This paper presents a novel multi-threaded quantum inspired optimization algorithm targeted at global search in continuous domains. The proposed approach is based on a Diffusion Monte Carlo (DMC) physical model and is characterized by a set of parallel quantum walk processes. The effectiveness of the proposed algorithm is demonstrated by experimental results on the 24 noiseless functions from the Black Box Optimization Benchmark of the Comparing Continuous Optimization benchmarking platform (COCO).
This paper presents a novel multi-threaded quantum inspired optimization algorithm targeted at global search in continuous domains. The proposed approach is based on a Diffusion Monte Carlo (DMC) physical model and is characterized by a set of parallel quantum walk processes. The effectiveness of the proposed algorithm is demonstrated by experimental results on the 24 noiseless functions from the Black Box Optimization Benchmark of the Comparing Continuous Optimization benchmarking platform (COCO).
This paper investigates the application of quantum-inspired concepts to enhance the performance of random walk algorithms for optimization problems. Classical random walk algorithms are susceptible to getting trapped in local optima, limiting their efficacy in tackling complex and high-dimensional search spaces. To address this limitation, we propose a novel approach that incorporates principles of quantum superposition and tunneling into the random walk process. The algorithm leverages these concepts to enable more extensive exploration of the search space, thereby increasing the probability of converging towards the global optimum. We present a detailed formulation of the algorithm, outlining the key parameters and their influence on the optimization process. The theoretical analysis demonstrates the potential advantages of this quantum-inspired approach compared to traditional random walk methods. The algorithm's ability to escape local minima is evaluated through simulations, showcasing its effectiveness in a variety of benchmark optimization problems. The results highlight the promise of quantum-inspired techniques in improving the robustness and efficiency of random walk algorithms, offering a viable strategy for solving challenging optimization tasks.
One of the significant breakthroughs in quantum computation is Grover’s algorithm for unsorted database search. Recently, the applications of Grover’s algorithm to solve global optimization problems have been demonstrated, where unknown optimum solutions are found by iteratively improving the threshold value for the selective phase shift operator in Grover rotation. In this paper, a hybrid approach that combines continuous-time quantum walks with Grover search is proposed. By taking advantage of quantum tunneling effect, local barriers are overcome and better threshold values can be found at the early stage of search process. The new algorithm based on the formalism is demonstrated with benchmark examples of global optimization. The results between the new algorithm and the Grover search method are also compared.
This paper investigates the application of quantum-inspired concepts to enhance the performance of random walk algorithms, specifically within the domain of global optimization. Classical random walk algorithms frequently struggle with convergence issues, frequently becoming trapped within local optima, a significant limitation when dealing with complex, high-dimensional search spaces. This research proposes a novel approach where random walk behavior is modeled based on principles derived from quantum mechanics, incorporating superposition and interference effects to facilitate more extensive and efficient exploration of the solution landscape. The core idea is to replace the deterministic step size in traditional random walks with a probabilistic movement governed by a quantum-like probability distribution. We explore the mathematical formulation of this process, detailing the probabilities of transition between states and the impact of interference. The resulting algorithms demonstrate improved convergence rates and a reduced tendency to get stuck in local optima compared to standard random walk methods. The paper concludes by outlining potential future research directions, including adaptive parameter tuning and integration with other optimization techniques.
The application of quantum annealing to the optimization of continuous-variable functions is a relatively unexplored area of research. We test the performance of quantum annealing applied to a one-dimensional continuous-variable function with a rugged energy landscape. After domain-wall encoding to map a continuous variable to discrete Ising variables, we first benchmark the performance of the real hardware, the D-Wave 2000Q, against several state-of-the-art classical optimization algorithms designed for continuous-variable problems to find that the D-Wave 2000Q matches the classical algorithms in a limited domain of computation time. Beyond this domain, classical global optimization algorithms outperform the quantum device. Next we examine several optimization algorithms that are applicable to the Ising formulation of the problem, such as the time-evolving block decimation (TEBD) to simulate ideal coherent quantum annealing, simulated annealing, simulated quantum annealing, and spin-vector Monte Carlo. The data show that TEBD's coherent quantum annealing achieves far better results than the other approaches, demonstrating the effectiveness of coherent tunneling. From these two types of benchmarks, we conclude that the hardware realization of quantum annealing has the potential to significantly outperform the best classical algorithms if thermal noise and other imperfections are sufficiently suppressed and the device operates coherently, as demonstrated in recent short-time quantum simulations.
One of the significant breakthroughs in quantum computation is Grover's algorithm for unsorted database search. Recently, the applications of Grover's algorithm to solve global optimization problems have been demonstrated, where unknown optimum solutions are found by iteratively improving the threshold value for the selective phase shift operator in Grover rotation. In this paper, a hybrid approach that combines continuous-time quantum walks with Grover search is proposed so that the search is accelerated with improved threshold values. By taking advantage of the quantum tunneling effect, better threshold values can be found at the early stage of the search process so that the sharpness of probability improves. The results between the new algorithm, existing Grover search, and classical heuristic algorithms are compared.
This paper presents a novel framework for iterative optimization that draws inspiration from quantum-inspired algorithms. Traditional optimization methods often struggle with convergence issues, particularly in complex, high-dimensional spaces. This work introduces a quantum-inspired iterative approach, utilizing a novel process of candidate generation and evaluation to accelerate convergence and improve solution quality. We demonstrate the effectiveness of this framework through a series of simulations and analysis, highlighting its potential to overcome limitations of conventional optimization techniques. The core mechanism centers around employing quantum-mechanical concepts to guide the exploration of potential solutions, thereby fostering a more efficient and robust optimization process. This research explores the potential for leveraging quantum-inspired algorithms to achieve superior performance compared to existing methods, specifically targeting scenarios with complex landscapes and high-dimensional parameter spaces.