Dborin, James; (2023) Implementing Tensor Network Algorithms on Quantum Computers. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Quantum computing is an exciting area of research with potentially significant impacts on studying physics, developing new medicines, and understanding complex materials. However, current quantum hardware is too noisy to achieve the anticipated speed-ups that quantum computing promises over classical computers. While waiting for powerful devices that can perform quantum error correction, so-called NISQ devices will become available with the capability to perform computations beyond those possible classically. However, whether these NISQ devices will permit the acceleration of a scientifically or industrially relevant problem is still unknown. Tensor network methods are state-of-the-art techniques for the simulation of 1D and 2D quantum systems. NISQ circuits can generate and manipulate tensor network states with larger bond dimensions than can be simulated classically. This thesis explores methods to map insights and algorithms from the classical tensor network toolbox to NISQ devices to extend and improve NISQ-powered quantum simulation. This thesis outlines algorithms for representing and time-evolving infinite, translationally-invariant quantum states on finite NISQ devices utilising translationally invariant MPS states. This thesis also outlines an initialisation technique for variational quantum algorithms based on pre-training classical matrix product states and demonstrates its effectiveness for quantum simulation and machine learning.

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