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An increasingly popular method for solving a constrained combinatorial optimisation problem is to first convert it into a quadratic unconstrained binary optimisation (QUBO) problem, and solve it using a standard QUBO solver. However, this…

Machine Learning · Computer Science 2021-03-22 Tian Huang , Siong Thye Goh , Sabrish Gopalakrishnan , Tao Luo , Qianxiao Li , Hoong Chuin Lau

In the field of quantum computing, combinatorial optimization problems are typically addressed using QUBO (Quadratic Unconstrained Binary Optimization) solvers. However, these solvers are often insufficient for tackling higher-order…

Quantum Physics · Physics 2024-07-24 Yuichiro Minato

Quadratic Unconstrained Binary Optimization (QUBO) sits at the heart of many industries and academic fields such as logistics, supply chain, finance, pharmaceutical science, chemistry, IT, and energy sectors, among others. These problems…

Quantum Physics · Physics 2025-12-02 Chia-Tso Lai , Carsten Blank , Peter Schmelcher , Rick Mukherjee

The quantum approximate optimization algorithm (QAOA) is designed to determine optimum and near optimum solutions of quadratic (and higher order) unconstrained binary optimization (QUBO or HUBO) problems, which in turn accurately model…

Quantum Physics · Physics 2025-03-18 Prashanti Priya Angara , Danylo Lykov , Ulrike Stege , Yuri Alexeev , Hausi Müller

Simulated annealing (SA) is a key algorithm for solving combinatorial optimization problems, which model numerous real-world systems. While SA is commonly used to solve quadratic unconstrained binary optimization (QUBO) problems, many…

Statistical Mechanics · Physics 2026-05-05 Kohei Suzuki

With the development of quantum computing, the use of quantum algorithms to solve combinatorial optimization problems on quantum computers has become a major research focus. The Quadratic Unconstrained Binary Optimization (QUBO) model…

Computational Engineering, Finance, and Science · Computer Science 2025-04-10 Haoqian Pan , Changhong Lu

We investigate the use of amplitude amplification on the gate-based model of quantum computing as a means for solving combinatorial optimization problems. This study focuses primarily on QUBO (quadratic unconstrained binary optimization)…

Quantum Physics · Physics 2023-02-02 Daniel Koch , Massimiliano Cutugno , Saahil Patel , Laura Wessing , Paul M. Alsing

The Travelling Salesman Problem (TSP) is an important combinatorial optimisation problem, and is usually solved on a quantum computer using a Quadratic Unconstrained Binary Optimisation (QUBO) formulation or a Higher Order Binary…

Quantum Physics · Physics 2024-06-21 Daniel Goldsmith , Joe Day-Evans

Quantum approximate optimization is one of the promising candidates for useful quantum computation, particularly in the context of finding approximate solutions to Quadratic Unconstrained Binary Optimization (QUBO) problems. However, the…

We propose and analyze a set of variational quantum algorithms for solving quadratic unconstrained binary optimization problems where a problem consisting of $n_c$ classical variables can be implemented on $\mathcal O(\log n_c)$ number of…

Quadratic Unconstrained Binary Optimization (QUBO) is a combinatorial optimization to find an optimal binary solution vector that minimizes the energy value defined by a quadratic formula of binary variables in the vector. As many NP-hard…

Performance · Computer Science 2023-10-19 Koji Nakano , Daisuke Takafuji , Yasuaki Ito , Takashi Yazane , Junko Yano , Shiro Ozaki , Ryota Katsuki , Rie Mori

The Pseudo-Boolean Optimization (PBO) and Maximum Satisfiability (MaxSAT) problems are natural optimization extensions of Boolean Satisfiability (SAT). In the recent past, different algorithms have been proposed for PBO and for MaxSAT,…

Artificial Intelligence · Computer Science 2009-03-06 Vasco Manquinho , Joao Marques-Silva , Jordi Planes

In recent years, formulating various combinatorial optimization problems as Quadratic Unconstrained Binary Optimization (QUBO) has gained significant attention as a promising approach for efficiently obtaining optimal or near-optimal…

Optimization and Control · Mathematics 2025-04-14 Kyo Kuroki , Thiem Van Chu , Masato Motomura , Kazushi Kawamura

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)…

Optimization and Control · Mathematics 2024-06-21 Kentaro Ohno , Nozomu Togawa

We introduce a physics-inspired continuous relaxation framework that yields substantially improved solutions for NP-hard combinatorial optimization problems, including Quadratic Unconstrained Binary Optimization (QUBO), binary sparse…

Statistical Mechanics · Physics 2026-05-26 Khen Cohen , Mark Glass , Meir Feder , Yaron Oz

Many of the envisioned use-cases for quantum computers involve optimisation processes. While there are many algorithmic primitives to perform the required calculations, all eventually lead to quantum gates operating on quantum bits, with an…

Quantum Physics · Physics 2026-03-26 Lukas Schmidbauer , Elisabeth Lobe , Ina Schaefer , Wolfgang Mauerer

This paper proposes a hybrid quantum-classical algorithm to solve a fundamental power system problem called unit commitment (UC). The UC problem is decomposed into a quadratic subproblem, a quadratic unconstrained binary optimization (QUBO)…

Quantum Physics · Physics 2022-04-19 Reza Mahroo , Amin Kargarian

This paper presents a new method to reduce the optimization of a pseudo-Boolean function to QUBO problem which can be solved by quantum annealer. The new method has two aspects, one is coefficient optimization and the other is variable…

Cryptography and Security · Computer Science 2022-11-21 Anpeng Zhang , Xiutao Feng

Neural network pruning can be formulated as a combinatorial optimization problem, yet most existing approaches rely on greedy heuristics that ignore complex interactions between filters. Formal optimization methods such as Quadratic…

Computer Vision and Pattern Recognition · Computer Science 2026-04-08 Osama Orabi , Artur Zagitov , Hadi Salloum , Viktor A. Lobachev , Kasymkhan Khubiev , Yaroslav Kholodov

Solving combinatorial optimization problems of the kind that can be codified by quadratic unconstrained binary optimization (QUBO) is a promising application of quantum computation. Some problems of this class suitable for practical…

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