molecular structure optimization process according to this embodiment.

[0073] The molecular structure optimization process described above can be appropriately added, modified, or deleted without departing from the spirit and scope of the present invention. As an example, the display, storage, and / or transfer of the optimal values ​​Xopt and Θopt in step S406 is not essential. The molecular structure optimization process according to this embodiment may be terminated when it is determined in step S405 that the update is to be terminated (step S405: YES). As another example, the order of the Bayesian update on the circuit parameter Θ (steps S401 and S402) and the Bayesian update on the coordinate parameter X (steps S403 and S404) may be reversed. In other words, the first parameter to be updated by the first update unit 115 may be the circuit parameter Θ, and the second parameter to be updated by the second update unit 116 may be the coordinate parameter X. While the above description describes searching for circuit parameters and coordinate parameters that minimize a loss function, it is also possible to search for circuit parameters and coordinate parameters that maximize a loss function. This makes it possible to calculate the energy of the transition state.

[0074] 1 is an example, and the present embodiment is not limited to this. As an example, the quantum computer 200 and the classical computer 100 may be incorporated into a single hardware device. Furthermore, the storage devices, input devices, and circuits provided in the classical computer 100 and the quantum computer 200 do not have to be provided in a single computer. It is sufficient that the respective devices are electrically connected to function as a single computer.

[0075] (Example) Next, an example of molecular structure optimization according to this embodiment will be described.

[0076] The target molecule in this example is the H2 molecule. Numerical simulations were performed using the electron Hamiltonian of the H2 molecule. In the examples, we use existing open source libraries, PySCF (The Python-based Simulations of Chemistry Framework, see Reference 1 (Q. Sun, T. C. Berkelbach, N.S. Blunt, G.H. Booth, S. Guo, Z. Li, J. Liu, J.D. McClain, E.R. Sayfutyarova, S. Sharma, S.Wouters, and G.K. Chan, Wiley Interdisciplinary Reviews: Computational Molecular Science 8, e1340 (2017))) and OpenFermion (Reference 2 (J.R. McClean, K.J. Sung, I.D. Kivlichan, Y. Cao, C. Dai, E.S. Fried, C. Gidney, B. Gimby, P. Gokhale, T. Hner, T. Hardikar, V. Havlek, O. Higgott, C. Huang, J. Izaac, Z. Jiang, X. Liu, S. McArdle, M. Neeley, T. O'Brien, B. O'Gorman, I. Ozdan, MD Radin, J. Romero, N. Rubin, NPD Sawaya, K. Setia, S. Sim, DS Steiger, M. Steudtner, Q. Sun, W. Sun, D. Wang, F. Zhang, and R. Babbush, (2017), arXiv:1710.07629.) to calculate the Hamiltonian.

[0077] The simulation of quantum circuits is carried out using Qiskit (Reference 3 (G. Aleksandrowicz, T. Alexander, P. Barkoutsos, L. Bello, Y. Ben-Haim, D. Bucher, F.Jose Cabrera-Hernandez, J. Carballo-Franquis, A. Chen, C. Chen, J. Chow, A. Corcoles-Gonzales, A. Cross, A. Cross, J. Cruz-Benito, C. Culver, S. Gonzalez, E. Torre, D, Ding, E. Dumitrescu, I.Duran, P. Eendebak, M. Everitt, I. Sertage, A. Frisch, A. Fuhrer, J. Gambetta, B. Gago, J. Gomez-Mosquera, D. Greenberg, I. Hamamura, V. Havlicek, J. Hellmers, L. Herok, H. Horii, S. Hu, T. Imamichi, T. Itoko, A. Javadi-Abhari, N. Kanazawa, A. Karazeev, K. Krsulich, P. Liu, Y. Luh, Y. Maeng, M. Marques, F. Martin-Fernandez, D. McClure, D. McKay, S. Meesala, A. Mezzacapo, N. Moll, D. Rodriguez, G. Nannicini, P. Nation, P. Ollitrault, L. O'Riordan, H. Paik, J. Perez, A. Phan, M. Pistoia, V. Prutyanov, M. Reuter, J. Rice, A. Davila, R. Rudy, M. Ryu, N. Sathaye, C. Schnabel, E. Schoute, K. Setia, Y. Shi, A. Silva, Y. Siraichi, S. Sivarajah, J. Smolin, M. Soeken, H. Takahashi, I. Tavernelli, C.Taylor, P. Taylor, K. Trabing, M. Treinish, W. Turner, D. Vogt-Lee, C. Vuillot, J. Wildstrom, J. Wilson, E. Winston, C. Wood, S. Wood, S. Worner, I. Akhalwaya, C. Zoufal (see https: / / doi.org / 10.5281 / zenodo.2562111, (2019) An Open-source Framework for Quantum Computing).

[0078] Bayesian optimization was performed using the existing open source libraries GPy (Reference 4 (“GPy: Gaussian process framework in Python,” http: / / github.com / SheffieldML / GPy)) and GpyOpt (“GPyOpt: A Bayesian Optimization framework in Python” http: / / github.com / SheffieldML / GPyOpt).

[0079] Hereinafter, for convenience, the method according to the technology of this embodiment will be referred to as bmgo (Bayesian molecular geometry optimization). The calculation conditions for the structural optimization according to this embodiment were set as follows.

[0080] Basis function: STO-3G Spin multiplicity: 2S+1=1, charge=0 Completely active space: CAS(2e,2o) Parametrized quantum circuits: Hardware Efficient ansatz (depth=1 or 2)

[0081] As a benchmark, molecular structure optimization was performed using the quantum chemistry calculation software PySCF. The total energy was -1.13730605 Hr, the atomic positions were "H" (0.0325770423, -0.0000000000, -0.0000000000), "H" (0.7674229577, -0.0000000000, 0.0000000000), the inter-hydrogen atom distance was 0.734845915 Å, and the energy E = -1.1373 Hr was obtained as the most stable structure.

[0082] Next, we present the results of bmgo. The calculation conditions for Bayesian optimization were set as follows:

[0083] Surrogate model: GP Acquisition function: EI Initial sampling number: 10

[0084] First, we applied Bayesian optimization according to the comparative example and optimized all of these vectors using {Θ,X} as input parameters. Here, for the coordinate parameter X, the coordinate of one hydrogen atom was fixed to H(0,0,0) and the other was set to H(x,0,0), and only the x coordinate of one hydrogen atom was used as an atomic coordinate variable, taking into account the symmetry of the molecule.

[0085] Fig. 5 is a schematic diagram of a molecular structure optimization process according to a comparative example. As shown in Fig. 5, the molecular structure optimization process according to the comparative example updates both the circuit parameter Θ and the coordinate parameter X for each Bayesian update, unlike the molecular structure optimization process according to the present embodiment shown in Fig. 3.

[0086] Below, we show the results of numerical simulations of 24 circuit parameters and one coordinate parameter (distance between hydrogen atoms) in the case of D=2 in Hardware Efficient Ansatz.

[0087] FIG. 6 is a graph showing the total energy according to a comparative example. FIG. 7 is a graph showing the energy error at the most stable structure according to a comparative example. The vertical axis of FIG. 6 is defined as the total energy (energy) [Hr], and the horizontal axis is defined as the number of steps (iterations) of Bayesian updating. The vertical axis of FIG. 7 is defined as the error (energy difference) [Hr] between the total energy and the energy of the most stable structure E = -1.1373 Hr, and the horizontal axis is defined as the number of steps (iterations) of Bayesian updating. As shown in FIGS. 6 and 7, the energy drop stops around 100 steps, and the error with the energy of the most stable structure (dotted line) remains large, indicating that the system does not converge to an optimal solution. The solution for the final step at this time is total energy E=-0.910093344874445Hr, and circuit parameters Θ=[3.14159265,-3.14159265,3.14159265,-3.14159265,3.14159265,-3.14159265,3.14159265,3.14159265,3.14159265,-3.14159265,-0.11182639,3.14159 265,-3.14159265,3.14159265,3.14159265,3.14159265,3.14159265,3.14159265,3.14159265,-3.14159265,3.14159265,-3.14159265,-3.14159265,-3.14159265,3.14159265], and the coordinate parameter x = 15. This indicates that the parameters remain within the search boundary and do not move at all. To confirm, calculations were performed on several samples, and the results were also x = 15. This suggests that the predicted distribution of the energy expectation in {Θ,X} is not well-fitted by Gaussian process regression, and that the energy expectation may behave significantly differently with changes in the circuit parameter Θ and the coordinate parameter X. Furthermore, it is known that in ordinary Bayesian optimization, the more dimensions there are, the more likely it is that the optimization will fall into a local solution. Therefore, when it comes to practical molecular systems with a larger number of atoms, the Bayesian optimization according to the comparative example shown in FIG. 5 is at a disadvantage.

[0088] Next, we will show the results of bmgo, which performs sequential Bayesian optimization as shown in Figure 3. In bmgo, sequential optimization was performed using the following procedure.

[0089] Step 1. Fix the coordinate parameter X and perform 50 Bayesian updates on E(Θ,X). Step 2. Fix the Θ that minimizes E(Θ,X) as the temporary optimal value Θbest, and perform 50 Bayesian updates on E(Θbest,X). Step 3. Fix X, which minimizes E(Θbest,X), as the provisional optimum value Xbest. Step 4. Steps 1 to 3 are considered as one step and are repeated p times. Step 5. Determine the optimal values ​​Θopt and Xopt

[0090] In this example, p = 20 iterations were performed in step 4 above. The energy trend of the system with respect to the atomic coordinate X is expected to remain qualitatively unchanged, although the absolute value will change if the circuit parameter Θ is not fully optimized. Therefore, when optimizing Θ in steps 1 and 2, it is not necessary to obtain a highly accurate optimal solution; in other words, making the quantum circuit shallower is expected not to significantly affect the value of Xopt. Therefore, in order to reduce the computational load, a hardware efficient answer with D = 1 was used here.

[0091] FIG. 8 is a graph showing the total energy according to the embodiment. FIG. 9 is a graph showing the energy error in the most stable structure according to the embodiment. As shown in FIGS. 8 and 9, it can be seen that an energy value close to that of the most stable structure is obtained in about six steps where p>5. It can also be seen that a more accurate energy expectation value is finally obtained compared to FIGS. 6 and 7, which use the HE ansatz with D=2. At the final step, the total energy E=-1.135331506112484Hr, and the circuit parameters Θ=[-0.24188404, 3.14159265, -3.14159265, -3.14159265, -1.36057888, -3.14159265, 1.90104979, -3.141 The coordinate parameter (distance between hydrogen atoms) x = 0.7344096462252. The distance between hydrogen atoms was calculated by a classical computer, CASCI (Complete Active Space Configuration Interaction) (= 0.7348) and 10 -4 The energy is also in agreement with an error of 10 -3 The results match with an error of one order of magnitude, indicating that the most stable structure was obtained with high accuracy.

[0092] FIG. 10 is a diagram showing another graph representing the total energy according to the embodiment. FIG. 11 is a diagram showing another graph representing the energy error in the most stable structure according to the embodiment. FIGS. 10 and 11 show the results when the energy does not converge sufficiently after 20 steps of Bayesian optimization. As shown in FIGS. 10 and 11, it can be seen that the energy has not dropped completely and has fallen into a local solution. In other words, even if the error in the most stable energy is large, the error in the atomic coordinates of the most stable structure becomes small. The final step in this case is the total energy E= The time is -1.119713435544261Hr, the circuit parameters Θ = [0.27941586, -0.07554233, -0.01952159, -3.14159265, 2.70094774, 0.74961037, -2.08077215, 1.33821656, 3.14159265, 0.28885805, -3.14159265, 3.14159265, -1.54402765, 1.53511816, 3.1024391, -2.6263595], and the coordinate parameter (distance between hydrogen atoms) x = 0.759282304006334. The energy value is larger than the value for the most stable structure (= -1.1373), confirming the large error. On the other hand, the value of x is 0.7592, which is within an error range of about 3% compared to the interatomic distance of the most stable structure, 0.7348. This means that, as mentioned above, when using this method, even if the circuit parameter Θ is not fully optimized, it does not have a significant impact on the optimization of the atomic coordinates themselves. Test calculations using hydrogen molecules show that a sufficiently high level of structural optimization is possible with a hardware efficient analysis with D=1.

[0093] In the above example, Θ and X were optimized to minimize E(Θ,X), and the stable molecular structure with the lowest energy was obtained. However, if this example is used for -E(Θ,X), which is the cost function with the opposite sign, the molecular structure with the highest energy can be obtained. This means that by appropriately setting the range of the coordinate parameter X, it is possible to determine the molecular structure of the transition state in a chemical reaction. In this way, this example can be used not only to determine stable molecular structures, but also to search for transition states in chemical reactions.

[0094] The molecular structure optimization system 1 according to this embodiment includes a quantum computer 200 and a classical computer 100. The quantum computer 200 calculates a loss function from the coordinate parameters of a target molecule using a parameterized quantum circuit 210 defined by circuit parameters. The classical computer 100 includes an update unit 112 and an optimization unit 113. The update unit 112 updates the coordinate parameters and circuit parameters based on the loss function. The optimization unit 113 iterates a variational optimization procedure, including the calculation of the loss function by the quantum computer 200 and the updating of the coordinate parameters and circuit parameters by the update unit 112, until a stopping condition is satisfied, and determines optimal values ​​of the circuit parameters and coordinate parameters that minimize or maximize the loss function. Here, the update unit 112 includes a first update unit 115 and a second update unit 116. The first update unit 115 estimates a second provisional optimal value of the second parameter while fixing the first parameter among the circuit parameters and the coordinate parameters to a first provisional optimal value and changing the second parameter among the circuit parameters and the coordinate parameters in accordance with a Bayesian optimization algorithm based on a loss function. The second update unit 116 updates the first provisional optimal value of the first parameter while fixing the second parameter to the second provisional optimal value and changing the first parameter in accordance with a Bayesian optimization algorithm based on a loss function.

[0095] According to the above configuration, circuit parameters and coordinate parameters are optimized using Bayesian optimization in molecular structure optimization based on VQE. Here, rather than performing Bayesian updating on both the circuit parameters and the coordinate parameters at each time step, Bayesian updating is performed alternately on the circuit parameters and the coordinate parameters. This reduces the risk of falling into a local solution compared to when performing Bayesian updating on both the circuit parameters and the coordinate parameters, thereby reducing the computational cost of optimizing the circuit parameters and the coordinate parameters and improving accuracy. Furthermore, as described above, it is possible to obtain highly accurate coordinate parameters and loss functions (e.g., energy) without fully optimizing the circuit parameters, thereby reducing the computational cost of the coordinate parameters and the loss function.

[0096] Thus, according to this embodiment, it is possible to improve the calculation efficiency in molecular structure optimization using a parametrized quantum circuit.

[0097] Although several embodiments of the present invention have been described, these embodiments are presented as examples and are not intended to limit the scope of the invention. These novel embodiments can be embodied in various other forms, and various omissions, substitutions, and modifications can be made without departing from the spirit of the invention. These embodiments and their modifications are included within the scope and spirit of the invention, and are also included in the scope of the invention and its equivalents as defined in the claims.

[0098] The inventions disclosed in the specification and claims at the time of filing of this application are as follows: [1] a quantum computing unit that calculates a loss function from coordinate parameters of a target molecule using a parametrized quantum circuit defined by circuit parameters; an update unit that updates the coordinate parameters and the circuit parameters based on the loss function; an optimization unit that iterates a variational optimization procedure, including the calculation of the loss function by the quantum computing unit and the updating of the coordinate parameters and the circuit parameters by the updating unit, until a stopping condition is satisfied, and determines optimal values ​​of the circuit parameters and the coordinate parameters that minimize or maximize the loss function; The update unit a first update unit that estimates a second tentative optimum value of a second parameter among the circuit parameters and the coordinate parameters while fixing the first parameter among the circuit parameters and the coordinate parameters at a first tentative optimum value and changing the second parameter among the circuit parameters and the coordinate parameters in accordance with a Bayesian optimization algorithm based on the loss function; a second update unit that updates the first tentative optimal value of the first parameter by changing the first parameter based on the loss function in accordance with a Bayesian optimization algorithm while fixing the second parameter at the second tentative optimal value, Molecular structure optimization system. [2] The molecular structure optimization system according to [1], wherein the circuit parameters are rotation angle vectors of quantum gates that constitute the parametrized quantum circuit. [3] The molecular structure optimization system according to any one of [1] and [2], wherein the coordinate parameters are vectors of coordinates of atoms included in the target molecule. [4] The molecular structure optimization system according to any one of [1] to [3], wherein the loss function is a Hamiltonian defined by the coordinate parameters of the target molecule. [5] The molecular structure optimization system according to any one of [1] to [4], wherein the variational optimization procedure is a variational quantum eigenvalue method. [6] The molecular structure optimization system according to any one of [1] to [5], wherein the optimization unit determines optimal values ​​of the coordinate parameters when the target molecule has a ground state molecular structure by minimizing the loss function. [7] The molecular structure optimization system according to any one of [1] to [6], wherein the optimization unit determines optimal values ​​of the coordinate parameters when the target molecule assumes a transition state molecular structure by maximizing the loss function. [8] a quantum computing step of calculating a loss function from coordinate parameters of a target molecule using a parametrized quantum circuit defined by circuit parameters; an updating step of sequentially updating the coordinate parameters and the circuit parameters based on the loss function; an optimization step of repeating a variational optimization procedure, including the calculation of the loss function by the quantum calculation step and the updating of the coordinate parameters and the circuit parameters by the update step, until a stopping condition is satisfied, to determine optimal values ​​of the circuit parameters and the coordinate parameters that minimize or maximize the loss function; The updating step includes: a first updating step of estimating a second tentative optimum value of a second parameter among the circuit parameters and the coordinate parameters while fixing the first parameter among the circuit parameters and the coordinate parameters at a first tentative optimum value and changing the second parameter among the circuit parameters and the coordinate parameters in accordance with a Bayesian optimization algorithm based on the loss function; a second updating step of changing the first parameter according to a Bayesian optimization algorithm based on the loss function while fixing the second parameter at the second interim optimal value, thereby updating the first interim optimal value of the first parameter; Molecular structure optimization method. The above inventions [2] to [7] can be applied to the molecular structure optimization method. [9] On the computer, a quantum computing function that calculates a loss function from the coordinate parameters of a target molecule using a parametrized quantum circuit defined by circuit parameters; an update function that sequentially updates the coordinate parameters and the circuit parameters based on the loss function; an optimization function that iterates a variational optimization procedure, including the calculation of the loss function by the quantum computing function and the updating of the coordinate parameters and the circuit parameters by the update function, until a stopping condition is satisfied, and determines optimal values ​​of the circuit parameters and the coordinate parameters that minimize or maximize the loss function; The update function: a first update function that estimates a second tentative optimal value of a second parameter among the circuit parameters and the coordinate parameters while fixing the first parameter among the circuit parameters and the coordinate parameters at a first tentative optimal value and changing the second parameter among the circuit parameters and the coordinate parameters in accordance with a Bayesian optimization algorithm based on the loss function; a second update function that updates the first interim optimal value of the first parameter by changing the first parameter according to a Bayesian optimization algorithm based on the loss function while fixing the second parameter at the second interim optimal value, Molecular structure optimization program. The above inventions [2] to [7] can be applied to the molecular structure optimization program.

[10] a quantum computing step of calculating a loss function from coordinate parameters of a target molecule using a parametrized quantum circuit defined by circuit parameters; an updating step of updating the coordinate parameters and the circuit parameters based on the loss function; an optimization step of repeating a variational optimization procedure, including the calculation of the loss function by the quantum calculation step and the updating of the coordinate parameters and the circuit parameters by the update step, until a stopping condition is satisfied, to determine optimal values ​​of the circuit parameters and the coordinate parameters that minimize or maximize the loss function; a parametrized quantum circuit to which the optimal values ​​of the circuit parameters are assigned, the optimal values ​​being determined by a molecular structure optimization method including: The updating step includes: a first updating step of estimating a second tentative optimum value of a second parameter among the circuit parameters and the coordinate parameters while fixing the first parameter among the circuit parameters and the coordinate parameters at a first tentative optimum value and changing the second parameter among the circuit parameters and the coordinate parameters in accordance with a Bayesian optimization algorithm based on the loss function; a second updating step of changing the first parameter according to a Bayesian optimization algorithm based on the loss function while fixing the second parameter at the second interim optimal value, thereby updating the first interim optimal value of the first parameter; Parametrized quantum circuits. The above inventions [2] to [7] are applicable to the parametrized quantum circuit. [Explanation of symbols]

[0099] 1...molecular structure optimization system, 100...classical computer, 110...processing circuit, 111...quantum computing control unit, 112...update unit, 113...optimization unit, 114...display control unit, 115...first update unit, 116...second update unit, 120...memory device, 130...input device, 140...communication device, 150...display device, 200...quantum computer, 210...parametrized quantum circuit.

Claims

1. a quantum computing unit that calculates a loss function from coordinate parameters of a target molecule using a parametrized quantum circuit defined by circuit parameters; an update unit that updates the coordinate parameters and the circuit parameters based on the loss function; an optimization unit that iterates a variational optimization procedure, including the calculation of the loss function by the quantum computing unit and the updating of the coordinate parameters and the circuit parameters by the updating unit, until a stopping condition is satisfied, and determines optimal values ​​of the circuit parameters and the coordinate parameters that minimize or maximize the loss function; The update unit a first update unit that estimates a second tentative optimum value of a second parameter among the circuit parameters and the coordinate parameters while fixing the first parameter among the circuit parameters and the coordinate parameters to a first tentative optimum value and changing the second parameter among the circuit parameters and the coordinate parameters, the second parameter being different from the first parameter, in accordance with a Bayesian optimization algorithm based on the loss function; a second update unit that updates the first interim optimal value of the first parameter by changing the first parameter based on the loss function in accordance with a Bayesian optimization algorithm while fixing the second parameter at the second interim optimal value, Molecular structure optimization system.

2. 2. The molecular structure optimization system according to claim 1, wherein the circuit parameter is a rotation angle vector of a quantum gate that constitutes the parametrized quantum circuit.

3. 2. The molecular structure optimization system according to claim 1, wherein the coordinate parameters are vectors of coordinates of atoms included in the target molecule.

4. 2. The molecular structure optimization system according to claim 1, wherein the loss function is a Hamiltonian defined by the coordinate parameters of the target molecule.

5. 2. The molecular structure optimization system according to claim 1, wherein the variational optimization procedure is a variational quantum eigenvalue method.

6. 2. The molecular structure optimization system according to claim 1, wherein the optimization unit determines optimal values ​​of the coordinate parameters when the target molecule has a ground state molecular structure by minimizing the loss function.

7. 2. The molecular structure optimization system according to claim 1, wherein the optimization unit determines optimal values ​​of the coordinate parameters when the target molecule has a molecular structure in a transition state by maximizing the loss function.

8. a quantum computing step of calculating a loss function from coordinate parameters of a target molecule using a parametrized quantum circuit defined by circuit parameters; an updating step of sequentially updating the coordinate parameters and the circuit parameters based on the loss function; an optimization step of repeating a variational optimization procedure, including the calculation of the loss function by the quantum calculation step and the updating of the coordinate parameters and the circuit parameters by the update step, until a stopping condition is satisfied, to determine optimal values ​​of the circuit parameters and the coordinate parameters that minimize or maximize the loss function; The updating step includes: a first updating step of estimating a second tentative optimum value of a second parameter among the circuit parameters and the coordinate parameters, while fixing a first parameter among the circuit parameters and the coordinate parameters at a first tentative optimum value and changing a second parameter among the circuit parameters and the coordinate parameters, the second parameter being different from the first parameter, based on the loss function and in accordance with a Bayesian optimization algorithm; a second updating step of changing the first parameter according to a Bayesian optimization algorithm based on the loss function while fixing the second parameter at the second interim optimal value, thereby updating the first interim optimal value of the first parameter. Molecular structure optimization method.

9. On the computer, a quantum computing function that calculates a loss function from coordinate parameters of a target molecule using a parametrized quantum circuit defined by circuit parameters; an update function that sequentially updates the coordinate parameters and the circuit parameters based on the loss function; an optimization function that iterates a variational optimization procedure, including the calculation of the loss function by the quantum computing function and the updating of the coordinate parameters and the circuit parameters by the update function, until a stopping condition is satisfied, and determines optimal values ​​of the circuit parameters and the coordinate parameters that minimize or maximize the loss function; The update function: a first update function that estimates a second tentative optimum value of a second parameter among the circuit parameters and the coordinate parameters while fixing the first parameter among the circuit parameters and the coordinate parameters to a first tentative optimum value and changing the second parameter among the circuit parameters and the coordinate parameters, the second parameter being different from the first parameter, in accordance with a Bayesian optimization algorithm based on the loss function; a second update function that updates the first interim optimal value of the first parameter by changing the first parameter according to a Bayesian optimization algorithm based on the loss function while fixing the second parameter at the second interim optimal value, Molecular structure optimization program.

10. a quantum computing step of calculating a loss function from coordinate parameters of a target molecule using a parametrized quantum circuit defined by circuit parameters; an updating step of updating the coordinate parameters and the circuit parameters based on the loss function; an optimization step of repeating a variational optimization procedure, including the calculation of the loss function by the quantum calculation step and the updating of the coordinate parameters and the circuit parameters by the update step, until a stopping condition is satisfied, to determine optimal values ​​of the circuit parameters and the coordinate parameters that minimize or maximize the loss function; a parametrized quantum circuit to which the optimal values ​​of the circuit parameters are assigned, the optimal values ​​being determined by a molecular structure optimization method including: The updating step includes: a first updating step of estimating a second tentative optimum value of a second parameter among the circuit parameters and the coordinate parameters, while fixing a first parameter among the circuit parameters and the coordinate parameters at a first tentative optimum value and changing a second parameter among the circuit parameters and the coordinate parameters, the second parameter being different from the first parameter, based on the loss function and in accordance with a Bayesian optimization algorithm; a second updating step of changing the first parameter according to a Bayesian optimization algorithm based on the loss function while fixing the second parameter at the second interim optimal value, thereby updating the first interim optimal value of the first parameter; Parametrized quantum circuits.

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