Genetic algorithm enhanced Solovay-Kitaev algorithm for quantum compiling of Fibonacci anyons

TL;DR

This paper introduces a genetic algorithm-enhanced Solovay-Kitaev algorithm for quantum compiling with Fibonacci anyons, achieving high-precision gate approximations efficiently in large search spaces.

Contribution

It develops a novel GA-enhanced SKA method for quantum gate approximation using Fibonacci anyons, outperforming Monte Carlo methods and rivaling deep reinforcement learning in accuracy.

Findings

Achieves gate distances of 5.9*10^-7 with optimized braidwords.

Surpasses Monte Carlo-enhanced SKA in approximation precision.

Comparable to deep reinforcement learning for braidword lengths over 25.

Abstract

Quantum compiling, which aims to approximate target qubit gates by finding optimal sequences (braidwords) of basic braid operations, constitutes a fundamental challenge in quantum computing. We develop a genetic algorithm (GA)-enhanced Solovay-Kitaev algorithm (SKA) for approximating single-qubit gates using four elementary braiding matrices (EBMs) derived from Fibonacci anyons. The GA-enhanced SKA demonstrates robust performance, efficiently identifying optimal braidwords within exponentially large search spaces. Notably, the approximation precision achieved by our method surpasses that of Monte Carlo (MC)-enhanced SKA and becomes comparable to deep reinforcement learning (RL) approaches when braidword lengths exceed 25. Implementing 2- and 3-order approximations with the GA-enhanced SKA yields optimal braidword (initial braiding lengths l0=50 and 30 respectively) achieving gate distances of 5.9*10-7 - sufficient precision for most quantum computing applications. This work develops an optimized compilation framework for non-Abelian anyon gates, providing an essential methodology for enhancing future topological quantum computation architectures through gate optimization.