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Journal of quantum computing

State-Space Reduction Techniques Exploiting Specific Constraints for Quantum Search Initialization, Application to an Outage Planning Problem

Rodolphe Griset, Ioannis Lavdas, Jiří Guth Jarkovský

Published Jan 1, 2025• 1 citation
Publisher

Abstract

Quantum search has emerged as one of the most promising fields in quantum computing. State-of-the-art quantum search algorithms enable the search for specific elements in a distribution by monotonically increasing the density... | Find, read and cite all the research you need on Tech Science Press
DOI
10.32604/jqc.2025.066064

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Quantum search has emerged as one of the most promising fields in quantum computing. State-of-the-art quantum search algorithms enable the search for specific elements in a distribution by monotonically increasing the density of these elements until reaching a high density. This kind of algorithms demonstrate a theoretical quadratic speed-up on the number of queries compared to classical search algorithms in unstructured spaces. Unfortunately, the major part of the existing literature applies quantum search to problems which size grows exponnentialy with the input size without exploiting any specific problem structure, rendering this kind of approach not exploitable in real industrial problems. In contrast, this work proposes exploiting specific constraints of scheduling problems to build an initial superposition of states with size almost quadraticaly increasing as a function of the problem size. This state space reduction, inspired by the quantum walk algorithm, constructs a state superposition corresponding to all paths in a state-graph embedding spacing constraints between jobs. Our numerical results on quantum emulators highlights the potential of state space reduction approach, which could lead to more efficient quantum search processes by focusing on a smaller, more relevant, solution space.
A groundbreaking advancement in computing theory, quantum search algorithms leverage quantum mechanics to outperform their classical counterparts in solving search issues. With a focus on their theoretical underpinnings, practical applications, and performance in a variety of computational contexts, this systematic review carefully investigates the evolution, progress, and current state of quantum search algorithms. We present a thorough analysis of significant algorithms, such as Grover’s search algorithm, together with recent developments in quantum optimization and quantum-enhanced search techniques. We also go over the challenges with quantum error correction, scalability, and hardware constraints that prevent the broad application of quantum search techniques.
Quantum computers are designed to outperform standard computers by running quantum algorithms. Fields in which quantum algorithms can be applied include cryptography, search and optimization, simulation of quantum systems and solving large systems of linear equations. Here we briefly survey some known quantum algorithms, with an emphasis on a broad overview of their applications rather than their technical details. We focus to introduce the development of entire field, and provide a comprehensive and accurate understanding concerning this field, which may be helpful for interested researchers in this area.