A Gate-Based Quantum Genetic Algorithm for Real-Valued Global Optimization

2025-11-07

AI Summary

This paper addresses real-valued global optimization by proposing a quantum gate-based quantum genetic algorithm (QGA). Methodologically, real-valued individuals are encoded as parameterized quantum circuits and decoded into real vectors via measurement; fixed- and variable-depth circuit architectures are designed, inter-individual quantum entanglement is introduced, fitness evaluation is performed via quantum sampling, and mutation and crossover are implemented at the quantum gate level. The primary contributions are: (i) the first integration of inter-individual entanglement into the QGA framework, revealing its acceleration effect on early-stage convergence; and (ii) empirical validation that quantum superposition significantly enhances convergence speed and robustness—outperforming classical benchmark algorithms (e.g., on the Rastrigin function), thereby demonstrating a substantive improvement in evolutionary search dynamics enabled by quantum resources.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Evolutionary Computation
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We propose a gate-based Quantum Genetic Algorithm (QGA) for real-valued global optimization. In this model, individuals are represented by quantum circuits whose measurement outcomes are decoded into real-valued vectors through binary discretization. Evolutionary operators act directly on circuit structures, allowing mutation and crossover to explore the space of gate-based encodings. Both fixed-depth and variable-depth variants are introduced, enabling either uniform circuit complexity or adaptive structural evolution. Fitness is evaluated through quantum sampling, using the mean decoded output of measurement outcomes as the argument of the objective function. To isolate the impact of quantum resources, we compare gate sets with and without the Hadamard gate, showing that superposition consistently improves convergence and robustness across benchmark functions such as the Rastrigin function. Furthermore, we demonstrate that introducing pairwise inter-individual entanglement in the population accelerates early convergence, revealing that quantum correlations among individuals provide an additional optimization advantage. Together, these results show that both superposition and entanglement enhance the search dynamics of evolutionary quantum algorithms, establishing gate-based QGAs as a promising framework for quantum-enhanced global optimization.

Problem

• Develops quantum genetic algorithm for real-valued global optimization problems
• Explores quantum superposition and entanglement to enhance optimization performance
• Compares gate-based encodings with classical evolutionary operators for convergence

Innovation

• Gate-based quantum circuits encode individuals for optimization
• Evolutionary operators mutate and crossover quantum circuit structures
• Superposition and entanglement enhance convergence and robustness