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Article Dans Une Revue Quantum Rep. Année : 2022

Fricke Topological Qubits

Résumé

We recently proposed that topological quantum computing might be based on representations of the fundamental group for the complement of a link K in the three-sphere. The restriction to links whose associated character variety contains a Fricke surface is desirable due to the connection of Fricke spaces to elementary topology. Taking K as the Hopf link , one of the three arithmetic two-bridge links (the Whitehead link , the Berge link or the double-eight link ) or the link , the for those links contains the reducible component , the so-called Cayley cubic. In addition, the for the latter two links contains the irreducible component , or , respectively. Taking to be a representation with character (), with , then fixes a unique point in the hyperbolic space and is a conjugate to a representation (a qubit). Even though details on the physical implementation remain open, more generally, we show that topological quantum computing may be developed from the point of view of three-bridge links, the topology of the four-punctured sphere and Painlevé VI equation. The 0-surgery on the three circles of the Borromean rings L6a4 is taken as an example.

Dates et versions

hal-03934068 , version 1 (11-01-2023)

Identifiants

Citer

Michel Planat, David Chester, Marcelo M. Amaral, Klee Irwin. Fricke Topological Qubits. Quantum Rep., 2022, 4 (4), pp.523-532. ⟨10.3390/quantum4040037⟩. ⟨hal-03934068⟩
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