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IEEE International Conference on Quantum Computing and Engineering (QCE)

QUBO Simplification Method for Improving Solution Convergence Speed Using an Ising Machine

Shinnosuke Inaba, Takeru Ota, Chihiro Dogo, Kazuhiro Saito, Nozomu Togawa

Published Aug 30, 2025• 0 citations
Publisher

Abstract

With the increasing emphasis on energy efficiency and sustainability, optimizing the energy supply of base stations, the major energy consumers in communication networks, has become a critical problem. In addition, for real-time and scalable energy optimization in sustainable base station systems, it is necessary to obtain highly-efficient solutions in a shorter time. We formulate the base station power optimization problem as a Quadratic Unconstrained Binary Optimization (QUBO) problem, where the goal is to minimize a combination of power costs while satisfying operational constraints. Furthermore, to improve computational efficiency, we propose a QUBO simplification method that cuts down QUBO coefficients with small absolute values to zero. We solve both the original and simplified QUBOs using an Ising machine. Experimental results show that our QUBO simplification approach accelerates computation by up to 10 X on large-scale instances, with minimal degradation in solution quality.

DOI
10.1109/qce65121.2025.10411

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With the increasing emphasis on energy efficiency and sustainability, optimizing the energy supply of base stations, the major energy consumers in communication networks, has become a critical problem. In addition, for real-time and scalable energy optimization in sustainable base station systems, it is necessary to obtain highly-efficient solutions in a shorter time. We formulate the base station power optimization problem as a Quadratic Unconstrained Binary Optimization (QUBO) problem, where the goal is to minimize a combination of power costs while satisfying operational constraints. Furthermore, to improve computational efficiency, we propose a QUBO simplification method that cuts down QUBO coefficients with small absolute values to zero. We solve both the original and simplified QUBOs using an Ising machine. Experimental results show that our QUBO simplification approach accelerates computation by up to 10 X on large-scale instances, with minimal degradation in solution quality.
Ising machines, including quantum annealing machines, can efficiently solve combinatorial optimization problems by formulating them as Quadratic Unconstrained Binary Optimization (QUBO). However, it is known that the solving performance of Ising machines deteriorates as the energy landscape represented by the QUBObecomes more complex. Simplifying the coefficients of QUBOmatrix can improve the performance of solving combinatorial optimization problems using an Ising machine. In this paper, we propose QUBO simplification methods for Ising machines using singular value decomposition (SVD) and coefficient elimination based on their absolute value (ABS). The proposed SVD method simplifies QUBO by capturing the global structure of the QUBO matrix. QUBO is further simplified by combining it with the simple ABS method. The simplified QUBO is expected to have a less complex energy landscape, while maintaining the global structure of the original, enabling the Ising machine to efficiently find the (semi-)ground state.We demonstrate the numerical experiments using an Ising machine to evaluate the effectiveness of the SVD method alone, the ABS method alone, and the two methods combined.
As global energy demand continues to rise, efficient energy management is essential to support the growing integration of renewable energy in the energy mix while controlling operational costs. This paper introduces a method that leverages non-exact Quadratic Unconstrained Binary Optimization (QUBO) formulation combined with tailored post-processing to boost the optimization of the energy management problem of 5G base stations. Unlike traditional rule-based approaches, which rely heavily on domain expertise and manual design, we propose a systematic QUBO-based framework suitable for Quantum Annealing (QA). The proposed formulation significantly reduces the number of decision variables (from 1995 in an exact QUBO to approximately 144) making it compatible with current QA hardware while producing high-quality solutions. Furthermore, the post-processing steps further improve solution quality, increasing the global optimal solution achievement rate by 10–15% depending on the solver. Experimental results demonstrate that the proposed method is deployable on current hardware and achieves performance comparable to conventional rule-based systems. Such observations highlight the potential of such designs in solving real-world optimization challenges.
The performance of an Ising machine in solving combinatorial optimization problems is significantly influenced by the energy landscape of an input quadratic unconstrained binary optimization (QUBO). Previous studies have shown that the number of non-zero terms in QUBO can control the energy landscape. In this paper, we propose a QUBO conversion method, which efficiently removes non-zero coefficient terms in QUBO to improve the solving performance of Ising machines. Our pro-posed method uses the removal ratio parameter, which defines the amount of removed non-zero terms, and efficiently removes the non-zero coefficient terms in QUBO. We confirm the effectiveness of the proposed method compared to the conventional method using the capacitated vehicle routing problem (CVRP) on an Ising machine. Experimental results demonstrate that our proposed method improves the path length in CVRP up to 17% compared to the conventional method.
This paper develops an algorithmic solution using Ising machines to solve large-scale higher-order binary optimization (HOBO) problems with inequality constraints for resource optimization in wireless communications systems. Quadratic unconstrained binary optimization (QUBO) aims to solve a special category of these problems widely encountered in engineering and science. To solve QUBO instances, specialized Ising machines have been designed, while sophisticated quantum annealing algorithm and quantum-inspired classical heuristics have been developed. However, the application of QUBO in wireless communications has limited practical interest mainly due to the complexity of resource optimization problems which are often characterized by high-order polynomial terms and strict inequality constraints. To overcome these bottlenecks and take advantage of recent advancements in Ising machines, in this paper, we propose an iterative algorithmic solution to solve HOBO problems, which is based on the augmented Lagrangian method to handle constraints. Specifically, Taylor expansion is employed to approximate higher-order polynomials to quadratic ones in the augmented Lagrangian function, which enables the solution of a single QUBO problem at each iteration without auxiliary variables. As an illustrative case study, we consider the problem of phase optimization in a simultaneous wireless information and power transfer system, where a reconfigurable intelligent surface with 1-bit phase resolution is used to facilitate information/energy transfer. Simulation results verify that the proposed algorithm achieves satisfactory performance and outperforms heuristic benchmark schemes.
Ising machines have attracted much attention in recent years because of their potential in solving combinatorial optimization problems that are difficult to be solved using conventional computers. Ising machines solve the optimization problem that can be transformed into a quadratic unconstrained binary optimization (QUBO) problem. In the case of a problem with constraints, named a constraint problem, an objective function and constraint function with penalty coefficients are combined into a single Hamiltonian of a QUBO problem. When solving a constraint problem, the accuracy of the solution decreases compared to a QUBO problem with an objective function only. This is because penalty coefficients are set to excessively large values to prevent constraint violations. As a result, it becomes difficult to minimize the objective function. To solve this problem, this paper proposes a method that partitions constraint functions and reduces the value of the penalty coefficients. The performance evaluation using the traveling salesperson problem (TSP) with one-hot constraints demonstrates that the proposed method can improve the solution accuracy compared to the conventional method.
Ising machines are next-generation computers expected to efficiently sample near-optimal solutions of combinatorial optimization problems. Combinatorial optimization problems are modeled as quadratic unconstrained binary optimization (QUBO) problems to apply an Ising machine. However, current state-of-the-art Ising machines still often fail to output nearoptimal solutions due to the complicated energy landscape of QUBO problems. Furthermore, the physical implementation of Ising machines severely restricts the size of QUBO problems to be input as a result of limited hardware graph structures. In this study, we take a new approach to these challenges by injecting auxiliary penalties preserving the optimum, which reduces quadratic terms in QUBO objective functions. The process simultaneously simplifies the energy landscape of QUBO problems, allowing the search for near-optimal solutions, and makes QUBO problems sparser, facilitating encoding into Ising machines with restriction on the hardware graph structure. We propose linearization of QUBO problems using variable posets as an outcome of the approach. By applying the proposed method to synthetic QUBO instances and to multi-dimensional knapsack problems, we empirically validate the effects on enhancing minorembedding of QUBO problems and the performance of Ising machines.