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

Abstract

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.

29 pages, 5 figures

References in corpus (20)

• Non-Abelian Anyons and Topological Quantum Computation
• Surface codes: Towards practical large-scale quantum computation
• Fault-tolerant quantum computation with high threshold in two dimensions
• Ordered and tunable Majorana-zero-mode lattice in naturally strained LiFeAs
• Topological Quantum Compiling
• Topological Quantum Compiling with Reinforcement Learning
• Hunting for Majoranas
• Theory of Majorana zero modes in unconventional superconductors
• Fibonacci Anyons From Abelian Bilayer Quantum Hall States
• Universal Gates via Fusion and Measurement Operations on SU$(2{)}_4$ Anyons
• Constructing Functional Braids for Low-Leakage Topological Quantum Computing
• Fibonacci anyons versus Majorana fermions
• Tunable vortex Majorana modes controlled by strain in homogeneous LiFeAs
• Genetic braid optimization: A heuristic approach to compute quasiparticle braids
• Universal quantum computation using Ising anyons from a non-semisimple Topological Quantum Field Theory
• Topological quantum compilation of two-qubit gates
• Topological quantum compilation of metaplectic anyons based on the genetic optimized algorithms
• Optimized Topological Quantum Compilation of Three-Qubit Controlled Gates in the Fibonacci Anyon Model: A Controlled-Injection Approach
• Entangling gates from cabling of knots
• Genetic algorithm enhanced Solovay-Kitaev algorithm for quantum compiling of Fibonacci anyons