aiqbench analysis
The paper applies a genetic algorithm to speed up the Solovay-Kitaev procedure for compiling single-qubit gates from Fibonacci-anyon braids, a topological approach to quantum computation. It reports gate distances around 5.9×10⁻⁷ and says the method matches deep reinforcement learning once braidwords exceed about 25 elements. These are simulation results, not hardware demonstrations, and Fibonacci anyon platforms remain experimentally unproven, so readers should treat the gains as algorithmic progress rather than practical topological hardware.
Genetic algorithm enhanced Solovay-Kitaev algorithm for quantum compiling of Fibonacci anyons
arXiv:2501.01746v4 Announce Type: replace 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 braidwords (with initial braiding lengths $l_{0} = 50$ and $l_{0} = 30$, respectively) achieving gate distances of $5.9 \times 10^{-7}$ --- 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.
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 braidwords (with initial braiding lengths $l_{0} = 50$ and $l_{0} = 30$, respectively) achieving gate distances of $5.9 \times 10^{-7}$ --- 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.
arXiv:2501.01746 [quant-ph]
(or arXiv:2501.01746v4 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2501.01746 Focus to learn more arXiv-issued DOI via DataCite
Phys. Scr. (2025)
https://doi.org/10.1088/1402-4896/ae1d30 Focus to learn more DOI(s) linking to related resources
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