Quantum Knitting

Details Quantum Knitting Quantum Knitting

2006-06-16

arxiv.org/abs/quant-ph/0606137v1

Laser Physics Vol. 16 No. 11 (2006) 1582-1594

Physics

Quantum Physics

29 pages, 5 figures; to appear in Laser Journal

Scientific paper

10.1134/S1054660X06110120

We analyze the connections between the mathematical theory of knots and quantum physics by addressing a number of algorithmic questions related to both knots and braid groups. Knots can be distinguished by means of `knot invariants', among which the Jones polynomial plays a prominent role, since it can be associated with observables in topological quantum field theory. Although the problem of computing the Jones polynomial is intractable in the framework of classical complexity theory, it has been recently recognized that a quantum computer is capable of approximating it in an efficient way. The quantum algorithms discussed here represent a breakthrough for quantum computation, since approximating the Jones polynomial is actually a `universal problem', namely the hardest problem that a quantum computer can efficiently handle.

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