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arXiv 2505.01774quant-ph

基于遗传优化算法的SU(2)k(k=5,6,7)任意子模型通用量子门集构建

The construction of a universal quantum gate set for the SU(2)k (k=5,6,7) anyon models via genetic optimized algorithm

Jiangwei Long, Yizhi Li, Jianxin Zhong, Lijun Meng

AI总结:

本文针对SU(2)k(k=5,6,7)任意子模型,结合遗传优化算法与Solovay-Kitaev算法等构建通用量子门集,验证了其通用量子计算能力,还实现了SWAP等价类的精确构造。

摘要:

本文系统研究了利用SU(2)k任意子模型构建拓扑量子计算(TQC)通用量子门集的数值方法。研究通过SU(2)的q形变表示理论计算F矩阵与R符号,可精确确定SU(2)k任意子系统的基本编织矩阵(EBMs),量子门即由这些EBMs推导得到。单量子比特门采用遗传算法增强的Solovay-Kitaev算法(GA-enhanced SKA)合成,双量子比特门则通过穷举搜索或遗传算法优化构建,以逼近局域等价类[CNOT]。将该框架应用于SU(2)5、SU(2)6、SU(2)7模型,成功生成了标准通用门集{H门、T门、CNOT门}。这些数值结果确凿验证了SU(2)k任意子模型固有的通用量子计算能力,此外,研究在每个模型中均使用9个EBMs实现了局域等价类[SWAP]的精确构造。

英文摘要:

We study systematically numerical method into constructing a universal quantum gate set for topological quantum computation (TQC) using SU(2)k anyon models. The F-matrices and R-symbol were computed through the q-deformed representation theory of SU(2), enabling precise determination of elementary braiding matrices (EBMs) for SU(2)k anyon systems. Quantum gates were derived from these EBMs. One-qubit gates were synthesized using a genetic algorithm-enhanced Solovay-Kitaev algorithm (GA-enhanced SKA), while two-qubit gates were constructed through brute-force search or GA optimization to approximate local equivalence classes [CNOT]. Implementing this framework for SU(2)5, SU(2)6, and SU(2)7 models successfully generated the canonical universal gate set {H-gate, T-gate, CNOT-gate}. These numerical results provide conclusive verification of the universal quantum computation capabilities inherent in SU(2)k anyon models. Furthermore, we get exact implementations of the local equivalence class [SWAP] using nine EBMs in each model.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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