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Estimating Jones and HOMFLY polynomials with one clean qubit

Jordan, Stephen P. and Wocjan, Pawel (2009) Estimating Jones and HOMFLY polynomials with one clean qubit. Quantum Information and Computation, 9 (3-4). pp. 264-289. ISSN 1533-7146.

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The Jones and HOMFLY polynomials are link invariants with close connections to quantum computing. It was recently shown that finding a certain approximation to the Jones polynomial of the trace closure of a braid at the fifth root of unity is a complete problem for the one clean qubit complexity class[18]. This is the class of problems solvable in polynomial time on a quantum computer acting on an initial state in which one qubit is pure and the rest are maximally mixed. Here we generalize this result by showing that one clean qubit computers can efficiently approximate the Jones and single-variable HOMFLY polynomials of the trace closure of a braid at any root of unity.

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Additional Information:© 2009 Rinton Press. Received August 13, 2008. Revised October 21, 2008. We thank Peter Shor for useful discussions. During the research and writing of this paper SJ was at Center for Theoretical physics at MIT, the Digital Materials Laboratory at RIKEN, and the Institute for Quantum Information at Caltech. SJ thanks these institutions as well as the Army Research Office (ARO), the Disruptive Technology Office (DTO), the Department of Energy (DOE), Eddie Farhi at MIT, Franco Nori and Sahel Ashab at RIKEN, and John Preskill at Caltech. PW gratefully acknowledges support from NSF grants CCF-0726771 and CCF-0746600. PW would like to thank Eddie Farhi’s group for their hospitality and the W. M. Keck Foundation for partial support.
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W. M. Keck FoundationUNSPECIFIED
Subject Keywords:Jones Polynomial; HOMFLY; One Clean Qubit
Issue or Number:3-4
Record Number:CaltechAUTHORS:20090904-134456902
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:15625
Deposited By: Ruth Sustaita
Deposited On:15 Sep 2009 17:44
Last Modified:03 Oct 2019 01:00

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