Solving the Hubbard model using the variational quantum eigensolver

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)


Simulating quantum-mechanical systems relating to quantum chemistry or solid-state physics is one of the most important problems that quantum computers are anticipated to tackle. However, near-term quantum computers will be noisy and have a limited number of qubits, restricting the types of computations that can be performed. This has lead to the development of hybrid quantum-classical algorithms, which are suitable for use on these near-term devices. Systematic studies involving high-performance classical simulations are required to thoroughly assess the effectiveness of these algorithms.

In this thesis, we address this challenge for the variational quantum eigensolver applied to the Hubbard model, an important model from condensed-matter physics used to describe the behaviour of correlated electrons. We consider both the solution of instances of this model directly and a compressed form obtained using density matrix embedding theory. All aspects of this hybrid quantum-classical algorithm are considered, from the initial encoding of the fermionic Hamiltonian onto the quantum computer, to the ansatz circuits and the classical optimisation routine.

For the purpose of speeding up future simulations of variational quantum algorithms, we develop a new high-performance quantum simulator. We describe the efficient algorithms used for performing gates and measurement. We also discuss how certain circuit properties, such as number or spin preservation, can lead to further algorithmic speed-ups. Implementing these techniques on high-performance classical hardware may facilitate the numerical exploration of larger problems.
Date of Award22 Mar 2022
Original languageEnglish
Awarding Institution
  • The University of Bristol
SponsorsPhasecraft Ltd
SupervisorAshley M R Montanaro (Supervisor)

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