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Verhandlungen der Deutschen Physikalischen Gesellschaft

Communicating at the quantum speed limit using optimal control

Michael Murphy, Simone Montangero, Tommaso Calarco, Tommaso Caneva, Giuseppe E. Santoro, Vittorio Giovannetti, Rosario Fazio

Published Jan 1, 2009• 0 citations
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We study quantum information processing by means of optimal control theory. To this end, we analyze the damped Jaynes-Cummings model, and derive optimal control protocols that minimize the heating or energy dispersion rates, and controls that drive the system at the quantum speed limit. Special emphasis is put on analyzing the subtleties of optimal control theory for our system. In particular, it is shown how two fundamentally different approaches to the quantum speed limit can be reconciled by carefully formulating the problem.
The quantum speed limit sets the minimum time required to transfer a quantum system completely into a given target state. At shorter times the higher operation speed results in a loss of fidelity. Here we quantify the trade-off between the fidelity and the duration in a system driven by a time-varying control. The problem is addressed in the framework of Hilbert space geometry offering an intuitive interpretation of optimal control algorithms. This approach leads to a necessary criterion for control optimality applicable as a measure of algorithm convergence. The time fidelity trade-off expressed in terms of the direct Hilbert velocity provides a robust prediction of the quantum speed limit and allows one to adapt the control optimization such that it yields a predefined fidelity. The results are verified numerically in a multilevel system with a constrained Hamiltonian and a classification scheme for the control sequences is proposed based on their optimizability.