Learning models in quantum computation and quantum control

Thesis

We investigate learning models for implementing arbitrary unitary operations and perform quantum machine learning tasks. First, we discuss efficient constructions for building unitary transformations in U(d), thus providing upper bounds on the minimum time required to implement them. Second, we study the hardness of learning unitary operations in U(d) via gradient descent on the time parameters of an alternating operator sequence, and numerically find that, despite the nonconvexity of the loss landscape, gradient descent always converges to the target unitary when the sequence contains d² or more parameters. Third, we introduce the first quantum boosting algorithm for converting a weak quantum learner into a strong accurate quantum learner for a Boolean concept class C; thereby achieving a quadratic quantum improvement over classical AdaBoost in terms of VC(C).

Authors: Maity, R

• Alternative title: Learning models in quantum computation and quantum control
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: Quantum machine learning; Quantum mechanics; Quantum computation
• Subjects: Machine learning; Physics