Quantum-Inspired Optimization for Large-Scale Combinatorial Problems

Jincheng Zhang

Published Aug 29, 2026• 0 citations

Abstract

Large-scale combinatorial optimization problems, arising in diverse fields such as logistics, finance, and operations research, pose a significant challenge to classical optimization algorithms. These problems typically involve searching through an exponentially large solution space, making exhaustive search methods computationally intractable. This paper proposes a novel quantum-inspired optimization algorithm designed to address this challenge. The algorithm leverages techniques inspired by amplitude estimation, a core concept in quantum computing, to accelerate the search process. Specifically, we employ a Monte Carlo-based approach that utilizes amplitude estimation to efficiently sample from the probability distribution governing the solution space. The resulting algorithm demonstrates promising performance in tackling large-scale combinatorial problems, offering a computationally efficient alternative to traditional optimization methods. We demonstrate the algorithm's effectiveness through theoretical analysis and provide insights into its advantages and limitations. The primary goal is to provide a viable method for tackling complex optimization tasks, drawing inspiration from quantum principles without the need for full quantum hardware.

DOI: 10.5281/zenodo.22153708

Related papers

Quantum-Inspired Algorithms for Optimization of Large-Scale Combinatorial Problems

Jincheng Zhang

This paper investigates the application of quantum-inspired algorithms to the optimization of large-scale combinatorial problems. Recognizing the limitations of current quantum computing hardware, this research focuses on developing classical algorithms that emulate key quantum principles – superposition and interference – to achieve significant performance improvements over traditional optimization methods. The core idea is to leverage amplitude amplification and interference cancellation techniques, inspired by quantum mechanics, to efficiently explore the solution space. We present a framework for designing such algorithms, detailing the mathematical formulations and the core mechanisms involved. The research aims to demonstrate that, without the need for actual quantum computers, these quantum-inspired approaches can offer a compelling alternative for tackling complex optimization challenges. The presented algorithms are evaluated conceptually, focusing on the mathematical foundations and design principles rather than empirical testing.

Aug 28, 20260 citations

Quantum-Inspired Search Algorithms for Large-Scale Optimization

Jincheng Zhang

Large-scale optimization problems, prevalent in diverse fields such as machine learning, logistics, and engineering design, pose significant challenges to classical optimization algorithms. These algorithms often suffer from slow convergence rates, premature convergence, and difficulty in exploring complex solution spaces. This paper explores the application of quantum-inspired search algorithms to address these limitations. We introduce a novel approach that draws inspiration from quantum measurement theory, specifically superposition and interference, to enhance the exploration capabilities of classical optimization techniques. The core idea is to mimic the probabilistic nature of quantum measurements to navigate the solution space more effectively. This approach allows for a more efficient exploration of potential solutions, leading to improved convergence rates and the ability to tackle larger and more complex problems. The algorithms presented are designed to be implementable within standard computational environments without requiring specialized quantum hardware. The performance of these algorithms is evaluated through simulations, demonstrating their potential to outperform traditional optimization methods in specific scenarios.

Sep 6, 20260 citations

Quantum-Inspired Optimization of Large-Scale Distributed Algorithms

Jincheng Zhang

This paper investigates the application of quantum-inspired optimization techniques to accelerate the convergence of large-scale distributed algorithms. Traditional distributed algorithm design often relies on classical optimization methods, which can struggle with the complexity and scale inherent in these systems. We propose a novel approach that borrows concepts from quantum mechanics, specifically amplitude amplification and interference, to guide the search for optimal solutions. The core idea is to utilize superposition and interference effects to explore a broader solution space more efficiently than conventional methods. We formulate a generalized framework for integrating these techniques, focusing on the iterative refinement of algorithm parameters. Preliminary analysis and theoretical considerations suggest that this approach holds promise for significant performance improvements in areas such as sensor network routing, distributed machine learning, and consensus protocols. This research aims to bridge the gap between quantum computing concepts and classical distributed systems, offering a potentially transformative method for optimizing algorithm performance.

Aug 31, 20260 citations

Quantum-Inspired Search Algorithms for Combinatorial Optimization

Jincheng Zhang

This paper explores the application of quantum-inspired concepts to the field of combinatorial optimization. Traditional search algorithms often struggle with the complexity of problems involving numerous possible solutions. We propose a novel approach that leverages the principles of quantum superposition and interference, albeit within a classical computing framework, to enhance the efficiency of search processes. The core of our method involves a hybrid algorithm that combines established classical search techniques with probabilistic sampling strategies informed by quantum mechanics. We aim to demonstrate that by mimicking these quantum phenomena, we can significantly improve the speed and effectiveness of solving complex combinatorial optimization problems. The algorithm's performance is evaluated through theoretical analysis and conceptual design, focusing on the potential for achieving performance gains without requiring actual quantum hardware. The key contribution lies in the strategic application of probabilistic sampling to explore solution spaces in a manner analogous to quantum superposition, followed by interference-like mechanisms to guide the search towards promising regions. This approach represents a new direction in optimization, bridging the gap between classical and quantum computing paradigms.

Aug 28, 20260 citations

Quantum-Inspired Optimization for Large-Scale Constraint Satisfaction Problems

Jincheng Zhang

Large-Scale Constraint Satisfaction Problems (LSCsPS) represent a significant challenge in computational science due to their inherent complexity and the exponential growth of the search space. Traditional optimization techniques often struggle to find optimal or even near-optimal solutions within reasonable timeframes. This paper introduces a novel quantum-inspired optimization algorithm designed to accelerate the solution of LSCsPS. The core idea is to mimic key principles from quantum mechanics, namely superposition and entanglement, to facilitate more efficient exploration of the solution space. The proposed algorithm utilizes probabilistic representations of variables and employs entanglement-inspired search strategies to navigate the complex solution landscape. We present a detailed formulation of the algorithm and analyze its potential benefits in tackling LSCsPS. The approach aims to overcome limitations of classical methods by leveraging the inherent parallelism and non-deterministic nature of quantum systems, although without explicitly employing quantum hardware. The algorithm's performance is evaluated through theoretical analysis and conceptual demonstrations, highlighting its promise as a viable approach for addressing this important class of problems.

Sep 1, 20260 citations

Quantum-Inspired Stochastic Search for Combinatorial Optimization

Jincheng Zhang

This paper introduces a novel stochastic search algorithm, Quantum-Inspired Stochastic Search (QISS), designed to tackle complex combinatorial optimization problems. QISS draws inspiration from the principles of quantum superposition and entanglement, adapting them into a classical probabilistic framework. Unlike traditional stochastic search methods that rely solely on classical probability distributions, QISS represents potential solutions as a superposition of states, exhibiting entanglement-like correlations to guide exploration. This approach aims to dramatically accelerate the search process by effectively exploring a wider range of the solution space. The core mechanism involves iteratively updating the probabilities associated with each state in the superposition, influenced by both random fluctuations and the observed correlations between states. The algorithm is formulated as a Markov chain Monte Carlo method, where the state transition probabilities are governed by a probability distribution derived from the problem's cost function. The effectiveness of QISS is evaluated through theoretical analysis and, importantly, through a conceptual framework that highlights its potential advantages over existing stochastic optimization techniques. The ultimate goal is to demonstrate that incorporating quantum-inspired concepts, even within a purely classical setting, can lead to significant improvements in the efficiency and robustness of combinatorial optimization algorithms.

Sep 6, 20260 citations