Genetic algorithm enhanced Solovay-Kitaev algorithm for quantum compiling

Abstract: Quantum compiling trying to approximate the target qubit gate by finding an optimal sequence (braid word) of basic braid operations is a fundamental problem in quantum computing. We develop a genetic algorithm (GA) enhanced Solovay-Kitaev algorithm (SKA) to approximate single qubit gates with four basic braid matrices of Fibonacci anyons. The GA-enhanced SKA demonstrates that the algorithm performs strongly and can easily find the ideal braid word from an exponentially large space. The resulting precision of the approximate single-qubit quantum gate is superior to that of the Monte Carlo (MC) enhanced SKA, as well as comparable to that of the deep reinforcement learning (RL) for the length of braid word greater than 25. The 2(3)-order approximation of GA-enhanced SKA for basic braiding length l0=50(30) leads to an optimal braid word at a distance of 5.9*10^-7, which is sufficient for most cases of quantum computing. Our work provides an alternative approach to solving and optimizing quantum compilation of non-Abelian anyon quantum gates and is useful for realizing topological quantum computation in the future.