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International Journal of Modern Physics C

GENETIC ALGORITHMS AND OPTIMIZATION PROBLEMS IN QUANTUM COMPUTING

Yorick Hardy, W.‐H. Steeb

Published Nov 1, 2010• 4 citations
Publisher

Abstract

We solve a number of problems in quantum computing by applying genetic algorithms. We use the bitset class of C ++ to represent any data type for genetic algorithms. Thus we have a flexible way to solve any optimization problem. The Bell-CHSH inequality and entanglement measures are studied using genetic algorithms. Entangled states form the backbone for teleportation. The C ++ code is also provided.

DOI
10.1142/s0129183110015890

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We solve a number of problems in quantum computing by applying genetic algorithms. We use the bitset class of C ++ to represent any data type for genetic algorithms. Thus we have a flexible way to solve any optimization problem. The Bell-CHSH inequality and entanglement measures are studied using genetic algorithms. Entangled states form the backbone for teleportation. The C ++ code is also provided.
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This paper proposes a novel approach to optimization problems by integrating quantum entanglement with the Genetic Algorithm (GA). The core idea is to leverage the inherent parallelism and enhanced information transfer capabilities of quantum entanglement to significantly improve the search performance of the GA. We represent genetic algorithm chromosomes as quantum states and employ quantum entanglement to facilitate rapid information exchange and crossover operations across multiple qubits. This mechanism allows for parallel exploration of the search space, mitigating the limitations of traditional GA's tendency towards local optima. The theoretical framework and the underlying principles are presented, demonstrating the potential for the Quantum Entanglement Genetic Algorithm (QGA) to accelerate the solution of complex optimization problems. The algorithm's effectiveness is discussed through a mathematical formulation, focusing on the key components of the QGA and its advantages over conventional GA. The ultimate goal is to demonstrate a robust and efficient method for tackling challenging optimization tasks.
Problems of optimization are very common in several areas like engineering, physics, economics and mathematics and usually, they are very difficult to solve. Basically, one has to find the minimum or maximum of an objective function. In this work, we chose two optimization problems and we present quantum algorithms to solve them. The problems are: (1) to find the best decomposition of a unitary operation achievable by a programmable quantum circuit; (2) to find the minimal distance of a linear code. The quantum algorithms used are asymptotic quantum search and their main property is the fact that only one measurement is required.
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