Compiling single-qubit braiding gate for Fibonacci anyons topological quantum computation

Abstract

Topological quantum computation is an implementation of a quantum computer in a way that radically reduces decoherence. Topological qubits are encoded in the topological evolution of two-dimensional quasi-particles called anyons and universal set of quantum gates can be constructed by braiding these anyons yielding to a topologically protected circuit model. In the present study we remind the basics of this emerging quantum computation scheme and illustrate how a topological qubit built with three Fibonacci anyons might be adopted to achieve leakage free braiding gate by exchanging the anyons composing it. A single-qubit braiding gate that approximates the Hadamard quantum gate to a certain accuracy is numerically implemented using a brute force search method. The algorithms utilized for that purpose are explained and the numerical programs are publicly shared for reproduction and further use.

Experimental quantum simulation of a topologically protected Hadamard gate via braiding Fibonacci anyons

“…One can realize any single-qubit gate on the logical qubit with arbitrarily high precision by sequentially implementing the and . As an example, a Hadamard gate can be realized by implementing the following sequence of braiding operations, 20 …”

Non-Abelian braiding of Majorana-like edge states and topological quantum computations in electric circuits

“…However, its demerit is that one needs an infinite number of gate operations in order to make a conventional quantum gate whose components are simple numbers such as i n with i = 0, 1, 2, 3. For example, 30 braidings are necessary for the Hadamard gate with the error 0.00657 [55]. A recent experiment [56] shows that 15 braidings realize the Hadamard gate with the fidelity 0.9718.…”

Topological quantum computation on supersymmetric spin chains

“…They are non-Abelian anyons associated to irreducible representations of the quantum group SU(2) k [9,10], appearing at levels k = 2, 3 and k = 4, respectively. Among them, the Fibonacci anyons have found importance in quantum computing as they help generate a universal set of gates by braiding alone [11][12][13][14][15]. On the other hand the level k = 4 anyons can realize universal quantum computing by supplementing the braiding gates with non-topological ones [16,17].…”