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Quantum computation by measurements

Leung, Debbie W. (2004) Quantum computation by measurements. International Journal of Quantum Information, 2 (1). pp. 33-43. ISSN 0219-7499. doi:10.1142/S0219749904000055.

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We first consider various methods for the indirect implementation of unitary gates. We apply these methods to rederive the universality of 4-qubit measurements based on a scheme much simpler than Nielsen's original construction [quant-ph/0108020]. Then, we prove the universality of simple discrete sets of 2-qubit measurements, again using a scheme simplifying the initial construction [quant-ph/0111122]. Finally, we show how to use a single 4-qubit measurement to achieve universal quantum computation, and outline a proof for the universality of almost all maximally entangling 4-qubit measurements.

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Additional Information:© 2004 World Scientific Publishing Company. Received 31 October 2003. We thank Michael Nielsen and David DiVincenzo for interesting discussions motivating part of the current result. Jim Harrington corrected a mistaken omission of Z in S_(0,1,2,3), and Daniel Gottesman drew our attention to Ref. 26. We thank Allen Knutson and Eric Rains for insightful ideas on the universality of the set <P,U PU> P∈P2. DWL is indebted to Charles Bennett, Isaac Chuang, Beth Ruskai, John Smolin, and Barbara Terhal for helpful discussion and encouragements. Duncan Mortimer made an extensive study of measurement models in his senior thesis, University of Queensland, 2002. Part of this work was completed when DWL was at IBM TJ Watson Research Center and at ITP, UCSB. DWL is partially supported by the US NSF under grant no. EIA-0086038 and by the Richard C. Tolman Endowment Fund at Caltech.
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Caltech Richard C. Tolman Endowment FundUNSPECIFIED
Subject Keywords:Quantum computation by measurements; universality
Issue or Number:1
Record Number:CaltechAUTHORS:20110817-134542392
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:24915
Deposited By: Tony Diaz
Deposited On:17 Oct 2011 16:41
Last Modified:09 Nov 2021 16:27

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