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Title: Quantum chemistry and quantum computers : testing the Bravyi-Kitaev mapping and Trotter order optimisations
Author: Tranter, Andrew
ISNI:       0000 0004 7658 8381
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2019
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The quantum simulation of quantum chemistry is often cited as one of the most important potential uses for emerging quantum technology. Quantum computing methods are expected to be able to perform full configuration interaction level quantum chemistry calculations with tractable computational resource requirements. However, early quantum computers are likely to be constrained in both the number of qubits available, and the number of gates that can be performed. Implementing chemical algorithms on such quantum devices will require algorithmic improvements. In this thesis, two avenues for optimisation of the canonical method for the simulation of quantum chemistry on quantum computers are discussed. The Bravyi-Kitaev transformation is an alternative to the Jordan-Wigner transformation, the canonical method of mapping electronic states and operators to states and operators of qubits. The resource implications of this transformation scheme are assessed using a variety of chemical examples. Known techniques for optimising quantum circuits for quantum chemistry are applied, and the implications for the use of the Bravyi-Kitaev transformation are considered. Trotterization - the use of Trotter-Suzuki formulae to approximate the evolution operator for the molecular Hamiltonian - is discussed. In particular, ordering schemes designed to minimise the Trotter error are described. Finally, the importance of Trotter ordering when using the Bravyi-Kitaev transformation is considered. The performance of either transformation scheme is found to be highly dependent on the Trotter ordering and level of optimisation chosen. As such, the relative merits of either transformation scheme are found to be not as simple as previously thought, although in most cases the Bravyi-Kitaev transformation is found to be advantageous. The relative merits of both mapping and ordering schemes are considered in the context of performing quantum simulation of quantum chemistry on real quantum devices. Particular focus is paid to molecular systems which are intractable to classical computational simulation. The results emphasise the need for thorough analysis of optimisation schemes, such that quantum chemistry may indeed be a principal use of early quantum computation.
Supervisor: Coveney, Peter V. ; Mintert, Florian ; Love, Peter J. Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral