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16 April 2010 Lifted Jacobi equation for varying penalty parameter in the Riemannian geometry of quantum computation
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Abstract
Recent developments in the differential geometry of quantum computation are exposited. The quantum evolution is described in terms of the special unitary group of n-qubit unitary operators with unit determinant. The group manifold is taken to be Riemannian. In the present work, the lifted Jacobi equation and geodesic derivative are reviewed. This is applicable to investigations of conjugate points and the global characteristics of geodesic paths in the group manifold, and the determination of optimal quantum circuits for carrying out a quantum computation.
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Howard E. Brandt "Lifted Jacobi equation for varying penalty parameter in the Riemannian geometry of quantum computation", Proc. SPIE 7702, Quantum Information and Computation VIII, 770205 (16 April 2010); https://doi.org/10.1117/12.849650
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