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Laser Physics

, Volume 16, Issue 11, pp 1582–1594 | Cite as

Quantum knitting

  • S. Garnerone
  • A. Marzuoli
  • M. Rasetti
Quantum Information and Quantum Computation

Abstract

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.

PACS numbers

03.67.Lx 02.10.Kn 

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Copyright information

© MAIK “Nauka/Interperiodica” 2006

Authors and Affiliations

  • S. Garnerone
    • 1
    • 3
  • A. Marzuoli
    • 2
    • 3
  • M. Rasetti
    • 1
    • 3
  1. 1.Dipartimento di FisicaPolitecnico di TorinoTorinoItaly
  2. 2.Dipartimento di Fisica Nucleare e TeoricaUniversità degli Studi di Pavia and Istituto Nazionale di Fisica NuclearePaviaItaly
  3. 3.ISI FoundationVilla GualinoTorinoItaly

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