Recognizing small-circuit structure in two-qubit operators

Journal Article · Thu Jul 01 00:00:00 EDT 2004 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.70.012310· OSTI ID:20643882

Shende, Vivek V ^[1]; Bullock, Stephen S ^[2]; Markov, Igor L ^[3]

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1. Department of Mathematics, The University of Michigan, Ann Arbor, Michigan 48109-1109 (United States)
2. Mathematical and Computational Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899 (United States)
3. Department of Electrical Engineering and Computer Science, The University of Michigan, Ann Arbor, Michigan 48109-2122 (United States)

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.

• OSTI ID: 20643882
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 1 Vol. 70; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ALGORITHMS
COMMUNICATIONS
CORRELATIONS
GATING CIRCUITS
HAMILTONIANS
INFORMATION THEORY
QUANTUM MECHANICS
USES