Systematically generated two-qubit anyon braids

Abstract

Fibonacci anyons are non-Abelian particles for which braiding is universal for quantum computation. Reichardt has shown how to systematically generate nontrivial braids for three Fibonacci anyons which yield unitary operations with off-diagonal matrix elements that can be made arbitrarily small in a particular natural basis through a simple and efficient iterative procedure. This procedure does not require brute force search, the Solovay-Kitaev method, or any other numerical technique, but the phases of the resulting diagonal matrix elements cannot be directly controlled. We show that despite this lack of control the resulting braids can be used to systematically construct entangling gates for two qubits encoded by Fibonacci anyons.

9 pages, 6 figures

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Cited by in corpus (8)

• Introduction to topological quantum computation with non-Abelian anyons
• Topological Quantum Compiling with Reinforcement Learning
• Fibonacci Numbers and the Golden Ratio in Biology, Physics, Astrophysics, Chemistry and Technology: A Non-Exhaustive Review
• Universal quantum computation using Ising anyons from a non-semisimple Topological Quantum Field Theory
• Topological quantum compilation of two-qubit gates
• Optimized Topological Quantum Compilation of Three-Qubit Controlled Gates in the Fibonacci Anyon Model: A Controlled-Injection Approach
• Weighted Quantum Channel Compiling through Proximal Policy Optimization
• The construction of a universal quantum gate set for the SU(2)k (k=5,6,7) anyon models via genetic optimized algorithm