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Elementary Gates for Quantum Computation (1995)
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| Citations: | 280 - 11 self |
BibTeX
@MISC{Barenco95elementarygates,
author = {Adriano Barenco and Charles H. Bennett and Richard Cleve and David P. DiVincenzo and Norman Margolus and Peter Shor and Tycho Sleator and John Smolin and Harald Weinfurter},
title = {Elementary Gates for Quantum Computation},
year = {1995}
}
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Abstract
We show that a set of gates that consists of all one-bit quantum gates (U(2)) and the two-bit exclusive-or gate (that maps Boolean values (x, y)to(x, x⊕y)) is universal in the sense that all unitary operations on arbitrarily many bits n (U(2 n)) can be expressed as compositions of these gates. We investigate the number of the above gates required to implement other gates, such as generalized Deutsch-Toffoli gates, that apply a specific U(2) transformation to one input bit if and only if the logical AND of all remaining input bits is satisfied. These gates play a central role in many proposed constructions of quantum computational networks. We derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two- and three-bit quantum gates, the asymptotic number required for n-bit Deutsch-Toffoli gates, and make some observations about the number required for arbitrary n-bit unitary operations.
Keyphrases
input bit asymptotic number arbitrary n-bit unitary operation two-bit exclusive-or gate boolean value many proposed construction quantum computational network elementary gate many bit one-bit quantum gate unitary operation generalized deutsch-toffoli gate exact number central role n-bit deutsch-toffoli gate three-bit quantum gate
