Quantum-Inspired Optimization of Large-Scale Matrix Computations

Jincheng Zhang

Published Sep 6, 2026• 0 citations

Abstract

This paper investigates the application of quantum-inspired optimization techniques to accelerate large-scale matrix computations. Traditional optimization algorithms often encounter significant challenges when dealing with the complexity inherent in these computations. We propose a novel approach leveraging concepts derived from quantum annealing and superposition to explore the solution space more efficiently. The core idea is to mimic the probabilistic exploration characteristic of quantum systems within a classical framework. Specifically, we utilize an iterative optimization process, adapting parameters based on simulated "quantum fluctuations," aiming to converge towards optimal solutions faster than conventional methods. The theoretical framework is presented, and we detail the implementation strategy, focusing on the design of a suitable objective function and a corresponding optimization algorithm. Preliminary results suggest the potential for significant speedups, particularly for computationally demanding matrix operations, though further investigation and refinement are needed. The key contribution lies in the direct translation of quantum-inspired principles into a practical optimization strategy for matrix computations.

DOI: 10.5281/zenodo.22458527

Related papers

Quantum-Inspired Optimization for Large-Scale Machine Learning

Jincheng Zhang

The rapid growth of machine learning (ML) has been accompanied by a significant challenge: the scaling of optimization algorithms to handle the immense parameter spaces of modern models, such as deep neural networks. Traditional optimization methods, including gradient descent and its variants, often encounter difficulties in efficiently exploring these spaces, leading to slow training times and potential stagnation. This paper investigates the application of quantum-inspired optimization techniques to address this scaling problem. We explore algorithms inspired by quantum annealing and other quantum phenomena, adapting their core principles to classical computation. Specifically, we propose a novel optimization framework utilizing a stochastic search strategy based on quantum superposition and measurement, designed to navigate high-dimensional parameter spaces more effectively. The efficacy of this approach is evaluated through theoretical analysis and conceptual simulations, demonstrating its potential to accelerate the training of large-scale machine learning models. We demonstrate how these methods can improve convergence speed and potentially escape local minima more effectively than conventional techniques. The core contribution lies in providing a theoretical foundation and a practical framework for applying quantum-inspired concepts to optimization within the context of machine learning.

Sep 6, 20260 citations

Quantum-Inspired Optimization of Large-Scale Machine Learning Algorithms

Jincheng Zhang

Large-scale machine learning (ML) models, particularly deep neural networks, often present significant challenges for traditional optimization algorithms. These algorithms, rooted in classical mechanics, frequently encounter issues such as getting trapped in local optima, high computational cost, and difficulty in handling complex, non-convex landscapes. This paper investigates the application of quantum-inspired optimization techniques to address these challenges. We explore how concepts derived from quantum phenomena – such as quantum annealing and quantum walks – can be adapted to efficiently navigate and optimize large-scale ML models. The core idea is to leverage the probabilistic and superposition properties inherent in quantum mechanics to escape local optima and accelerate the convergence process. We present a framework for designing and implementing quantum-inspired optimization strategies, focusing on the theoretical foundations and potential benefits. The proposed approach aims to provide a novel and effective solution for optimizing complex ML models, ultimately improving model performance and reducing training time. This work contributes to the growing field of quantum machine learning and offers a promising avenue for tackling the optimization problems inherent in large-scale ML.

Sep 7, 20260 citations

Quantum-Inspired Algorithms for Large-Scale Optimization

Jincheng Zhang

This paper explores the potential of quantum-inspired algorithms for tackling large-scale optimization problems. Traditional optimization methods often struggle with the computational complexity of problems involving numerous variables and constraints. Quantum mechanics, particularly concepts like superposition and entanglement, offers a radically different approach to problem-solving. This work investigates how these concepts can be translated into algorithmic designs, aiming to improve the efficiency and speed of optimization processes. We propose a framework for developing algorithms that mimic quantum phenomena, focusing on techniques that enable exploration of the solution space in a more parallel and potentially faster manner. The core of this approach lies in leveraging mathematical structures derived from quantum mechanics to guide search strategies. We outline key algorithmic ideas, emphasizing the potential for improved convergence rates and scalability. The presented concepts represent a novel application of quantum-inspired ideas to the field of optimization, offering a promising avenue for addressing complex real-world problems.

Sep 7, 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 Algorithms for Optimization Problems

Jincheng Zhang

This paper explores the development and application of novel optimization algorithms inspired by the principles of quantum mechanics. Recognizing the potential of quantum phenomena like superposition and tunneling for enhancing computational efficiency, we propose a new algorithmic framework that mimics these behaviors within a classical computing environment. The core idea is to construct an optimization algorithm that incorporates probabilistic search strategies, analogous to quantum tunneling, and explores multiple solution possibilities concurrently, similar to superposition. This approach aims to overcome the limitations of traditional optimization methods, particularly in tackling complex, high-dimensional problems. We detail the algorithm's design, emphasizing the key mathematical formulations and probabilistic elements. The proposed algorithm's performance is evaluated through theoretical analysis and conceptual demonstrations, showcasing its potential to offer improved convergence rates and solution quality compared to established classical optimization techniques. The research contributes to the burgeoning field of quantum-inspired computing, providing a practical and accessible approach for leveraging quantum concepts for optimization challenges.

Sep 6, 20260 citations

Quantum-Inspired Heuristics for Complex Optimization

Jincheng Zhang

This paper explores the application of quantum-inspired heuristics to tackle complex optimization problems. The core idea stems from leveraging quantum mechanical principles, specifically superposition and interference, to design novel heuristic algorithms. Instead of relying on traditional approaches like simulated annealing or genetic algorithms, we propose algorithms that mimic the evolution of wave functions within complex search spaces. These algorithms incorporate principles analogous to quantum annealing, allowing them to effectively navigate local minima and accelerate convergence rates. The novelty of this work lies in its direct application of quantum concepts to classical optimization, offering a potentially more efficient solution method without the need for specialized quantum computing hardware. The methodology outlined herein provides a framework for developing a new generation of optimization algorithms inspired by the underlying principles of quantum mechanics. The performance of these algorithms is evaluated through theoretical analysis and conceptual demonstrations, highlighting their potential advantages over conventional heuristic techniques.

Aug 28, 20260 citations