arXiv:2511.05254quant-phcs.AI2025-11

用量子门电路表示个体,实现真实值全局优化的量子遗传算法。

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

  • 用量子门电路编码个体,通过测量解码为实数向量。
  • 含叠加和纠缠的量子特性显著提升收敛速度与鲁棒性。
  • 适合对量子优化算法感兴趣的科研人员或工程师。

我们提出一种基于量子门的量子遗传算法(QGA),用于实值全局优化。个体由量子电路表示,其测量结果经二进制离散化解码为实数向量。进化算子直接作用于电路结构,实现变异与交叉对门级编码空间的探索。引入固定深度与可变深度两种变体,支持统一或自适应的电路复杂度演化。通过量子采样评估适应度,以测量输出均值作为目标函数输入。为隔离量子资源影响,对比含与不含哈达玛门的门集,发现叠加在如Rastrigin函数等基准测试中持续提升收敛性与鲁棒性。进一步证明,在种群中引入个体间成对纠缠可加速早期收敛,表明个体间的量子关联带来额外优化优势。结果表明,叠加与纠缠均能增强进化量子算法的搜索动态,确立了基于门的QGA在量子增强全局优化中的前景。

原文摘要 · Abstract (English)

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.

量子优化遗传算法量子门全局优化

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