Scalable approaches to the characterization of open quantum system dynamics

Abstract

One of the biggest challenges in the physical realization of quantum information processing (QIP) is the precise control of the system. In order to achieve this, we characterize the gates, errors, and noise occurring in experimental setups. In this thesis we develop and further study characterization methods, putting particular emphasis on the scalability problem: O(D4) parameters describe the dynamics of an open quantum system of dimension D, thus O(D4) resources are in principle required to characterize it -- which is a problem in QIP where the desired systems are large (D = 2n for n qubits). We first study the fidelity decay (also called Loschmidt echo) of the system, for many steps under the progressive randomization due to a one-qubit twirl. We show how this quantity encodes useful information about the process begin twirled. We then present a method to measure the magnitude of the multi-body correlations that scales as O(nw), when only up to w-body interactions are expected among the n qubits. We implemented this method in a four-qubit liquid-state Nuclear Magnetic Resonance (NMR) QIP device, demonstrating its potential and feasibility. The experimental work also pointed out the need for robust procedures and the role of implementation errors, while deepening our knowledge of NMR QIP dynamics. We also report on several practical aspects of the experiment, including details on twirls using random rotations and Clifford operators. We furthermore relate this work to recent developments in the community, arriving to a more comprehensive protocol and establishing an intrinsic hierarchy of characterization algorithms. Finally, we study the many-step fidelity decay when using a flawed twirl, thus acknowledging the most realistic scenario where we have a faulty device attempting to characterize itself. Our preliminary work points towards the use of a many-step scheme that promises robust scalable tools to characterize the twirl operators themselves.