Optimal control, geometry, and quantum computing

Details Optimal control, geometry, and quantum computing Optimal control, geometry, and quantum computing

2006-03-19

arxiv.org/abs/quant-ph/0603160v2

Physics

Quantum Physics

7 Pages Added Full Names to Authors

Scientific paper

10.1103/PhysRevA.73.062323

We prove upper and lower bounds relating the quantum gate complexity of a unitary operation, U, to the optimal control cost associated to the synthesis of U. These bounds apply for any optimal control problem, and can be used to show that the quantum gate complexity is essentially equivalent to the optimal control cost for a wide range of problems, including time-optimal control and finding minimal distances on certain Riemannian, subriemannian, and Finslerian manifolds. These results generalize the results of Nielsen, Dowling, Gu, and Doherty, Science 311, 1133-1135 (2006), which showed that the gate complexity can be related to distances on a Riemannian manifold

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