This thesis is intended in part to summarize and also to contribute to the newest developments in passive linear optics that have resulted, directly or indirectly, from the somewhat shocking discovery in 2010 that the BosonSampling problem is likely hard for a classical computer to simulate. In doing so, I hope to provide a historic context for the original result, as well as an outlook on the future of technology derived from these newer developments. An emphasis is made in each section to provide a broader conceptual framework for understanding the consequences of each result in light of the others. This framework is intended to be comprehensible even without a deep understanding of the topics themselves. The fi_x000C_rst three chapters focus more closely on the BosonSampling result itself, seeking to understand the computational complexity aspects of passive linear optical networks, and what consequences this may have. Some e_x000B_ort is spent discussing a number of issues inherent in the BosonSampling problem that limit the scope of its applicability, and that are still active topics of research. Finally, we describe two other linear optical settings that inherit the same complexity as BosonSampling. The _x000C_final chapters focus on how an intuitive understanding of BosonSampling has led to developments in optical metrology and other closely related _x000C_fields. These developments suggest the exciting possibility that quantum sensors may be viable in the next few years with only marginal improvements in technology. Lastly, some open problems are presented which are intended to lay out a course for future research that would allow for a more complete picture of the scalability of the architecture developed in these chapters.
This thesis is intended in part to summarize and also to contribute to the newest developments in passive linear optics that have resulted, directly or indirectly, from the somewhat shocking discovery in 2010 that the BosonSampling problem is likely hard for a classical computer to simulate. In doing so, I hope to provide a historic context for the original result, as well as an outlook on the future of technology derived from these newer developments. An emphasis is made in each section to provide a broader conceptual framework for understanding the consequences of each result in light of the others. This framework is intended to be comprehensible even without a deep understanding of the topics themselves. The fi_x000C_rst three chapters focus more closely on the BosonSampling result itself, seeking to understand the computational complexity aspects of passive linear optical networks, and what consequences this may have. Some e_x000B_ort is spent discussing a number of issues inherent in the BosonSampling problem that limit the scope of its applicability, and that are still active topics of research. Finally, we describe two other linear optical settings that inherit the same complexity as BosonSampling. The _x000C_final chapters focus on how an intuitive understanding of BosonSampling has led to developments in optical metrology and other closely related _x000C_fields. These developments suggest the exciting possibility that quantum sensors may be viable in the next few years with only marginal improvements in technology. Lastly, some open problems are presented which are intended to lay out a course for future research that would allow for a more complete picture of the scalability of the architecture developed in these chapters.
Abstract BosonSampling is a recent development in linear optics which has stimulated a number of new computational models and algorithms in quantum computing. Much of this interest follows from the computational complexity arguments which show that the particular quantum system in which BosonSampling resides is difficult to simulate with a classical computer (assuming highly plausible conjectures) Arkhipov and Aaronson (2011 Proc. ACM STOC (New York) , p 333). These arguments, however, require some understanding of both quantum optics and complexity theory—topics that are rarely seen together. This tutorial is intended to introduce a reader to the topic who has at least a basic knowledge of quantum mechanics or quantum information theory, but may be unfamiliar with either quantum optics or complexity theory. Included is some historic context as well as an outlook on the potential for BosonSampling to be the first experimental demonstration of quantum supremacy. The emphasis of the first section is to develop a general context for the subfields of quantum optics and computer science that intersect to form the BosonSampling problem. This begins with a historical introduction and a background of quantum optics. We then progress to the physical system—quantum optical networks—where BosonSampling is defined. Finally, we provide a short introduction to computational complexity theory to provide a structure where the essence behind the BosonSampling result can be discerned. The second section focuses on the BosonSampling result itself, seeking to understand the computational complexity aspects of passive linear optical networks, and what consequences this may have. Some effort is spent discussing a number of issues inherent in the BosonSampling problem that are roadblocks to limiting the scope of its applicability, but that have made progress recently and remain active topics of research. The third short section touches on the relationship between BosonSampling and other quantum computing protocols. Namely, other settings and architectures that inherit the same complexity as BosonSampling will be presented, as well as giving a summary of experimental efforts to implement BosonSampling . We discuss similarities between BosonSampling and other quantum algorithms. In the final section, some comments are presented considering future research related to the problems and protocols found in this tutorial. We suggest other unexplored directions of study which may have some bearing on the complexity of quantum optics. Also included is a glossary of complexity terms used throughout the tutorial.
As this century unfolds we will witness the rise of the quantum computer. A quantum computer is a device that utilizes the laws of one of the most fundamental theories of physics— quantum mechanics. By utilizing properties of quantum mechanics a quantum computer is able to perform certain information processing tasks much more effciently than an ordinary classical computer. The last century of modern society was revolutionized by some of the simplest ideas in quantum mechanics like energy quantization and quantum tunnelling, which led to technologies like the laser and the transistor. We can expect to see additional technological revolutions occur in this century since we are beginning to build technologies with some of the more complex properties of quantum mechanics such as quantum entanglement and quantum superposition. These quantum effects make more radical technologies like the quantum computer possible. This thesis is based upon the work I have done during my PhD candidature at Macquarie University. In this work we develop quantum technologies that are directed towards realising a quantum computer. Specifically, we have made many theoretical advancements in a type of quantum information processing protocol called Boson Sampling. This device effciently simulates the interaction of quantum particles called bosons, which no classical computer can effciently simulate. In this thesis we explore quantum random walks, which are the basis of how the bosons in Boson Sampling interfere with each other. We explore implementing BosonSampling using the most readily available photon source technology. We invented a completely new architecture which can implement Boson Sampling in time rather than space and has since been used to make the worlds largest Boson Sampling experiment ever performed. We look at variations to the traditional Boson Sampling architecture by considering other quantum states of light. We show a worlds first application inspired by Boson Sampling in quantum metrology where measurements may be made more accurately than with any classical method. Lastly, dealing with Boson Sampling, we look at reformulating the formalism of Boson Sampling using a quantum optics approach. In addition, but not related to BosonSampling, we show a protocol for effciently generating large-photon Fock states, which are a type of quantum state of light, that are useful for quantum computation. Also, we show a method for generating a specific quantum state of light that is useful for quantum error correction — an essential component of realising a quantum computer — by coupling together light and atoms.
In this dissertation we begin with a brief introduction of quantum mechanics, its impact on technology in the 20th century, and the likely impact quantum optics will have on the next generation of technology. The following chapters display research performed in many of these next generation areas. In Chapter 2 we describe work performed in the area of designing quantum optical logic gates for use in quantum computing. In Chapter 3 we discuss findings made in regards to using quantum states of light for remote sensing and imaging. We move on to Fabry-Perot interferometers in Chapter 4 and show discoveries made in the differences between classical and non-classical detection schemes with non-classical states of light. Lastly, in Chapter 5 we discuss how to create photonic bandgap coatings that have unique thermal emissivity properties that could have benefits ranging from increased energy efficiency in light bulbs to better thermal management of satellites.
One intriguing but difficult route to scalable quantum information processing (QIP) is linear optical quantum computing (LOQC). The systematic growth of LOQC is examined in this research. It focuses on significant experimental developments, fault-tolerant methods, and the enduring difficulties influencing the field area. In addition, it highlights the incorporation of Gottesman-Kitaev-Preskill (GKP) encoding which is an essential step towards fault-tolerant quantum computation. We analyze the importance of the Knill-Laflamme-Milburn (KLM) protocol in addressing the probabilistic limits of two-qubit gates. Strong quantum structures are made possible by this synergy, which increases resistance to phase errors and photon loss. Notwithstanding these developments, problems with state preparation, measurement accuracy, and error correction still exist, requiring multidisciplinary efforts to improve methods and investigate fresh ideas.Beyond its scope, the knowledge gathered from LOQC may have an impact on secure quantum communication networks and hybrid quantum systems. Enhancing error correction codes, creating new quantum optical technologies, and encouraging cooperation within quantum computing paradigms should be the main goals of future research. The present work intends to stimulate more developments and push QIP towards scalable and useful quantum computation by reviewing the state of LOQC today and defining strategic directions.
Over the last few decades, quantised excitations of the electromagnetic field have proven to be an ideal system with which to investigate and harness quantum optical phenomena. The techniques developed have enabled fundamental tests of quantum mechanics as well as practical applications in quantum metrology and quantum information processing. Advancing to larger-scale entangled quantum systems will open up new regimes of quantum many-body physics, allowing us to probe the limits of quantum mechanics and enabling truly quantum-enhanced technologies. However, moving towards this goal will require further experimental and theoretical innovations. The work described in this thesis focuses on several different aspects of optical quantum information, but are ultimately all linked by this long-term aim. The first part of this thesis describes a novel method for strain-based active control of quantum optical circuits and a new method for the characterisation of high efficiency detectors. Building on this, I discuss in detail two different fields of quantum optics that stand to benefit from these techniques. I initially consider quantum-enhanced metrology, including work aimed towards demonstrating a truly better-than-classical phase measurement, and a theoretical exploration of multiple-phase estimation. Finally, I focus on linear-optical quantum information processing, exploring in detail the use of time-frequency encodings for quantum computing.
The level of experimental control and the detailed theoretical understanding of matter wave physics have led to a renaissance of experiments testing the very foundations of quantum mechanics and general relativity, as well as to applications in metrology. A variety of interferometric quantum sensors surpasses, or will surpass, the limits of their classical counterparts, for instance in the measurement of frequency and time or forces such as accelerations due to rotation and gravity with applications in basic science, navigation and the search for natural resources. The collection of original articles published in this focus issue of New Journal of Physics is intended as a snapshot of the current research pursued by a number of leading teams working on the development of new matter wave physics, devices and techniques. A number of contributions also stress the close relation between the historic roots of quantum mechanics and aspects of modern quantum information science which are relevant for matter wave physics.