Quantum mechanics, which describes the behaviour of matter and energy on very small scales, is one of the most successful theories in the history of science. Einstein's theory of special relativity, which describes the relationship between space and time, is likewise a highly successful and widely accepted theory. And yet there is a well-documented tension between the two theories, to the extent that it is still not clear that the two can ever be reconciled. This thesis is concerned with furthering the current understanding of the relationship between quantum mechanics and special relativity. In the first part of the thesis we study the behaviour of quantum information in relativistic spacetime. The field of quantum information arose from the realisation that quantum information has a number of crucial properties that distinguish it from classical information, such as the no-cloning property, quantum contextuality, and quantum discord. More recently, it has been realised that placing quantum information under relativistic constraints leads to the emergence of further unique features which are not exhibited by either non-relativistic quantum information or relativistic classical information; as part of this ongoing research programme we develop a new relativistic quantum `paradox' which puts pressure on conventional views about the spatiotemporal persistence of quantum states over time. We then study a new set of relativistic quantum protocols which involve the distribution of entangled states over spacetime, defining one task involving the distribution of the two halves of a known entangled state, and another task involving the distribution of the two halves of an unknown entangled state. The second part of the thesis deals with relativistic quantum cryptography, a field which first began attracting serious attention when it was realised that a cryptographic task known as `bit commitment,' can be implemented with perfect security under relativistic constraints. This result was highly significant, since it is provably impossible to implement bit commitment with perfect security in a purely classical or purely quantum context, and hence bit commitment is an ideal starting point for probing the power of relativistic quantum cryptography. In this thesis we propose several new relativistic quantum bit commitment protocols which have notable advantages over previously known protocols. We then move to a related task, a generalization of zero-knowledge proving which we refer to as knowledge-concealing evidencing of knowledge of a quantum state; we prove no-go theorems concerning the possibility of implementing this task with perfect security, and then set out a relativistic protocol for the task which is asymptotically secure as the dimension of the state in question becomes large. These results have interesting foundational significance above and beyond their applications in the field of cryptography, providing a new perspective on the connections between knowledge, realism and quantum states.

A major challenge in the field of condensed matter physics is to harness the quantum mechanical properties of atomic systems coupled to large environments. Thermal fluctuations destroy quantum information and obstruct the development of quantum technologies such as quantum computers and memory devices. Recent advances in quantum control enable the manipulation of complex quantum states, providing new paths to preserve quantum information and to employ the environment as a resource. In this dissertation, we develop practical quantum control protocols which quickly and efficiently transfer energy to/from an environment. A major contribution of this work is the design of powerful and efficient quantum engines and refrigerators, which use the environment either to generate useful work or to freeze a system to its ground state. In achieving its core objectives, this work has also expanded on several areas of condensed matter quantum physics, including (i) the characterization of special classes of entangled system-environment states, (ii) the discovery of novel quantum chaotic phases of matter, (iii) the design of control schemes which speed-up efficient adiabatic protocols, and (iv) the development of experimentally viable control schemes in trapped ion systems, semiconductors, and nano-diamonds.

This project was motivated by the following question: what information do the properties of a random graph contain about the performance of a quantum search acting on it? To investigate this problem, we define a notion of search time to quantify the behavior of a quantum search, and find strong evidence of a relation between its distribution and the model of random graph on which the search was performed. Surprisingly, we also find strong evidence that the return time of a classical random walk initialized at the marked vertex is closely related to its search time, and that the distribution of degrees over the graph vertices may play a significant role in this relation. / Mathematics

Quantum information technologies offer significantly more computational power for certain tasks and secure communication lines compared to the available classical machines. In recent years there have been numerous proposals for the implementation of quantum computers in several different systems that each come with their own advantages and challenges. This dissertation primarily focuses on challenges, specifically interactions with the environment, and applications of two of such systems: Semiconductor quantum dots and topological insulators. The first part of the dissertation is devoted to the study of semiconductor quantum dots as candidates for quantum information storage and sources of single-photon emission. The spin of the electron trapped in a self-assembled quantum dot can be used as a quantum bit of information for quantum technology applications. This system possesses desirable photon emission properties, including efficiency and tunability, which make it one of the most advanced single-photon emitters. This interface is also actively explored for the generation of complex entangled photonic states with applications in quantum computing, networks, and sensing. First, an overview of the relevant developments in the field will be discussed and our recent contributions, including protocols for the control of the spin and a scheme for the generation of entangled photon states from coupled quantum dots, will be presented. We then look at the interaction between the electron and the surrounding nuclear spins and describe how its interplay with optical driving can lead to dynamic nuclear polarization. The second part of the dissertation follows a similar study in topological insulators: The role of time-reversal breaking magnetic impurities in topological materials and how spinful impurities enable backscattering mechanisms by lifting the topological protection of edge modes. I will present a model that allows for an analytical study of the effects of magnetic impurities within an experimental framework. It will be discussed how the same platform also enables a novel approach for applications of spintronics and quantum information, such as studying the entanglement entropy between the impurities and chiral modes of the system. / Doctor of Philosophy / Quantum information science has received special attention in recent years due to its promising advantages compared to classical machines. Building a functional quantum processor is an ongoing effort that has enjoyed enormous advancements over the past few years. Several different condensed matter platforms have been considered as potential candidates for this purpose. This dissertation addresses some of the major challenges in two of the candidate platforms: Quantum dots and topological insulators. We look at methods for achieving high-performance optical control of quantum dots. We further utilize quantum dots special ability to emit photons for specific quantum technology applications. We also address the nuclear spin problem in these systems which is the main source of destruction of quantum information and one of the main obstacles in building a quantum computer. This is followed by the study of a similar problem in topological insulators: Addressing the interaction with magnetic impurities of topological insulators. Included with each of these topics is a description of relevant experimental setups. As such, the studies presented in this dissertation pave the way for a better understanding of the two major obstacles of hyperfine interactions and the optical controllability of these platforms.

published_or_final_version / Computer Science and Information Systems / Master / Master of Philosophy

No description available.

<p> Successful implementation of fault-tolerant quantum computation on a system of qubits places severe demands on the hardware used to control the many-qubit state. It is known that an accuracy threshold <i>P_a</i> exists for any quantum gate that is to be used for such a computation to be able to continue for an unlimited number of steps. Specifically, the error probability Pe for such a gate must fall below the accuracy threshold: <i> P_e</i> &lt; <i>P_a.</i> Estimates of <i> P_a</i> vary widely, though <i>P_a</i> &sim; 10^&minus;4 has emerged as a challenging target for hardware designers. I present a theoretical framework based on neighboring optimal control that takes as input a good quantum gate and returns a new gate with better performance. I illustrate this approach by applying it to a universal set of quantum gates produced using non-adiabatic rapid passage. Performance improvements are substantial comparing to the original (unimproved) gates, both for ideal and non-ideal controls. Under suitable conditions detailed below, all gate error probabilities fall by 1 to 4 orders of magnitude below the target threshold of 10^&minus;4. </p><p> After applying the neighboring optimal control theory to improve the performance of quantum gates in a universal set, I further apply the general control theory in a two-step procedure for fault-tolerant logical state preparation, and I illustrate this procedure by preparing a logical Bell state fault-tolerantly. The two-step preparation procedure is as follow: Step 1 provides a one-shot procedure using neighboring optimal control theory to prepare a physical qubit state which is a high-fidelity approximation to the Bell state |&beta;₀₁&rang; = 1/&radic;2(|01&rang; + |10&rang;). I show that for ideal (non-ideal) control, an approximate |&beta;₀₁&rang; state could be prepared with error probability &epsis; &sim; 10^&minus;6 (10^&minus;5) with one-shot local operations. Step 2 then takes a block of <i>p</i> pairs of physical qubits, each prepared in |&beta;₀₁&rang; state using Step 1, and fault-tolerantly prepares the logical Bell state for the <i>C</i>₄ quantum error detection code.</p>

A dissertation submitted to the faculty of Science, University of the Witwatersrand, Johannesburg, in fulfillment of the requirements for the degree of Master of Science. Degree awarded with distinction on 4 December 1996. / This dissertation is divided into two parts: the first part deals with the concepts of angular momentum and spin in classical mechanics and quantum mechanics and relativistic quantum mechanics and their connection with magnetic moments. In the second part, a model is set up of a relativistic three particle system, based on the previou.s.ly introduced concepts, which will serve as a template for a nucleon. The spatial component of the Lorentz invariant electrcmagnetic current is computed, and on the basis of it, the magnetic moment in the non-relativistic limit. It will be seen that the ratio -1 for the magnetic moment of the proton to the neutron will be recovered, in accordance 'with the static quark model, static QeD and very close to experiment. / MT2018

Thesis advisor: Ying Ran / Classification and simulation of quantum phases are one of main themes in condensed matter physics. Quantum phases can be distinguished by their symmetrical and topological properties. The interplay between symmetry and topology in condensed matter physics often leads to exotic quantum phases and rich phase diagrams. Famous examples include quantum Hall phases, spin liquids and topological insulators. In this thesis, I present our works toward a more systematically understanding of symmetric topological quantum phases in bosonic systems. In the absence of global symmetries, gapped quantum phases are characterized by topological orders. Topological orders in 2+1D are well studied, while a systematically understanding of topological orders in 3+1D is still lacking. By studying a family of exact solvable models, we find at least some topological orders in 3+1D can be distinguished by braiding phases of loop excitations. In the presence of both global symmetries and topological orders, the interplay between them leads to new phases termed as symmetry enriched topological (SET) phases. We develop a framework to classify a large class of SET phases using tensor networks. For each tensor class, we can write down generic variational wavefunctions. We apply our method to study gapped spin liquids on the kagome lattice, which can be viewed as SET phases of on-site symmetries as well as lattice symmetries. In the absence of topological order, symmetry could protect different topological phases, which are often referred to as symmetry protected topological (SPT) phases. We present systematic constructions of tensor network wavefunctions for bosonic symmetry protected topological (SPT) phases respecting both onsite and spatial symmetries.

by Law Chi Kwong. / Parallel title in Chinese characters. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1989. / Bibliography: leaves 73-75. / by Law Chi Kwong.