Fault-tolerant quantum computation by anyons

1997/07/09 by Alexei Kitaev, A.Yu. Kitaev, A. Yu. Kitaev · 3 voices · 434 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #cond-mat.mes-hall #hep-th #quant-ph

paper · pdf · doi:10.1016/s0003-4916(02)00018-0

Abstract

A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer. Unitary transformations can be performed by moving the excitations around each other. Measurements can be performed by joining excitations in pairs and observing the result of fusion. Such computation is fault-tolerant by its physical nature.

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Discussions

• An important open mathematical problem in the theoretical foundation of topological order is to prove that the universal properties (braiding and fusion) of point-like excitations in any gapped phase [stackexchange, 3 points]
• 12/12 Finally, and most obscurely, this grill at Park Güell reminds me of Kitaev’s toric quantum error correcting code: arxiv.org/abs/quant-ph... [bsky, 1 points, 0 comments]
• Suppose a lattice system is $G$ -symmetric, when we try to gauge this symmetry, we follow the following steps (for example toric code Levin Gu Xie Chen ): minimal coupling: the original Hamiltonian is [stackexchange, 1 points]

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