Control of Open Quantum Systems

Abstract

Known as decoherence, the unavoidable interaction of a quantum system with its surrounding environment is usually considered to be detrimental for quantum information processing. In this thesis the coherent, open loop control of such open systems is studied. Concepts from quantum control theory and the theory of open quantum system are adopted in order to fight decoherence and implement quantum gates in a noiseless manner. In particular, Lie algebraic methods and numerical optimization tools are used to investigate the control properties of a single spin interacting with a spin environment. We show that, independent of the size of the environment, every unitary transformation can be implemented on the system spin through a single control field. We proceed by investigating dynamical decoupling, a method to suppress the interactions with the environment, for finite- and for in- finite dimensional systems. We prove that every finite dimensional system can be protected from decoherence, even if the environment is infinite dimensional, whereas for noise described by a Lindblad master equation dynamical decoupling will never succeed. This will lead to a new method to distinguish decoherence from intrinsic noise terms. We further prove that not every infinite dimensional system can be protected from decoherence through dynamical decoupling. Afterwards we investigate dynamical decoupling of systems that are described by quadratic Hamiltonians, showing that such interactions can always be suppressed with two simple operations. In the last part we investigate the coherent control of a Lindblad master equation. We show that a strong noise process exhibiting a decoherence free subspace can substantially increase the number of unitary operations that can be implemented, allowing us to fully control parts of the system. Afterwards we develop a scheme to make Hamiltonians and Lindbladians commutative by adding an auxiliary system. The old, possibly non-commutative dynamics, is recovered through a non-selective measurement.

Date of Award	05 May 2016
Original language	English
Awarding Institution	Aberystwyth University
Supervisor	Daniel Burgarth (Supervisor) & Rolf Gohm (Supervisor)