Quantum Computer Circuit Analysis and Design

Report No. ARL-TR-4730
Authors: Dr. Howard E. Brandt
Date/Pages: February 2009; 16 pages
Abstract: Recent developments in the Riemannian geometry of quantum computation offer a new approach to the analysis of quantum computation. A geodesic equation defined on the SU(2n) group manifold, representing quantum gate operations on n qubits, may be used to determine optimal quantum evolutions and minimum-complexity quantum circuits. The geodesic equation is a first order nonlinear differential matrix equation of the Lax type. This report gives derivations of the Levi-Civita connection, Riemann curvature, sectional curvature, and geodesic equation on the SU(2n) Riemannian manifold.
Distribution: Approved for public release
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Last Update / Reviewed: February 1, 2009