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Efficient Quantum Circuits for Schur and Clebsch-Gordan Transforms

Bacon, Dave and Chuang, Isaac L. and Harrow, Aram W. (2006) Efficient Quantum Circuits for Schur and Clebsch-Gordan Transforms. Physical Review Letters, 97 (17). Art. No. 170502. ISSN 0031-9007. doi:10.1103/PhysRevLett.97.170502.

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The Schur basis on n d-dimensional quantum systems is a generalization of the total angular momentum basis that is useful for exploiting symmetry under permutations or collective unitary rotations. We present efficient {size poly[n,d,log(1/epsilon)] for accuracy epsilon} quantum circuits for the Schur transform, which is the change of basis between the computational and the Schur bases. Our circuits provide explicit efficient methods for solving such diverse problems as estimating the spectrum of a density operator, quantum hypothesis testing, and communicating without a shared reference frame. We thus render tractable a large series of methods for extracting resources from quantum systems and for numerous quantum information protocols.

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Additional Information:©2006 The American Physical Society (Received 13 July 2004; revised 3 March 2006; published 27 October 2006) This work was partially funded by the NSF Center for Bits and Atoms Contract No. CCR-0122419, the NSF Institute for Quantum Information under Grant No. EIA-0086048, and ARO Contracts No. DAAD19-01-1-06 and No. W911NF-05-R-0009. We thank Nolan Wallach for useful discussions.
Issue or Number:17
Record Number:CaltechAUTHORS:BACprl06
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6186
Deposited By: Archive Administrator
Deposited On:28 Nov 2006
Last Modified:08 Nov 2021 20:31

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