In the Riemannian geometry of quantum computation, the quantum evolution is described in terms of the special unitary group of n-qubit unitary operators with unit determinant. To elaborate on some aspects of the methodology, the generic Jacobi equation and lifted Jacobi equation, together with solutions on the group manifold, are explicitly derived. This is important for investigations of the global characteristics of geodesic paths in the group manifold, and the determination of optimal quantum circuits for carrying out a quantum computation.

Date Published: 16 April 2010
PDF: 8 pages
Proc. SPIE 7702, Quantum Information and Computation VIII, 770208 (16 April 2010); doi: 10.1117/12.849648

Published in SPIE Proceedings Vol. 7702:
Quantum Information and Computation VIII
Eric J. Donkor; Andrew R. Pirich; Howard E. Brandt, Editor(s)