Hamiltonians generating optimal-speed evolutions

On Hamiltonians Generating Optimal-Speed Evolutions

We present a simple derivation of the formula for the Hamiltonian operator(s) that achieve the fastest possible unitary evolution between given initial and final states. We discuss how this formula is modified in pseudo-Hermitian quantum mechanics and show by explicit calculation that the minimum travel time and the optimal-speed Hamiltonians are determined by the metric operator (inner product...

Building all Time Evolutions with Rotationally Invariant Hamiltonians

All elementary Hamiltonians in nature are expected to be invariant under rotation. Despite this restriction, we usually assume that any arbitrary measurement or unitary time evolution can be implemented on a physical system, an assumption whose validity is not obvious. We introduce two different schemes by which any arbitrary unitary time evolution and measurement can be implemented with desire...

Optimal control of effective Hamiltonians.

We present a systematic scheme for the optimization of quantum simulations. Specifically, we show how polychromatic driving can be used to significantly improve the driving of Raman transitions in the Lambda system, which opens new possibilities for controlled driving-induced effective dynamics.

Optimal Technological Architecture Evolutions of Information Systems

Convex Optimal Control Problems with Smooth Hamiltonians

Optimal control problems with convex costs, for which Hamiltonians have Lipschitz continuous gradients, are considered. Examples of such problems, including extensions of the linear-quadratic regulator with hard and possibly state-dependent control constraints, and piecewise linear-quadratic penalties are given. Lipschitz continuous differentiability and strong convexity of the terminal cost ar...