Wimalaweera, Vinul; (2025) Tensor network inspired methods for near-term quantum computation. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

This thesis investigates how tensor networks can inform our design of algorithms for near-term quantum devices. We primarily work in the paradigm of variational quantum algorithms where tensor networks can be used as a variational model ansatz tuned to the underlying problem’s entanglement structure. This allows for the efficient use of resources, a problem of particular importance for today’s small-scale noisy quantum computers. In particular, this thesis focuses on studying quantum tensor networks for quantum simulation and machine learning. We develop algorithms designed to simulate large quantum systems in the thermodynamic limit, implementing tools from classical tensor network literature which allow us to represent these infinite states using finite circuits. In doing so, we design an algorithm to study the groundstate properties of the transverse field Ising model through the quantum critical point. We also design and implement a time evolution algorithm that utilises this infinite tensor network ansatz. The design of the algorithm allows for portability between various architectures, a feature we demonstrate by testing the algorithm on both Google’s superconducting and Quantinuum’s trapped-ion architectures. Collaborative benchmarking in this way provides data that can be used to investigate impacts of device specific characteristics such as device error or shot budgets on the performance of the algorithm. In addition, the testing highlighted specific areas of improvements for current generation device which provides vital information for hardware teams on directions towards quantum advantage. Tensor network ansatzes also provide a model family of interest for quantum machine learning. We utilise the close correspondence between classical and quantum tensor networks to demonstrate a heuristic technique to mitigate barren plateaus, a problem of significant importance for any quantum machine learning model. Subsequently, we propose a native tensor network algorithm to find supervised learning models. In summary, this thesis leverages the utility of the rich literature developed in classical tensor networks to design near-term quantum algorithms in a range of fields.

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