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.
分享
引用
