Topological Computation without Braiding

2006/10/31 by Héctor Bombín, H. Bombin, M. A. Martín-Delgado +1 · 12 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum many-body systems #cond-mat.str-el #hep-th #quant-ph

paper · pdf · doi:10.1103/physrevlett.98.160502

published as Phys.Rev.Lett.98:160502,2007 · revtex4, 4 pages, 4 figures

arxiv created 2007/03/29 · openalex publication_date 2007/04/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We show that universal quantum computation can be performed within the ground state of a topologically ordered quantum system, which is a naturally protected quantum memory. In particular, we show how this can be achieved using brane-net condensates in 3-colexes. The universal set of gates is implemented without selective addressing of physical qubits and, being fully topologically protected, it does not rely on quasiparticle excitations or their braiding.

Citations

• A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
• Topological quantum memory
• Good Quantum Error-Correcting Codes Exist
• Fault-tolerant quantum computation by anyons

Cited by

• A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
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• Optimizing glassyp-spin models
• Deformed quantum double realization of the toric code and beyond
• Fault-tolerant quantum gates with defects in topological stabilizer codes
• Quantum circuits for measuring Levin-Wen operators
• Braiding defects in topological stabiliser codes of any dimension cannot\n be universal
• Twins Percolation for Qubit Losses in Topological Color Codes
• Family of non-Abelian Kitaev models on a lattice: Topological condensation and confinement
• Poking Holes and Cutting Corners to Achieve Clifford Gates with the Surface Code
• Universal fault-tolerant measurement-based quantum computation
• Quantum measurements and gates by code deformation
• Protected gates for topological quantum field theories