Quantum computation with Turaev–Viro codes
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- 作者：Robert Koenig ; Greg Kuperberg ; Ben W. Reichardt
- 关键词：Quantum error-correcting codes ; Fault-tolerant quantum computation ; Topological quantum computation ; Turaev– ; Viro invariant
- 刊名：Annals of Physics
- 出版年：2010
- 出版时间：December 2010
- 年：2010
- 卷：325
- 期：12
- 页码：2707-2749
- 全文大小：12353 K
文摘
For a 3-manifold with triangulated boundary, the Turaev–Viro topological invariant can be interpreted as a quantum error-correcting code. The code has local stabilizers, identified by Levin and Wen, on a qudit lattice. Kitaev’s toric code arises as a special case. The toric code corresponds to an abelian anyon model, and therefore requires out-of-code operations to obtain universal quantum computation. In contrast, for many categories, such as the Fibonacci category, the Turaev–Viro code realizes a non-abelian anyon model. A universal set of fault-tolerant operations can be implemented by deforming the code with local gates, in order to implement anyon braiding. We identify the anyons in the code space, and present schemes for initialization, computation and measurement. This provides a family of constructions for fault-tolerant quantum computation that are closely related to topological quantum computation, but for which the fault tolerance is implemented in software rather than coming from a physical medium.