Framework for Learning and Control in the Classical and Quantum Domains
Date
2024-06-20
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Abstract
Control and learning are essential to technological advancement, both in the classical and quantum domains, yet their interrelationship is insufficiently clear in the literature, especially between classical and quantum definitions of control and learning. In this thesis, we aim to construct a framework that formally relates learning and control, both classical and quantum, to each other, with this formalism showing how learning can aid control. We formulate new versions of quantum learning and control that essentially quantise classical learning and control, respectively. Furthermore, our framework helps identify interesting unsolved problems in the nexus of classical and quantum control and learning and helps choose tools to solve problems. Our unification of these fields relies on diagrammatically representing the state of knowledge, which elegantly summarises existing knowledge and exposes knowledge gaps. As use cases, we cast the well-studied problem of adaptive quantum-enhanced interferometric phase estimation as a supervised learning problem for devising feasible control policies and develop effective quantum control for two-qubit gate design with trapped ions. Informed by the knowledge that the plant, i.e.~ion trap, is a channel, we develop a comprehensive model of controlled open-system dynamics described by a quantum master equation and validate our model based on empirical data gathered from a control system for preparing Bell states. We then employ global optimisation to design pulse sequences for achieving a robust, rapid two-qubit gate for a chain of seven trapped $^{171}$Yb$^{+}$ ions by optimising over numerically integrated quantum master equation solutions. We further explore the nexus of classical and quantum learning through hybrid classical-quantum learning algorithms. We introduce the ``analogue-quantum kitchen sinks'' algorithm, a quantum extension of the classical "random kitchen sinks," which employs an analogue-quantum computer for mapping data features into new features in a non-linear manner. A classical algorithm can then perform machine learning tasks using the new features. We show the effectiveness of our algorithm for performing binary classification on both a synthetic and a real-world data set through computer simulation of a quantum annealer's operation.
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Keywords
Quantum control, Quantum gates, Trapped ions, Machine learning
Citation
Vedaie, S. S. (2024). Framework for learning and control in the classical and quantum domains (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.