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Proceedings Paper

Finding small two-qubit circuits
Author(s): Vivek V. Shende; Igor L. Markov; Stephen S. Bullock
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Paper Abstract

An important result from the mid nineties shows that any unitary evolution may be realized as a sequence of controlled-not and one-qubit gates. This work surveys especially efficient circuits in this library, in the special case of evolutions on two-quantum bits. In particular, we show that to construct an arbitrary two-qubit state from |00>, one CNOT gate suffices. To simulate an arbitrary two-qubit operator up to relative phases, two CNOTs suffice. To simulate an arbitrary two-qubit operator up to global phase, three CNOTs suffice. In each case, we construct an explicit circuit and prove optimality in the generic case. We also contribute a procedure to determine the minimal number of CNOT gates necessary to simulate a given two-qubit operator up to global phase. We use this procedure to discuss timing a given Hamiltonian to simulate the CNOT and to determine an optimal circuit for the two-qubit Quantum Fourier Transform. Our constructive proofs amount to circuit synthesis algorithms and have been coded in C++.

Paper Details

Date Published: 24 August 2004
PDF: 12 pages
Proc. SPIE 5436, Quantum Information and Computation II, (24 August 2004); doi: 10.1117/12.542381
Show Author Affiliations
Vivek V. Shende, Univ. of Michigan (United States)
Igor L. Markov, Univ. of Michigan (United States)
Stephen S. Bullock, National Institute of Standards and Technology (United States)


Published in SPIE Proceedings Vol. 5436:
Quantum Information and Computation II
Eric Donkor; Andrew R. Pirich; Howard E. Brandt, Editor(s)

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