Recognizing Small-Circuit Structure in Two-Qubit Operators and Timing Hamiltonians to Compute Controlled-Not Gates

Details Recognizing Small-Circuit Structure in Two-Qubit Operators and Timing Hamiltonians to Compute Controlled-Not Gates Recognizing Small-Circuit Structure in Two-Qubit Operators and Timing Hamiltonians to Compute Controlled-Not Gates

2003-08-07

arxiv.org/abs/quant-ph/0308045v3

Physical Review A 70, 012310 (2004)

Physics

Quantum Physics

4 pages, circuit examples, an algorithm and a new application (v3)

Scientific paper

10.1103/PhysRevA.70.012310

This 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.

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