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… (More)

Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local HamiltonianH for a timet . In… (More)

We classify all unitary modular tensor categories (UMTCs) of rank ≤ 4. There are a total of 35 UMTCs of rank ≤ 4 up to ribbon tensor equivalence. Since the distinction between the modular S-matrix S… (More)

The Jones–Witten theory gives rise to representations of the (extended) mapping class group of any closed surface Y indexed by a semi-simple Lie group G and a level k . In the case G = SU(2) these… (More)

A (2+1)-dimensional topological quantum field theory (TQFT) determines, for each g ≥ 0, a projective representation (ρg, Vg) of the mapping class group Mg of a closed oriented surface of genus g.… (More)

We investigate a family of (reducible) representations of the braid groups Bn corresponding to a specific solution to the YangBaxter equation. The images of Bn under these representations are finite… (More)

Our understanding of Nature comes in layers, so should the development of logic. Classic logic is an indispensable part of our knowledge, and its interactions with computer science have recently… (More)

Abstract. An attempt is made to conceptualize the derivation as well as to facilitate the computation of Ohtsuki’s rational invariants λn of integral homology 3-spheres extracted from… (More)

Using a probabilistic interpretation of the Burau representation of the braid group offered by Vaughan Jones, we generalize the Burau representation to a representation of the semigroup of string… (More)