2018/06/30 by Guanyu Zhu, Ali Lavasani, Maissam Barkeshli · 16 citations
Computer Science · Mathematics · Physics and Astronomy · #Anyon #Combinatorics #Computer science #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum algorithm #Quantum and electron transport phenomena #Quantum circuit #Quantum computer #Quantum error correction #Quantum gate #Quantum mechanics #Quantum-Dot Cellular Automata #Qubit #Set (abstract data type) #Topological quantum computer #Topology (electrical circuits) #Universal set #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physrevlett.125.050502
published in Physical Review Letters 125(5), 050502 (American Physical Society) · 5 pages, 4 figures; updated the discussions on fault tolerance and time overhead for decoding; added appendices
openalex publication_date 2020/07/28 · arxiv created 2020/08/10 · arxiv updated 2020/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
A fundamental question in the theory of quantum computation is to understand the ultimate space-time resource costs for performing a universal set of logical quantum gates to arbitrary precision. Here we demonstrate that non-Abelian anyons in Turaev-Viro quantum error correcting codes can be moved over a distance of order of the code distance, and thus braided, by a constant depth local unitary quantum circuit followed by a permutation of qubits. Our gates are protected in the sense that the lengths of error strings do not grow by more than a constant factor. When applied to the Fibonacci code, our results demonstrate that a universal logical gate set can be implemented on encoded qubits through a constant depth unitary quantum circuit, and without increasing the asymptotic scaling of the space overhead. These results also apply directly to braiding of topological defects in surface codes. Our results reformulate the notion of braiding in general as an effectively instantaneous process, rather than as an adiabatic, slow process.