We introduce VeloxQ, a fast solver for Quadratic Unconstrained Binary Optimization (QUBO) problems, which are central to many real-world optimization tasks. Unlike approaches that depend on emerging quantum hardware, VeloxQ can be deployed on conventional computing infrastructure. We benchmark VeloxQ against state-of-the-art QUBO solvers from several families. These include quantum annealers, specifically D-Wave's Advantage and Advantage2 platforms; the digital-quantum BF-DCQO algorithm for Higher-Order Unconstrained Binary Optimization (HUBO) developed by Kipu Quantum; physics-inspired algorithms including Simulated Bifurcation, Parallel Annealing, and tropical tensor networks; and conventional methods including CPLEX, brute force, BEIT's Chimera solver, and Branch-and-Bound variants. The benchmark suite covers native quantum-annealer topologies, embedded all-to-all instances, HUBO-derived instances, planted-solution instances, certified-solver regimes, and dense Branch-and-Bound test cases. Across the benchmark suite, VeloxQ delivers competitive solution quality and runtime, and in several regimes outperforms the compared solvers. VeloxQ also demonstrates strong scalability. Among the solvers considered in this study, it was the only method we could run on the largest sparse instances within our computational budget, including problems with up to $10^{8}$ sparsely connected variables. These findings position VeloxQ as a competitive and practical tool for tackling large-scale QUBO/HUBO problems, offering a practical alternative to existing quantum and classical optimization methods.
We introduce VeloxQ, a fast solver for Quadratic Unconstrained Binary Optimization (QUBO) problems, which are central to many real-world optimization tasks. Unlike approaches that depend on emerging quantum hardware, VeloxQ can be deployed on conventional computing infrastructure. We benchmark VeloxQ against state-of-the-art QUBO solvers from several families. These include quantum annealers, specifically D-Wave's Advantage and Advantage2 platforms; the digital-quantum BF-DCQO algorithm for Higher-Order Unconstrained Binary Optimization (HUBO) developed by Kipu Quantum; physics-inspired algorithms including Simulated Bifurcation, Parallel Annealing, and tropical tensor networks; and conventional methods including CPLEX, brute force, BEIT's Chimera solver, and Branch-and-Bound variants. The benchmark suite covers native quantum-annealer topologies, embedded all-to-all instances, HUBO-derived instances, planted-solution instances, certified-solver regimes, and dense Branch-and-Bound test cases. Across the benchmark suite, VeloxQ delivers competitive solution quality and runtime, and in several regimes outperforms the compared solvers. VeloxQ also demonstrates strong scalability. Among the solvers considered in this study, it was the only method we could run on the largest sparse instances within our computational budget, including problems with up to 108 sparsely connected variables. These findings position VeloxQ as a competitive and practical tool for tackling large-scale QUBO/HUBO problems, offering a practical alternative to existing quantum and classical optimization methods.
Quadratic Unconstrained Binary Optimization (QUBO) provides a versatile framework for representing NP-hard combinatorial problems, yet existing solvers often face trade-offs among speed, accuracy, and scalability. In this work, we introduce a quantum-inspired solver (QIS) that unites branch-and-bound pruning, continuous gradient-descent refinement, and quantum-inspired heuristics within a fully adaptive control architecture. We benchmark QIS3 against eight state-of-the-art solvers, including genetic algorithms, coherent Ising machines, simulated bifurcation, parallel tempering, simulated annealing, our prior QIS2 version, D-Wave's simulated-annealing (Neal), and Gurobi on three canonical QUBO problem classes: Max-Cut, NAE-3SAT, and Sherrington-Kirkpatrick spin glass problems. Under a uniform runtime budget, QIS3 attains the best solution on nearly all instances, achieving optimality in 94% of max-cut instances. These results establish QIS3 as a robust, high-performance solver that bridges classical exact strategies and quantum-inspired heuristics for scalable QUBO optimization.
Abstract Quantum computers have strict requirements for the problems that they can efficiently solve. One of the principal limiting factor for the performances of noisy intermediate-scale quantum (NISQ) devices is the number of qubits required by the running algorithm. Several combinatorial optimization problems can be solved with NISQ devices once that a corresponding quadratic unconstrained binary optimization (QUBO) form is derived. Numerous techniques have been proposed to achieve such reformulations and, depending on the method chosen, the number of binary variables required, and therefore of qubits, can vary considerably. The aim of this work is to drastically reduce the variables needed for these QUBO reformulations in order to unlock the possibility to efficiently obtain optimal solutions for a class of optimization problems with NISQ devices. This goal is achieved by introducing novel tools that allow an efficient use of slack variables, even for problems with non-linear constraints, without the need to approximate the starting problem. We divide our new techniques in two independent parts, called the iterative quadratic polynomial and the master-satellite methods. Hence, we show how to apply our techniques in case of an NP-hard optimization problem inspired by a real-world financial scenario called Max-Profit Balance Settlement . We follow by submitting several instances of this problem to two D-wave quantum annealers, comparing the performances of our novel approach with the standard methods used in these scenarios. Moreover, this study allows to appreciate several performance differences between the D-wave Advantage and next-generation Advantage2 quantum annealers. We show that the adoption of our techniques in this context allows to obtain QUBO formulations with significantly fewer slack variables, i.e. around 90% less, and D-wave annealers provide considerably higher correct solution rates, which moreover do not decrease with the input size as fast as when adopting standard techniques.
Recent advancements in quantum computing have demonstrated significant potential for solving combinatorial optimization problems, like the quadratic knapsack problem, a constrained binary optimization problem. However, current quantum and quantum-inspired algorithms often require transforming these constrained problems into an unconstrained form, known as Quadratic Unconstrained Binary Optimization (QUBO). Such transformations can significantly impact the algorithms’ speed and efficiency. In this study, we evaluate five existing transformation methods and propose four novel approaches. We assess all nine methods using Simulated Annealing and find that three of our approaches outperform existing methods in terms of execution time and the quality and quantity of feasible solutions found. Additionally, we tested these transformations on quantum annealers, which were unable to solve even small problem instances, due to limitations in connectivity and error rates. However, our results highlight the advantages of the new approaches, which reduce the total number of variables in the QUBO representation. This is a critical factor for enhanced performance on emerging quantum hardware, since it also reduces the required number of qubits and the embedding chain lengths.
Recent advancements in quantum computing have demonstrated significant potential for solving combinatorial optimization problems, like the quadratic knapsack problem, a constrained binary optimization problem. However, current quantum and quantum-inspired algorithms often require transforming these constrained problems into an unconstrained form, known as Quadratic Unconstrained Binary Optimization (QUBO). Such transformations can significantly impact the algorithms’ speed and efficiency. In this study, we evaluate five existing transformation methods and propose four novel approaches. We assess all nine methods using Simulated Annealing and find that three of our approaches outperform existing methods in terms of execution time and the quality and quantity of feasible solutions found. Additionally, we tested these transformations on quantum annealers, which were unable to solve even small problem instances, due to limitations in connectivity and error rates. However, our results highlight the advantages of the new approaches, which reduce the total number of variables in the QUBO representation. This is a critical factor for enhanced performance on emerging quantum hardware, since it also reduces the required number of qubits and the embedding chain lengths.
As Moore’s Law slows, alternative computing paradigms are essential for tackling complex combinatorial optimization problems. This paper introduces DigiQUBO, a high-performance digital Quadratic Unconstrained Binary Optimization (QUBO) solver designed for quantum-inspired optimization. DigiQUBO leverages a advanced Digital Annealing (DA) approach to efficiently solve large-scale QUBO problems, offering a competitive alternative to traditional annealing methods. To evaluate its effectiveness, DigiQUBO is applied to the Traveling Salesman Problem (TSP), a well-known NP-hard problem with applications in logistics, network design, and computational biology. In solving a 40-city Traveling Salesman Problem (TSP), DigiQUBO achieved an average route distance improvement of 13% compared to Simulated Annealing (SA), and a reduction of 37% compared to D-Wave’s LeapHybridSampler, while maintaining comparable runtime to Fujitsu DA3. DigiQUBO significantly enhances solution quality and computational efficiency by integrating two key advanced techniques: two-way one-hot group encoding for improved constraint satisfaction and Bayesian Optimization for automated annealing parameter tuning. Performance comparisons against Simulated Annealing (SA), Fujitsu DA3, and D-Wave’s LeapHybridSampler demonstrate superior results in balancing accuracy and execution time. The results highlight DigiQUBO as a promising digital annealing technology that bridges the gap between classical and quantum optimization, offering a practical and efficient solution in the post-Moore’s Law era.
Recent advancements in quantum computing have demonstrated significant potential for solving combinatorial optimization problems, like the quadratic knapsack problem, a constrained binary optimization problem. How- ever, current quantum and quantum-inspired algorithms often require transforming these constrained problems into an unconstrained form, known as Quadratic Unconstrained Binary Optimization (QUBO). Such transfor- mations can significantly impact the algorithms’ speed and efficiency. In this study, we evaluate five existing transformation methods and propose four novel approaches. We assess all nine methods using Simulated An- nealing and find that three of our approaches outperform existing methods in terms of execution time and the quality and quantity of feasible solutions found. Additionally, we tested these transformations on quantum annealers, which were unable to solve even small problem instances, due to limitations in connectivity and error rates. However, our results highlight the advantages of the new approaches, which reduce the total num- ber of variables in the QUBO representation. This is a critical factor for enhanced performance on emerging quantum hardware, since it also reduces the required number of qubits and the embedding chain lengths.