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Efficient quantum circuits for arbitrary sparse unitaries

Jordan, Stephen P. and Wocjan, Pawel (2009) Efficient quantum circuits for arbitrary sparse unitaries. Physical Review A, 80 (6). Art. No. 062301. ISSN 1050-2947.

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Arbitrary exponentially large unitaries cannot be implemented efficiently by quantum circuits. However, we show that quantum circuits can efficiently implement any unitary provided it has at most polynomially many nonzero entries in any row or column, and these entries are efficiently computable. One can formulate a model of computation based on the composition of sparse unitaries which includes the quantum Turing machine model, the quantum circuit model, anyonic models, permutational quantum computation, and discrete time quantum walks as special cases. Thus, we obtain a simple unified proof that these models are all contained in BQP. Furthermore, our general method for implementing sparse unitaries simplifies several existing quantum algorithms.

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Additional Information:© 2009 The American Physical Society. Received 21 April 2009; revised 5 August 2009; published 1 December 2009. We thank Dominik Janzing for helpful discussions. S.P.J. gratefully acknowledges support from the Sherman Fairchild Foundation and the National Science Foundation under Grant No. PHY-0803371. P.W. gratefully acknowledges the support by NSF Grants No. CCF-0726771 and No. CCF-0746600.
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
NSFCCF- 0746600
Issue or Number:6
Classification Code:PACS: 03.67.Ac.
Record Number:CaltechAUTHORS:20100121-132802102
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:17268
Deposited By: Ruth Sustaita
Deposited On:25 Jan 2010 23:54
Last Modified:03 Oct 2019 01:25

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