Fault-tolerant quantum gates with defects in topological stabilizer codes

2019/06/30 by Paul Webster, Stephen D. Bartlett · 2 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Combinatorics #Computer science #Dimension (graph theory) #Engineering #Mathematics #Physics #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum computer #Quantum gate #Quantum mechanics #Stabilizer (aeronautics) #Topology (electrical circuits) #quant-ph

paper · pdf · doi:10.1103/physreva.102.022403

published as Phys. Rev. A 102, 022403 (2020) · 22 pages + appendices, 25 figures; v2 improvements to presentation; v3 published version

openalex created_date 2019/06/14 · openalex publication_date 2020/08/06 · arxiv created 2020/08/10 · arxiv updated 2020/08/11 · openalex updated_date 2026/08/05

Abstract

Universal quantum computing by braiding defects in topological stabilizer codes of any dimension is proven to be impossible. Notwithstanding this no-go theorem, it is shown how braiding defects can yield all Clifford gates in three or more dimensions, and that universal quantum computing in three-dimensional surface codes is possible by supplementing braiding with adaptive gates.

Citations

• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Topological Computation without Braiding
• Local stabilizer codes in three dimensions without string logical operators
• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• A Modular Functor Which is Universal¶for Quantum Computation
• Universal fault-tolerant quantum computation with Bacon-Shor codes
• 2D quantum computation with 3D topological codes
• Transversal gates and error propagation in 3D topological codes

Cited by

• Braiding defects in topological stabiliser codes of any dimension cannot\n be universal
• A Compact Fermion to Qubit Mapping Part 2: Alternative Lattice Geometries
• Fibonacci Anyons Versus Majorana Fermions: A Monte Carlo Approach to the Compilation of Braid Circuits in SU(2)k Anyon Models