Recognizing small-circuit structure in two-qubit operators

This work proposes numerical tests which determine whether a two-qubit operator has an atypically simple quantum circuit. Specifically, we describe formulas, written in terms of matrix coefficients, characterizing operators implementable with exactly zero, one, or two controlled-NOT (CNOT) gates and...

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Bibliographic Details
Published in:Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2004-07, Vol.70 (1)
Main Authors: Shende, Vivek V., Bullock, Stephen S., Markov, Igor L.
Format: Article
Language:English
Subjects:
ALGORITHMS
ATOMIC AND MOLECULAR PHYSICS
COMMUNICATIONS
CORRELATIONS
GATING CIRCUITS
HAMILTONIANS
INFORMATION THEORY
QUANTUM MECHANICS
USES
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Summary:This work proposes numerical tests which determine whether a two-qubit operator has an atypically simple quantum circuit. Specifically, we describe formulas, 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 gates. We give an algorithm for synthesizing two-qubit circuits with an 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 gate, when this is possible.
ISSN:1050-2947
1094-1622
DOI:10.1103/PhysRevA.70.012310