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29 March 2024
 
  » arxiv » quant-ph/0308045

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Recognizing Small-Circuit Structure in Two-Qubit Operators and Timing Hamiltonians to Compute Controlled-Not Gates
Vivek V. Shende ; Stephen S. Bullock ; Igor L. Markov ;
Date 7 Aug 2003
Journal Physical Review A 70, 012310 (2004)
Subject quant-ph
AbstractThis work proposes numerical tests which determine whether a two-qubit operator has an atypically simple quantum circuit. Specifically, we describe formulae, written in terms of matrix coefficients, characterizing operators implementable with exactly zero, one, or two controlled-not (CNOT) gates and all other gates being one-qubit. We give an algorithm for synthesizing two-qubit circuits with optimal number of CNOT gates, and illustrate it on operators appearing in quantum algorithms by Deutsch-Josza, Shor and Grover. In another application, our explicit numerical tests allow timing a given Hamiltonian to compute a CNOT modulo one-qubit gates, when this is possible.
Source arXiv, quant-ph/0308045
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