Unified approach to topological quantum computation with anyons: From qubit encoding to Toffoli gate

Abstract

Topological quantum computation may provide a robust approach for encoding and manipulating information utilizing the topological properties of anyonic quasi-particle excitations. We develop an efficient means to map between dense and sparse representations of quantum information (qubits) and a simple construction of multi-qubit gates, for all anyon models from Chern-Simons-Witten SU(2)${}_k$ theory that support universal quantum computation by braiding ($k\ge 3,k\ne 4$). In the process, we show how the constructions of topological quantum memory and gates for $k=2,4$ connect naturally to those for $k\ge 3,k\ne 4$, unifying these concepts in a simple framework. Furthermore, we illustrate potential extensions of these ideas to other anyon models outside of Chern-Simons-Witten field theory.

4.5 pages, 3 figures, published in PRA

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Cited by in corpus (7)

• A Short Introduction to Topological Quantum Computation
• Introduction to topological quantum computation with non-Abelian anyons
• Genetic braid optimization: A heuristic approach to compute quasiparticle braids
• Complete description of fault-tolerant quantum gate operations for topological Majorana qubit systems
• 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
• The construction of a universal quantum gate set for the SU(2)k (k=5,6,7) anyon models via genetic optimized algorithm