This paper proposes a novel model of QISA (Quantum-Inspired Simulated Annealing) which embeds quantum computation into the Simulated Annealing (SA) process for optimization problems. Compared with previous SA studies, QISA adopts Quantum Bits (Qubits) rather than the conventional binary bits as the coding scheme, and update the entries in the Qubits sequence with different probabilities by the proposed methods of heat observation and quantum rotation gate. By flexibly controlling the heating function and rotation angle, QISA does not have to either accept or reject, but can partially accept a new solution. The careful experiments on a number of numerical optimization and combinatorial optimization problems validate its better convergent performance and lower sensitivity to parameters.
This paper proposes a novel model of QISA (Quantum-Inspired Simulated Annealing) which embeds quantum computation into the Simulated Annealing (SA) process for optimization problems. Compared with previous SA studies, QISA adopts Quantum Bits (Qubits) rather than the conventional binary bits as the coding scheme, and update the entries in the Qubits sequence with different probabilities by the proposed methods of heat observation and quantum rotation gate. By flexibly controlling the heating function and rotation angle, QISA does not have to either accept or reject, but can partially accept a new solution. The careful experiments on a number of numerical optimization and combinatorial optimization problems validate its better convergent performance and lower sensitivity to parameters.
Quantum computing has emerged as a promising computational paradigm with the potential to solve problems that are intractable for classical computers. This paper provides an overview of the current state of quantum computing, including its historical development, hardware advancements, applications, and challenges. Special attention is given to combinatorial optimization, which is considered one of the most promising application domains. The limitations of current quantum systems and future research directions are also discussed. This paper presents a comparative study between a conventional D-Wave-based simulated annealing approach and a proposed hybrid optimization model for solving largescale combinatorial optimization problems. The study focuses on benchmark problems, including AES, TSP gr24, and a real-world load balancing problem, all formulated as QUBO models. The D-Wave approach employs the dwave-neal simulated annealing engine with various parameter settings, while the proposed model introduces a decomposition-based framework combined with adaptive parameter control and iterative refinement. The experimental results demonstrate that the proposed model consistently outperforms the conventional approach in terms of solution quality, achieving significantly lower energy values across all problem instances. In particular, for the TSP gr24 problem, the proposed model achieves near-optimal solutions with substantially reduced computation time. For large-scale problems such as AES and load balancing, the proposed model maintains scalability and robustness, whereas the conventional approach suffers from increased computational cost and performance degradation. Although the proposed method introduces additional computational steps, its hybrid structure effectively mitigates limitations related to local minima, parameter sensitivity, and scalability. These findings indicate that integrating classical optimization techniques with quantum-inspired methods is essential for practical applications. The proposed model provides a promising framework for solving complex real-world optimization problems and highlights the importance of hybrid approaches in advancing quantum annealing technologies.
Quantum-inspired genetic algorithm (QGA) is applied to simulated annealing (SA) to develop a class of quantum-inspired simulated annealing genetic algorithm (QSAGA) for combinatorial optimization. With the condition of preserving QGA advantages, QSAGA takes advantage of the SA algorithm so as to avoid premature convergence. To demonstrate its effectiveness and applicability, experiments are carried out on the knapsack problem. The results show that QSAGA performs well, without premature convergence as compared to QGA.
In the field of combinatorial optimization (CO), quantum computing is increasingly recognized for its potential to provide groundbreaking solutions. However, embedding the problems into quantum circuits presents significant challenges due to the complexities of scaling to large dimensions and the constraints in qubit count and circuit depth.In this paper, we introduce a quantum neural simulated annealing (QNSA) framework, combining both simulated annealing (SA) in the classical domain and quantum neural networks (QNNs) in the quantum domain to address the computational challenges for large-scale problems. By employing an SA algorithm, we can explore the vast combination space of optimization problems. In addition, by incorporating QNNs with proposed adaptive embedding and observable, our approach extends beyond the standalone capabilities of quantum computing, leveraging the unique strengths of both quantum and classical computing paradigms. Our experimental results show that the QNSA framework significantly outperforms traditional classical computing methods, showcasing its potential for efficient problem-solving in complex scenarios.
Quantum annealing is an emerging metaheuristic used for solving combinatorial optimisation problems. However, hardware based physical quantum annealers are primarily limited to a single vendor. As an alternative, we can discretise the quantum annealing process (discretised quantum annealing or DiQA) and use it on gate-model quantum computers. In this work, we first benchmark DiQA against simulated annealing for a similar number of steps. We then propose and evaluate a hybrid quantum classical heuristic: Quantum Accelerated Simulated Annealing (QASA), where the traditional classical annealing procedure can be sped up with the use of (relatively) low depth DiQA circuits. This is done by (i) running a partial annealing scheme with a fraction of the depth of the complete circuit (ii) sampling the results from the circuit and fitting a Gibbs distribution on it and (iii) Using the inverse temperature of the Gibbs distribution and the best sample to initialise simulated annealing (SA). Our simulation results show QASA performing comparably to SA but for a reduced amount of steps. With the promising results of our work, we hope to generate interest for potential future work in the area of fixed-parameter quantum optimisation.
Recent advances in quantum computing have shown great potential for solving combinatorial optimization problems. A notable example is the quadratic knapsack problem, a constrained binary optimization problem. However, current quantum-inspired algorithms require Quadratic Unconstrained Binary Optimization (QUBO) formulations. Transforming constrained optimization into QUBO impacts the algorithms' speed and efficiency. In this study, we evaluate five existing transformation methods and propose four novel approaches. We assess them by using Simulated Annealing (SA), and find that three of our approaches outperform existing methods in terms of execution time as well as quality and quantity of feasible solutions found. Also, we tested these transformations on a quantum annealer, which was unable to solve even small instances, due to limitations in connectivity and error rates. In general, our results highlight the advantages of the new approaches, which reduce the number of variables in the QUBO representation.
Combinatorial optimization problems are frequently classified as NP-hard, which means that the time needed to find the optimal solution generally increases exponentially with the problem size. However, the existing research gap highlights the necessity to develop combinatorial optimization methods capable of scaling to large problems while maintaining low solution latency. In this paper, we introduce stochastic simulated quantum annealing (SSQA) for fast solution of combinatorial optimization problems. SSQA is designed based on stochastic computing, which can simulate quantum annealing (QA) by using multiple replicas of spins (probabilistic bits) in classical computing. The use of stochastic computing leads to an efficient parallel spin-state update algorithm, enabling quick search for a solution around the global minimum energy. Therefore, SSQA realizes quantum-like annealing for large-scale problems and can handle fully connected models in combinatorial optimization, unlike QA. The proposed method is evaluated in MATLAB on graph isomorphism problems, which are typical combinatorial optimization problems. It can handle a 100-times larger problem size compared to QA and a 25-times larger problem size compared to a traditional SA method, respectively, for similar convergence probabilities. The time to solution of SSQA is 11.5 times and 423 times smaller than that of the conventional stochastic simulated annealing method and traditional SA, respectively, when solving a 2,025-node combinatorial optimization problem.