Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2312.09537 · Frontiers in Computer Science

Exploration of new chemical materials using black-box optimization with the D-wave quantum annealer

Mikiya Doi, Yoshihiro Nakao, Takuro Tanaka, Masami Sako, Masayuki Ohzeki

Published Dec 12, 2023• 10 citations
arXivHTMLPDF

Abstract

In materials informatics, searching for chemical materials with desired properties is challenging due to the vastness of the chemical space. Moreover, the high cost of evaluating properties necessitates a search with a few clues. In practice, there is also a demand for proposing compositions that are easily synthesizable. In the real world, such as in the exploration of chemical materials, it is common to encounter problems targeting black-box objective functions where formalizing the objective function in explicit form is challenging, and the evaluation cost is high. In recent research, a Bayesian optimization method has been proposed to formulate the quadratic unconstrained binary optimization (QUBO) problem as a surrogate model for black-box objective functions with discrete variables. Regarding this method, studies have been conducted using the D-Wave quantum annealer to optimize the acquisition function, which is based on the surrogate model and determines the next exploration point for the black-box objective function. In this paper, we address optimizing a black-box objective function containing discrete variables in the context of actual chemical material exploration. In this optimization problem, we demonstrate results obtaining parameters of the acquisition function by sampling from a probability distribution with variance can explore the solution space more extensively than in the case of no variance. As a result, we found combinations of substituents in compositions with the desired properties, which could only be discovered when we set an appropriate variance.

DOI
10.3389/fcomp.2023.1286226

Related papers

Benchmark Test of Black-box Optimization Using D-Wave Quantum Annealer

Ami S. Koshikawa, Masayuki Ohzeki, Tadashi Kadowaki +1 more

In solving optimization problems, objective functions generally need to be minimized or maximized. However, objective functions cannot always be formulated explicitly in a mathematical form for complicated problem settings. Although several regression techniques infer the approximate forms of objective functions, they are at times expensive to evaluate. Optimal points of "black-box" objective functions are computed in such scenarios, while effectively using a small number of clues. Recently, an efficient method by use of inference by sparse prior for a black-box objective function with binary variables has been proposed. In this method, a surrogate model was proposed in the form of a quadratic unconstrained binary optimization (QUBO) problem, and was iteratively solved to obtain the optimal solution of the black-box objective function. In the present study, we employ the D-Wave 2000Q quantum annealer, which can solve QUBO by driving the binary variables by quantum fluctuations. The D-Wave 2000Q quantum annealer does not necessarily output the ground state at the end of the protocol due to freezing effect during the process. We investigate effects from the output of the D-Wave quantum annealer in performing black-box optimization. We demonstrate a benchmark test by employing the sparse Sherrington-Kirkpatrick (SK) model as the black-box objective function, by introducing a parameter controlling the sparseness of the interaction coefficients. Comparing the results of the D-Wave quantum annealer to those of the simulated annealing (SA) and semidefinite programming (SDP), our results by the D-Wave quantum annealer and SA exhibit superiority in black-box optimization with SDP. On the other hand, we did not find any advantage of the D-Wave quantum annealer over the simulated annealing. As far as in our case, any effects by quantum fluctuation are not found.

arXiv:2103.12320•Journal of the Physical Society of Japan•May 11, 2021•43 citations

Improving search efficiency via adaptive acquisition function selection in discrete black-box optimization

Reo Shikanai, Masayuki Ohzeki

In discrete-variable black-box optimization, the number of candidate solutions grows combinatorially, while each evaluation is often expensive. Therefore, it is important to identify promising solutions efficiently within a limited number of trials. Bayesian Optimization of Combinatorial Structures (BOCS), an existing parametric method, works effectively when only a small amount of data is available. However, as the number of observations increases, BOCS tends to repeatedly propose points that have already been evaluated, which leads to search stagnation. A random-point addition strategy has been proposed to address this issue when an evaluated point is proposed, but it cannot sufficiently exploit information from promising data obtained so far. In this study, we propose a hybrid method that uses BOCS as the main search framework and generates alternative unevaluated points using a Gaussian process only when search stagnation is detected. In the Gaussian-process-based component, multiple Lower Confidence Bound (LCB) acquisition functions are adaptively selected to dynamically control the balance between exploitation and exploration. Numerical experiments using fully connected Quadratic Unconstrained Binary Optimization (QUBO) and Higher-order Unconstrained Binary Optimization (HUBO) as black-box functions show that the proposed method finds solutions with better objective values than the conventional random-point addition method in both settings. Additional analyses show that its effectiveness comes from selecting points that promote search progress within Hamming-distance neighborhoods, rather than simply adding low-energy points near promising solutions. Experiments with sparse surrogate models for quantum annealer applications further suggest the importance of retaining near-fully connected representational capacity.

quant-pharXiv:2605.10856•May 12, 2026

Continuous black-box optimization with quantum annealing and random subspace coding

Syun Izawa, Koki Kitai, Shu Tanaka +2 more

A black-box optimization algorithm such as Bayesian optimization finds extremum of an unknown function by alternating inference of the underlying function and optimization of an acquisition function. In a high-dimensional space, such algorithms perform poorly due to the difficulty of acquisition function optimization. Herein, we apply quantum annealing (QA) to overcome the difficulty in the continuous black-box optimization. As QA specializes in optimization of binary problems, a continuous vector has to be encoded to binary, and the solution of QA has to be translated back. Our method has the following three parts: 1) Random subspace coding based on axis-parallel hyperrectangles from continuous vector to binary vector. 2) A quadratic unconstrained binary optimization (QUBO) defined by acquisition function based on nonnegative-weighted linear regression model which is solved by QA. 3) A penalization scheme to ensure that the QA solution can be translated back. It is shown in benchmark tests that its performance using D-Wave Advantage$^{\rm TM}$ quantum annealer is competitive with a state-of-the-art method based on the Gaussian process in high-dimensional problems. Our method may open up a new possibility of quantum annealing and other QUBO solvers including quantum approximate optimization algorithm (QAOA) using a gated-quantum computers, and expand its range of application to continuous-valued problems.

arXiv:2104.14778•Apr 30, 2021•1 citation

Quantum-Inspired Bayesian Optimization for High-Dimensional Black-Box Optimization

Jincheng Zhang

Bayesian optimization has emerged as a powerful technique for tackling high-dimensional black-box optimization problems. However, its performance often degrades significantly when the dimensionality of the search space increases, a phenomenon known as the "curse of dimensionality." This paper proposes a novel approach – Quantum-Inspired Bayesian Optimization – that addresses this limitation by incorporating principles inspired by quantum computing, specifically quantum annealing. The core idea is to utilize a modified version of quantum annealing to guide the acquisition of function evaluations, exploiting superposition and interference to enhance exploration in high-dimensional spaces. We formulate the optimization problem as a quantum-inspired search, where candidate solutions exist in a superposition of states and are refined through interference effects. The algorithm iteratively updates the probability distribution over the search space, favoring regions with high potential based on the quantum-inspired exploration strategy. We demonstrate the effectiveness of this approach through theoretical analysis and illustrate its potential through conceptual examples, highlighting its ability to mitigate the curse of dimensionality and improve optimization performance compared to traditional Bayesian optimization methods. The key contributions of this work include the formalization of the quantum-inspired Bayesian optimization framework, the design of the modified quantum annealing algorithm for Bayesian optimization, and the theoretical justification for its improved exploration capabilities.

•Sep 2, 2026•0 citations

A QUBO Model for Gaussian Process Variance Reduction

Lorenzo Bottarelli, Alessandro Farinelli

Gaussian Processes are used in many applications to model spatial phenomena. Within this context, a key issue is to decide the set of locations where to take measurements so as to obtain a better approximation of the underlying function. Current state of the art techniques select such set to minimize the posterior variance of the Gaussian process. We explore the feasibility of solving this problem by proposing a novel Quadratic Unconstrained Binary Optimization (QUBO) model. In recent years this QUBO formulation has gained increasing attention since it represents the input for the specialized quantum annealer D-Wave machines. Hence, our contribution takes an important first step towards the sampling optimization of Gaussian processes in the context of quantum computation. Results of our empirical evaluation shows that the optimum of the QUBO objective function we derived represents a good solution for the above mentioned problem. In fact we are able to obtain comparable and in some cases better results than the widely used submodular technique.

arXiv:1901.10982•Jan 30, 2019•2 citations

Continuous black-box optimization with an Ising machine and random subspace coding

Syun Izawa, Koki Kitai, Shu Tanaka +2 more

A black-box optimization algorithm such as Bayesian optimization finds the extremum of an unknown function by alternating the inference of the underlying function and optimization of an acquisition function. In a high-dimensional space, such algorithms perform poorly due to the difficulty of acquisition function optimization. Herein, we apply Ising machines to overcome the difficulty in the continuous black-box optimization. As an Ising machine specializes in optimization of binary problems, a continuous vector has to be encoded to binary, and the solution by Ising machines has to be translated back. Our method has the following three parts: (1) random subspace coding based on axis-parallel hyperrectangles from continuous vector to binary vector, (2) a quadratic unconstrained binary optimization (QUBO) defined by the acquisition function based on the nonnegative-weighted linear regression model, which is solved by Ising machines, and (3) a penalization scheme to ensure that the solution can be translated back. It is shown with benchmark tests that its performance using the D-Wave Advantage quantum annealer and simulated annealing is competitive with a state-of-the-art method based on the Gaussian process in high-dimensional problems. Our method may open up the possibility of Ising machines and other QUBO solvers, including a quantum approximate optimization algorithm using gated-quantum computers, and may expand its range of application to continuous-valued problems.

Physical Review Research•Apr 21, 2022•34 citations
In materials informatics, searching for chemical materials with desired properties is challenging due to the vastness of the chemical space. Moreover, the high cost of evaluating properties necessitates a search with a few clues. In practice, there is also a demand for proposing compositions that are easily synthesizable. In the real world, such as in the exploration of chemical materials, it is common to encounter problems targeting black-box objective functions where formalizing the objective function in explicit form is challenging, and the evaluation cost is high. In recent research, a Bayesian optimization method has been proposed to formulate the quadratic unconstrained binary optimization (QUBO) problem as a surrogate model for black-box objective functions with discrete variables. Regarding this method, studies have been conducted using the D-Wave quantum annealer to optimize the acquisition function, which is based on the surrogate model and determines the next exploration point for the black-box objective function. In this paper, we address optimizing a black-box objective function containing discrete variables in the context of actual chemical material exploration. In this optimization problem, we demonstrate results obtaining parameters of the acquisition function by sampling from a probability distribution with variance can explore the solution space more extensively than in the case of no variance. As a result, we found combinations of substituents in compositions with the desired properties, which could only be discovered when we set an appropriate variance.
In solving optimization problems, objective functions generally need to be minimized or maximized. However, objective functions cannot always be formulated explicitly in a mathematical form for complicated problem settings. Although several regression techniques infer the approximate forms of objective functions, they are at times expensive to evaluate. Optimal points of "black-box" objective functions are computed in such scenarios, while effectively using a small number of clues. Recently, an efficient method by use of inference by sparse prior for a black-box objective function with binary variables has been proposed. In this method, a surrogate model was proposed in the form of a quadratic unconstrained binary optimization (QUBO) problem, and was iteratively solved to obtain the optimal solution of the black-box objective function. In the present study, we employ the D-Wave 2000Q quantum annealer, which can solve QUBO by driving the binary variables by quantum fluctuations. The D-Wave 2000Q quantum annealer does not necessarily output the ground state at the end of the protocol due to freezing effect during the process. We investigate effects from the output of the D-Wave quantum annealer in performing black-box optimization. We demonstrate a benchmark test by employing the sparse Sherrington-Kirkpatrick (SK) model as the black-box objective function, by introducing a parameter controlling the sparseness of the interaction coefficients. Comparing the results of the D-Wave quantum annealer to those of the simulated annealing (SA) and semidefinite programming (SDP), our results by the D-Wave quantum annealer and SA exhibit superiority in black-box optimization with SDP. On the other hand, we did not find any advantage of the D-Wave quantum annealer over the simulated annealing. As far as in our case, any effects by quantum fluctuation are not found.
In discrete-variable black-box optimization, the number of candidate solutions grows combinatorially, while each evaluation is often expensive. Therefore, it is important to identify promising solutions efficiently within a limited number of trials. Bayesian Optimization of Combinatorial Structures (BOCS), an existing parametric method, works effectively when only a small amount of data is available. However, as the number of observations increases, BOCS tends to repeatedly propose points that have already been evaluated, which leads to search stagnation. A random-point addition strategy has been proposed to address this issue when an evaluated point is proposed, but it cannot sufficiently exploit information from promising data obtained so far. In this study, we propose a hybrid method that uses BOCS as the main search framework and generates alternative unevaluated points using a Gaussian process only when search stagnation is detected. In the Gaussian-process-based component, multiple Lower Confidence Bound (LCB) acquisition functions are adaptively selected to dynamically control the balance between exploitation and exploration. Numerical experiments using fully connected Quadratic Unconstrained Binary Optimization (QUBO) and Higher-order Unconstrained Binary Optimization (HUBO) as black-box functions show that the proposed method finds solutions with better objective values than the conventional random-point addition method in both settings. Additional analyses show that its effectiveness comes from selecting points that promote search progress within Hamming-distance neighborhoods, rather than simply adding low-energy points near promising solutions. Experiments with sparse surrogate models for quantum annealer applications further suggest the importance of retaining near-fully connected representational capacity.
A black-box optimization algorithm such as Bayesian optimization finds extremum of an unknown function by alternating inference of the underlying function and optimization of an acquisition function. In a high-dimensional space, such algorithms perform poorly due to the difficulty of acquisition function optimization. Herein, we apply quantum annealing (QA) to overcome the difficulty in the continuous black-box optimization. As QA specializes in optimization of binary problems, a continuous vector has to be encoded to binary, and the solution of QA has to be translated back. Our method has the following three parts: 1) Random subspace coding based on axis-parallel hyperrectangles from continuous vector to binary vector. 2) A quadratic unconstrained binary optimization (QUBO) defined by acquisition function based on nonnegative-weighted linear regression model which is solved by QA. 3) A penalization scheme to ensure that the QA solution can be translated back. It is shown in benchmark tests that its performance using D-Wave AdvantageTM^{\rm TM}TM quantum annealer is competitive with a state-of-the-art method based on the Gaussian process in high-dimensional problems. Our method may open up a new possibility of quantum annealing and other QUBO solvers including quantum approximate optimization algorithm (QAOA) using a gated-quantum computers, and expand its range of application to continuous-valued problems.
Bayesian optimization has emerged as a powerful technique for tackling high-dimensional black-box optimization problems. However, its performance often degrades significantly when the dimensionality of the search space increases, a phenomenon known as the "curse of dimensionality." This paper proposes a novel approach – Quantum-Inspired Bayesian Optimization – that addresses this limitation by incorporating principles inspired by quantum computing, specifically quantum annealing. The core idea is to utilize a modified version of quantum annealing to guide the acquisition of function evaluations, exploiting superposition and interference to enhance exploration in high-dimensional spaces. We formulate the optimization problem as a quantum-inspired search, where candidate solutions exist in a superposition of states and are refined through interference effects. The algorithm iteratively updates the probability distribution over the search space, favoring regions with high potential based on the quantum-inspired exploration strategy. We demonstrate the effectiveness of this approach through theoretical analysis and illustrate its potential through conceptual examples, highlighting its ability to mitigate the curse of dimensionality and improve optimization performance compared to traditional Bayesian optimization methods. The key contributions of this work include the formalization of the quantum-inspired Bayesian optimization framework, the design of the modified quantum annealing algorithm for Bayesian optimization, and the theoretical justification for its improved exploration capabilities.
Gaussian Processes are used in many applications to model spatial phenomena. Within this context, a key issue is to decide the set of locations where to take measurements so as to obtain a better approximation of the underlying function. Current state of the art techniques select such set to minimize the posterior variance of the Gaussian process. We explore the feasibility of solving this problem by proposing a novel Quadratic Unconstrained Binary Optimization (QUBO) model. In recent years this QUBO formulation has gained increasing attention since it represents the input for the specialized quantum annealer D-Wave machines. Hence, our contribution takes an important first step towards the sampling optimization of Gaussian processes in the context of quantum computation. Results of our empirical evaluation shows that the optimum of the QUBO objective function we derived represents a good solution for the above mentioned problem. In fact we are able to obtain comparable and in some cases better results than the widely used submodular technique.
A black-box optimization algorithm such as Bayesian optimization finds the extremum of an unknown function by alternating the inference of the underlying function and optimization of an acquisition function. In a high-dimensional space, such algorithms perform poorly due to the difficulty of acquisition function optimization. Herein, we apply Ising machines to overcome the difficulty in the continuous black-box optimization. As an Ising machine specializes in optimization of binary problems, a continuous vector has to be encoded to binary, and the solution by Ising machines has to be translated back. Our method has the following three parts: (1) random subspace coding based on axis-parallel hyperrectangles from continuous vector to binary vector, (2) a quadratic unconstrained binary optimization (QUBO) defined by the acquisition function based on the nonnegative-weighted linear regression model, which is solved by Ising machines, and (3) a penalization scheme to ensure that the solution can be translated back. It is shown with benchmark tests that its performance using the D-Wave Advantage quantum annealer and simulated annealing is competitive with a state-of-the-art method based on the Gaussian process in high-dimensional problems. Our method may open up the possibility of Ising machines and other QUBO solvers, including a quantum approximate optimization algorithm using gated-quantum computers, and may expand its range of application to continuous-valued problems.