Quantum-enabled technologies promise advancements across a huge range of industrial, metrological and medical applications and are already demonstrating significant impacts, especially in the realm of sensing and metrology. While the extreme sensitivity of quantum systems to their environment is fueling those applications, it also represents a major hurdle to technologies which require long-term stability such as quantum computing and quantum simulations. In addition to the inherent decoherence phenomenon, the challenge associated with controlling a quantum system accurately and precisely, does in fact impede all of the aforementioned applications. Such techniques have therefore been subject to extensive research in both the academic and industrial sector and as a result, sophisticated quantum control techniques are emerging in order to understand, characterize and mitigate errors in quantum systems.
This thesis presents how quantum control techniques can be employed to characterize and suppress both control imperfections and environmental noise in quantum systems, using experiments with trapped ions as a model quantum platform. We demonstrate two distinct but interrelated approaches that leverage either time-domain or frequency-domain information about the noise.
In the first approach, we show how supervised learning algorithms can efficiently extract time-domain correlations from time-stamped sequences of projective measurements on a qubit. This information can then be used to perform real-time predictive control in which we autonomously pre-compensate anticipated qubit noise in order to stabilize the system.
The second approach deploys provably optimal narrowband controls in order to characterize the specific spectral components of noise experienced by a qubit. Here, frequency-shifted Slepian functions permit reconstruction of system noise with maximum out-of-band rejection, and full spectrum reconstruction is enabled using techniques based on multitaper and Bayesian methods.