Variational quantum eigensolvers for the Hubbard Model

Lead Research Organisation: University of Bristol
Department Name: Physics

Abstract

It is necessary to determine which algorithms can be run on near-term intermediate-scale
quantum computers and which could potentially lead to a quantum advantage in the
coming years. Current devices have a limited number of qubits and gates that can be
applied and are very noisy. It is therefore important to find a resource efficient algorithm,
that can hold up against errors, and that preferably has useful applications.
The best candidates are hybrid quantum-classical algorithms which use quantum computers
to speed up a specific part of the algorithm. One of these is the Variational Quantum
Eigensolver (VQE) algorithm which is used to find the ground state of Hamiltonians, making
it useful for applications such as quantum chemistry. The VQE algorithm uses classical
optimisation techniques to optimise over the space of quantum circuits for constructing the
desired state. The quality of the states produced is determined by calls to the quantum
computer.

A lot of work has been done on applying the VQE to molecules, but not as much on lattice-
based models in physics. The Fermi-Hubbard model is one of the simplest models of

interacting particles in a lattice used in solid-state physics. Developing our understanding of

this model could lead to the design of revolutionary batteries, solar cells and high-
temperature superconductors. Calculating the ground state of the Fermi-Hubbard

Hamiltonian is difficult for classical computers because of the scaling in resources needed as
the lattice grows.
In this PhD, my focus will initially be on optimising the VQE algorithm for the Fermi-Hubbard
model. Anything from the initial state given to the algorithm and the family of circuits to
optimise over, to the way the measurements are performed, and the classical optimisation
technique used can be considered and tailored to the Fermi-Hubbard model. Work will also
be done to study how noise and errors affect the computation and how best to manage the
algorithm on various quantum architectures.

Publications

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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/R51245X/1 01/10/2017 30/09/2021
1934995 Studentship EP/R51245X/1 18/09/2017 30/09/2021 Lana Mineh