Controlling open quantum systems

Abstract

This thesis describes the development and experimental verification (via liquid state nuclear magnetic resonance techniques) of new methods for controlling open quantum systems. First, methods that improve coherent control through the use of both strong control fields and detailed knowledge of the system's Hamiltonian are demonstrated. With the aid of numerical search methods, pulsed irradiation schemes are obtained that perform accurate, arbitrary, selective gates on multi-qubit systems. For a 3-qubit system, implementations show that the control sequences faithfully implement unitary operations with simulated gate fidelities on the order of 0.999 and experimentally determined projections of 0.99. Next, methods for controlling a quantum information in the presence of collective phase noise is demonstrated through the use of a decoherence free subspace (DFS). In addition to demonstrating the robustness of the DFS memory for both engineered and natural noise processes, a universal set of logical manipulations over the encoded qubit is realized. Dynamical control methods at the encoded level are used to implement noise-tolerant control over the DFS qubit in the presence of engineered phase noise significantly stronger than observed from natural noise sources.

(cont.) Finally, we explore the use of noiseless subsystems, which offers the most general and efficient method for protecting quantum information in the presence of noise that has symmetry properties. We demonstrate the preservation of a bit of quantum information against all collective noise operators by encoding it into a 3 qubit noiseless subsystem. A complete set of input states were used to determine the superoperator for the implemented one-qubit process and confirm that the fidelity of entanglement is improved for a large, non-commuting set of engineered errors. To date, this is the largest set of error operators that have been successfully corrected for by any quantum code.