A Modular Functor Which is Universal¶for Quantum Computation

Abstract:We show that the topological modular functor from Witten–Chern–Simons theory is universal for quantum computation in the sense that a quantum circuit computation can be efficiently approximated by an intertwining action of a braid on the functor's state space. A computational model based on Chern–Simons theory at a fifth root of unity is defined and shown to be polynomially equivalent to the quantum circuit model. The chief technical advance: the density of the irreducible sectors of the Jones representation has topological implications which will be considered elsewhere.

• Publication year

  2000

• Venue

  Communications in Mathematical Physics

• Publication date

  2000-01-29

• Fields of study

  Mathematics, Physics, Computer Science

• Identifiers
  DOI 10.1007/S002200200645arXiv quant-ph/0001108
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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