Optimal Control Theory and Quantum Information Systems

Daniel Basilewitsch

Sebastian Deffner

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.

Hendra I. Nurdin, Naoki Yamamoto

Matthias M. Müller, Stefano Gherardini, Tommaso Calarco +2 more

Accurate manipulations of an open quantum system require a deep knowledge of its controllability properties and the information content of the implemented control fields. By using tools of information and quantum optimal control theory, we provide analytical bounds (information-time bounds) to characterize our capability to control the system when subject to arbitrary sources of noise. Moreover, since the presence of an external noise field induces open quantum system dynamics, we also show that the results provided by the information-time bounds are in very good agreement with the Kofman-Kurizki universal formula describing decoherence processes. Finally, we numerically test the scaling of the control accuracy as a function of the noise parameters, by means of the dressed chopped random basis (dCRAB) algorithm for quantum optimal control.

Colm A. Ryan, C. Negrevergne, Martin Laforest +2 more

In building a quantum-information processor (QIP), the challenge is to coherently control a large quantum system well enough to perform an arbitrary quantum algorithm and to be able to correct errors induced by decoherence. Nuclear magnetic resonance (NMR) QIPs offer an excellent testbed on which to develop and benchmark tools and techniques to control quantum systems. Two main issues to consider when designing control methods are accuracy and efficiency, for which two complementary approaches have been developed so far to control qubit registers with liquid-state NMR methods. The first applies optimal control theory to numerically optimize the control fields to implement unitary operations on low-dimensional systems with high fidelity. The second technique is based on the efficient optimization of a sequence of imperfect control elements so that implementation of a full quantum algorithm is possible while minimizing error accumulation. This paper summarizes our work in implementing both of these methods. Furthermore, we show that taken together, they form a basis to design quantum control methods for a block-architecture QIP so that large system size is not a barrier to implementing optimal control techniques.