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

IEEE Access

Construction of SubQUBOs by K-Means Clustering of QUBO Variables

Yuko Kamishima, Shuta Kikuchi, Shu Tanaka

Published Jan 1, 2025• 1 citation
Publisher

Abstract

Ising machines are specialized solvers for combinatorial optimization problems (COPs), which are typically formulated as quadratic unconstrained binary optimization (QUBO) models. To enhance their performance, various methods have been proposed to construct subQUBOs by reducing the number of variables in the original QUBO. This study proposes a general subQUBO construction method applicable to a wide range of problems. The variables are clustered based on their interaction structure using theK-means clustering. A subQUBO is constructed from a randomly selected cluster and a pre-obtained tentative solution and then solved. This process of cluster selection and subQUBOs is performed iteratively. We evaluated the performance of the method on the quadratic assignment problem and compared it with two baselines: one that randomly reduces variables and another that directly solves the original QUBO without any variable reduction. Experimental evaluations demonstrated that the proposed method achieves high-accuracy solutions within the same computation time, particularly for large problem sizes.

DOI
10.1109/access.2025.3638373

Related papers

SubQUBO Construction Based on Grid Reduction Method Using an Ising Machine

Koki Mita, Takeru Ota, Nozomu Togawa

Ising machines can efficiently solve combinatorial optimization problems by mapping them to Ising or QUBO formulations while satisfying given constraints. However, their hardware limits the size of QUBO instances. To overcome this, subQUBO annealing decomposes large problems into smaller ones. Meanwhile, conventional subQUBO construction methods often violate the constraints originally given. In this paper, we propose a grid reduction method for subQUBO construction that explicitly considers the 2-way 1-hot constraint. It recursively fixes a variable to 1 and sets all other variables in the same row and column to 0. Remaining variables are used to construct subQUBOs with three strategies: index-based, deviation-based, and random-based extraction. Evaluation experiments using a real Ising machine demonstrates significant energy reduction over existing subQUBO construction methods.

IEEE International Conference on Quantum Computing and Engineering (QCE)•Aug 30, 2025•0 citations

Variable Reduction Method for Quadratic Three-Dimensional Assignment Problem with FMQA

Sora Tomita, Tatsuhiko Shirai, Nozomu Togawa

Ising machines including quantum annealers have attracted attention as efficient solvers for combinatorial optimization problems (COPs). To use Ising machines, the objective function and constraints of a COP must be expressed in a QUBO (quadratic unconstrained binary optimization) form. However, their application range is practically limited since some COPs are difficult to formulate in a QUBO form, or require a large number of binary variables. Quadratic three-dimensional assignment problem (Q3AP) is a challenging problem for Ising machines to solve since the number of required binary variables rapidly increases with the problem size N. In this paper, to overcome the difficulty, we propose a method to reduce the number of necessary variables from$N^{3}$to$2N^{2}$by using a factorization machine with quantum annealing (FMQA) to estimate QUBO through machine learning. Experimental results with a real Ising machine demonstrate that the proposed method can obtain the best-known solution in a short time.

IEEE International Conference on Quantum Computing and Engineering (QCE)•Sep 15, 2024•0 citations

Distance-based clustering using QUBO formulations

Nasa Matsumoto, Yohei Hamakawa, Kosuke Tatsumura +1 more

In computer science, clustering is a technique for grouping data. Ising machines can solve distance-based clustering problems described by quadratic unconstrained binary optimization (QUBO) formulations. A typical simple method using an Ising machine makes each cluster size equal and is not suitable for clustering unevenly distributed data. We propose a new clustering method that provides better performance than the simple method, especially for unevenly distributed data. The proposed method is a hybrid algorithm including an iterative process that comprises solving a discrete optimization problem with an Ising machine and calculating parameters with a general-purpose computer. To minimize the communication overhead between the Ising machine and the general-purpose computer, we employed a low-latency Ising machine implementing the simulated bifurcation algorithm with a field-programmable gate array attached to a local server. The proposed method results in clustering 200 unevenly distributed data points with a clustering score 18% higher than that of the simple method. The discrete optimization with 2000 variables is performed 100 times per iteration, and the overhead time is reduced to approximately 20% of the total execution time. These results suggest that hybrid algorithms using Ising machines can efficiently solve practical optimization problems.

Scientific Reports•Feb 17, 2022•24 citations

Trip Planning Based on subQUBO Annealing

Tatsuya Noguchi, Keisuke Fukada, Siya Bao +1 more

The trip planning problem (TPP) can be formulated as a combinatorial optimization problem that searches for the best route to visit a series of landmarks and hotels. Meanwhile, Ising machines have attracted attention due to their efficiency in solving combinatorial optimization problems. The Ising machines solve the combinatorial optimization problems by transforming the problems into quadratic unconstrained binary optimization (QUBO) models. However, the possible input QUBO size of current Ising machines is quite limited. Thus, it is hard to directly embed a large-scale TPP onto the current Ising machines. In this paper, we propose a novel subQUBO annealing method based on the combined variable selection method to solve the TPP. The proposed method finds a quasi-optimal solution to a large problem by repeatedly partitioning the original QUBO model into small subQUBOs that can be embedded onto the Ising machine. Specifically, to construct a subQUBO, we select variables from the original QUBO model, which have small deviation values. Further, we select variables randomly from the original QUBO model, so as not to fall into the local optimum. We have conducted an evaluation experiment using Ising machines on TPP and confirmed that the proposed method outperforms the state-of-the-art methods in terms of POI satisfaction and POI cost.

IEEE Access•Jan 1, 2023•9 citations

Dynamic Variable Selection for subQUBO Annealing Using Hamming Weight

Yoshihito Saito, Koki Mita, Nozomu Togawa

Although Ising machines can efficiently solve combinatorial optimization problems, their direct application to largescale instances is infeasible due to an upper limit on the number of input variables. An effective approach to overcome this limitation is to partition the problem into smaller subproblems, known as subQUBOs. In this paper, we propose a dynamic variable selection method for subQUBOs that considers the Hamming weight of current solutions. Our proposed method constructs a subQUBO by dynamically selecting variables that are assigned a value of ‘1’—that is, focusing on the Hamming weight—in the current solution during the annealing process. This approach is expected to facilitate more substantial energy updates during iterations, thereby increasing the probability of finding optimal or near-optimal solutions. Finally, we demonstrate the effectiveness of our proposed method through experimental evaluations.

International Conference on Consumer Electronics•Feb 3, 2026•0 citations

SubQUBO Annealing Based on Efficient Binary Variable Selection for Combinatorial Optimization Problems with One-Hot Constraints

Tatsuya Noguchi, Keisuke Fukada, Siya Bao +1 more

In combinatorial optimization problems with one-hot constraints, the number of binary variables that have the value of one in the feasible solution becomes constant and small, so it is important to always consider them to escalate the solution searching process and obtain a more converged solution in annealing. In this paper, we propose a method to preferably select binary variables with the value of one in the subQUBO annealing process using Ising machines such as quantum annealers. Evaluation experiments show that the proposed method obtains a solution with lower energy than a conventional subQUBO method and a full QUBO method.

International Conference on Consumer Electronics•Jan 11, 2025•1 citation
Ising machines are specialized solvers for combinatorial optimization problems (COPs), which are typically formulated as quadratic unconstrained binary optimization (QUBO) models. To enhance their performance, various methods have been proposed to construct subQUBOs by reducing the number of variables in the original QUBO. This study proposes a general subQUBO construction method applicable to a wide range of problems. The variables are clustered based on their interaction structure using theK-means clustering. A subQUBO is constructed from a randomly selected cluster and a pre-obtained tentative solution and then solved. This process of cluster selection and subQUBOs is performed iteratively. We evaluated the performance of the method on the quadratic assignment problem and compared it with two baselines: one that randomly reduces variables and another that directly solves the original QUBO without any variable reduction. Experimental evaluations demonstrated that the proposed method achieves high-accuracy solutions within the same computation time, particularly for large problem sizes.
Ising machines can efficiently solve combinatorial optimization problems by mapping them to Ising or QUBO formulations while satisfying given constraints. However, their hardware limits the size of QUBO instances. To overcome this, subQUBO annealing decomposes large problems into smaller ones. Meanwhile, conventional subQUBO construction methods often violate the constraints originally given. In this paper, we propose a grid reduction method for subQUBO construction that explicitly considers the 2-way 1-hot constraint. It recursively fixes a variable to 1 and sets all other variables in the same row and column to 0. Remaining variables are used to construct subQUBOs with three strategies: index-based, deviation-based, and random-based extraction. Evaluation experiments using a real Ising machine demonstrates significant energy reduction over existing subQUBO construction methods.
Ising machines including quantum annealers have attracted attention as efficient solvers for combinatorial optimization problems (COPs). To use Ising machines, the objective function and constraints of a COP must be expressed in a QUBO (quadratic unconstrained binary optimization) form. However, their application range is practically limited since some COPs are difficult to formulate in a QUBO form, or require a large number of binary variables. Quadratic three-dimensional assignment problem (Q3AP) is a challenging problem for Ising machines to solve since the number of required binary variables rapidly increases with the problem size N. In this paper, to overcome the difficulty, we propose a method to reduce the number of necessary variables fromN3N^{3}N3to2N22N^{2}2N2by using a factorization machine with quantum annealing (FMQA) to estimate QUBO through machine learning. Experimental results with a real Ising machine demonstrate that the proposed method can obtain the best-known solution in a short time.
In computer science, clustering is a technique for grouping data. Ising machines can solve distance-based clustering problems described by quadratic unconstrained binary optimization (QUBO) formulations. A typical simple method using an Ising machine makes each cluster size equal and is not suitable for clustering unevenly distributed data. We propose a new clustering method that provides better performance than the simple method, especially for unevenly distributed data. The proposed method is a hybrid algorithm including an iterative process that comprises solving a discrete optimization problem with an Ising machine and calculating parameters with a general-purpose computer. To minimize the communication overhead between the Ising machine and the general-purpose computer, we employed a low-latency Ising machine implementing the simulated bifurcation algorithm with a field-programmable gate array attached to a local server. The proposed method results in clustering 200 unevenly distributed data points with a clustering score 18% higher than that of the simple method. The discrete optimization with 2000 variables is performed 100 times per iteration, and the overhead time is reduced to approximately 20% of the total execution time. These results suggest that hybrid algorithms using Ising machines can efficiently solve practical optimization problems.
The trip planning problem (TPP) can be formulated as a combinatorial optimization problem that searches for the best route to visit a series of landmarks and hotels. Meanwhile, Ising machines have attracted attention due to their efficiency in solving combinatorial optimization problems. The Ising machines solve the combinatorial optimization problems by transforming the problems into quadratic unconstrained binary optimization (QUBO) models. However, the possible input QUBO size of current Ising machines is quite limited. Thus, it is hard to directly embed a large-scale TPP onto the current Ising machines. In this paper, we propose a novel subQUBO annealing method based on the combined variable selection method to solve the TPP. The proposed method finds a quasi-optimal solution to a large problem by repeatedly partitioning the original QUBO model into small subQUBOs that can be embedded onto the Ising machine. Specifically, to construct a subQUBO, we select variables from the original QUBO model, which have small deviation values. Further, we select variables randomly from the original QUBO model, so as not to fall into the local optimum. We have conducted an evaluation experiment using Ising machines on TPP and confirmed that the proposed method outperforms the state-of-the-art methods in terms of POI satisfaction and POI cost.
Although Ising machines can efficiently solve combinatorial optimization problems, their direct application to largescale instances is infeasible due to an upper limit on the number of input variables. An effective approach to overcome this limitation is to partition the problem into smaller subproblems, known as subQUBOs. In this paper, we propose a dynamic variable selection method for subQUBOs that considers the Hamming weight of current solutions. Our proposed method constructs a subQUBO by dynamically selecting variables that are assigned a value of ‘1’—that is, focusing on the Hamming weight—in the current solution during the annealing process. This approach is expected to facilitate more substantial energy updates during iterations, thereby increasing the probability of finding optimal or near-optimal solutions. Finally, we demonstrate the effectiveness of our proposed method through experimental evaluations.
In combinatorial optimization problems with one-hot constraints, the number of binary variables that have the value of one in the feasible solution becomes constant and small, so it is important to always consider them to escalate the solution searching process and obtain a more converged solution in annealing. In this paper, we propose a method to preferably select binary variables with the value of one in the subQUBO annealing process using Ising machines such as quantum annealers. Evaluation experiments show that the proposed method obtains a solution with lower energy than a conventional subQUBO method and a full QUBO method.