Abstract
Looking at how to use the principles of quantum mechanics to drive progress in technology is an emerging and exciting direction of research, where quantum photonics is playing a key role. These quantum technologies cover applications in communication security, enhancing measurement sensitivitiesand creating new computation capabilities. Within the study of quantum computation, we can broadly think of two lines of research: near term hardware and theory challenges, often referred to as noisy intermediate scale quantum (NISQ), and longer term work on architectures and hardware for universal fault tolerant quantum computing (FTQC). The work presented here attempts to contribute to progress on photonic approaches to both of these directions by developing theoretical tools and performing experiments using silicon integrated photonics.The state of experimental quantum computing today is that we are crossing the milestone of quantum computational advantage. This means that the current largest and most advanced quantum computing experiments are claiming to be able to run certain problems faster than any available classical hardware, even the world's largest supercomputers. In photonics, the leading experiments claiming quantum computational advantage are running a protocol called Gaussian boson sampling, adapted to use threshold detectors. We investigate the classical complexity of this problem in Chapter 4 of this thesis, and find improvements to exact simulation methods. This helps to highlight the origins of the complexity in this problem, and improves our understanding of the extent of the quantum advantage seen in recent experiments. The results of Chapter 5 also help contribute to the understanding of the classical complexity of these photonic sampling problems by providing insights into the complexity of a closely related protocol, scattershot boson sampling in the presence of a physically relevant error, multiphoton contamination. In Chapter 6, we experimentally and theoretically investigate ideas around how to better verify the proper operation of these types of experiments.
In achieving quantum computational advantage, it is not required that the problem which is solved is useful, nor is it required that the device running the protocol is capable of universal quantum computation. Many additional further challenges must be solved before today's quantum computers can move into the domain of FTQC and deliver widespread impact. In Chapter 8, we investigate schemes to generate high dimensional photonic entanglement. This new ability to generate arbitrarily high dimensional entanglement may lead to future photonic quantum computing architectures with improved robustness to noise. In moving the hardware towards the necessary capabilities required for fault tolerant, universal quantum computing, the scale of experiments in terms of number of components must increase dramatically. In Chapter 7, we work to experimentally address challenges associated with making scalable sources of single mode squeezing using integrated photonics. These device designs may find application for overcoming the technical challenges in realising photonic fault tolerant quantum computing using a continuous variable approach.
We also identified that quantum photonics was missing theoretical tools for experiments which use threshold detectors, perhaps the most common measurement strategy in quantum photonics. In Chapter 3, we address this gap by introducing new matrix functions, the loop Torontonian and the Bristolian. We anticipate that these new functions will be useful for researchers working on NISQ or FTQC directions, both of which typically demand extensively use of threshold detection.
The work in this thesis aims to add to our understanding of where computational complexity arises in NISQ photonic quantum computers, and aims to provide ideas which may help to take steps towards the photonic FTQC era.
| Date of Award | 21 Jun 2022 |
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| Original language | English |
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| Supervisor | Anthony Laing (Supervisor) |