Quantum system characterization with limited resources.

The construction and operation of large-scale quantum information devices presents a grand challenge. A major issue is the effective control of coherent evolution, which requires accurate knowledge of the system dynamics that may vary from device to device. We review strategies for obtaining such knowledge from minimal initial resources and in an efficient manner, and apply these to the problem of characterization of a qubit embedded into a larger state manifold, made tractable by exploiting prior structural knowledge. We also investigate adaptive sampling for estimation of multiple parameters.

Coherent time evolution of a single-electron wave function.

Observation of coherent single-electron dynamics is severely limited by experimental bandwidth. We present a method to overcome this using moving quantum dots defined by surface acoustic waves. Each dot holds a single electron, and travels through a static potential landscape. When the dot passes abruptly between regions of different confinement, the electron is excited into a superposition of states, and oscillates unitarily from side to side. We detect these oscillations by using a weak, repeated measurement of the current across a tunnel barrier, and find close agreement with simulations.

Geometric phases for mixed states in interferometry.

We provide a physical prescription based on interferometry for introducing the total phase of a mixed state undergoing unitary evolution, which has been an elusive concept in the past. We define the parallel transport condition that provides a connection form for obtaining the geometric phase for mixed states. The expression for the geometric phase for mixed state reduces to well known formulas in the pure state case when a system undergoes noncyclic and unitary quantum evolution.