Utilising Non-Unitary Integrated Quantum Photonics to realise Variational Quantum Algorithms

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)

Abstract

When one considers quantum computation, one typically thinks about unitary evolution acting
on a system of two-level qubit systems. All the proposed fault-tolerant quantum algorithms can
be broken down into a series of unitary gates acting on one or more qubits at a time, evolving
their quantum state before measurement. However, when mapping this process to photonic path
encoded qubits, due transforming from the n-qubit basis states to photonic modes, this process is
no longer unitary. Thus, the Clements and Reck arbitrary unitary schemes are not sufficient to
implement these qubit evolutions.
In this thesis, we explore the implementation of quantum algorithms to a four-mode photonic
device designed to implement arbitrary non-unitary transformations. It achieves this using two,
four-mode Clements decompositions enclosing a region of tuneable loss modes. By carefully matching this interferometer to singular value decompositions of arbitrary non-unitary transformation,
we can implement a post-selected, non-unitary evolution on the input photonic modes. This is
extended further to apply two qubit Variational Quantum Algorithms on this device and demonstrate its ability to be reconfigured to a high fidelity. Along the way we provide mappings between
qubit evolutions and dual-rail encoded photonic qubits, and schemes of modelling multi-photon
emission terms.
Date of Award7 May 2024
Original languageEnglish
Awarding Institution
  • University of Bristol
SupervisorAnthony Laing (Supervisor) & David Tew (Supervisor)

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