Coherent Feedback Networks for Distributed Generation of Continuous-Variable Entanglement

Research interest in quantum information processing is spurred by non-classical phenomena such as entanglement. This thesis focuses on Einstein-Podolsky-Rosen (EPR)-like entanglement between a pair of Gaussian continuous-mode fields, which can be produced by a nondegenerate optical parametric amplifier (NOPA). The thesis aims to exploit coherent feedback networks in the form of the feedback interconnection of multiple NOPAs to generate entanglement in a distributed and power efficient manner. Firstly, we show how EPR entanglement can be generated by a dual-NOPA coherent feedback system connecting two NOPAs over two transmission channels. We analyse stability and EPR entanglement in a lossless scenario and under the effect of transmission losses, amplification losses, time delays and phase shifts in the transmission channels. It is shown that in an ideal scenario without losses and delays, and when only transmission losses are present, the feedback connection can yield an increase in the quality of the entanglement while consuming less power, compared to a single NOPA and a two cascaded NOPA system. The thesis is then concerned with linear quantum networks of multiple NOPAs. The NOPAs are interconnected in a coherent feedback chain, connecting two communicating parties over two transmission channels. We analyse stability and EPR entanglement between two outgoing fields of interest under the effect of losses and time delays, and bipartite entanglement of two-mode Gaussian states of internal cavity modes of the multiple-NOPA networks in the lossless case. It is numerically shown that the network with more NOPAs is more power efficient for EPR entanglement generation. Finally, we study optimization of EPR entanglement of linear quantum systems consisting of two NOPAs and a static linear passive network of optical devices. The passive network has six inputs and six outputs. By employing a steepest descent method, we find an optimized static passive network made of beamsplitters. Subsequently, we look at a special case of the above configuration, where the passive network has two inputs and two outputs, and the system is considered in the idealized infinite bandwidth limit. We show that the dual-NOPA coherent feedback system has a local optimality property for generation of EPR entanglement

Entanglement generation and self-correcting quantum memories

Building a working quantum computer that is able to perform useful calculations remains a challenge. With this thesis, we are trying to contribute a small piece to this puzzle by addressing three of the many fundamental questions one encounters along the way of reaching that goal. These questions are: (i) What is an easy way to create highly entangled states as a resource for quantum computation? (ii) What can we do to efficiently quantify states of noisy entanglement in systems coupled to the outside world? (iii) How can we protect and store fragile quantum states for arbitrary long times? The first two questions are the subject of part one of this thesis, `Entanglement Measures & Highly Entangled States'. We devise a particular proposal for generating entanglement within a solid-state setup, starting first with the tripartite case and continuing with a generalization to four and more qubits. The main idea there is to realize systems with highly entangled ground states in order for entanglement to be created by merely cooling to low enough temperatures. We have addressed the issue of quantifying entanglement in these systems by numerically calculating mixed-state entanglement measures and maximizing the latter as a function of the external magnetic field strength. The research along these lines has led to the development of the numerical library 'libCreme'. The second part of the thesis, 'Self-Correcting Quantum Memories', addresses the question how to reliably store quantum states long enough to perform useful calculations. Every computer, be it classical or quantum, needs the information it processes to be protected from corruption caused by faulty gates and perturbations from interactions with its environment. However, quantum states are much more susceptible to these adverse effects than classical states, making the manipulation and storage of quantum information a challenging task. Promising candidates for such 'quantum memories' are systems exhibiting topological order, because they are robust against local perturbations, and information encoded in their ground state can only be manipulated in a non-local fashion. We extend the so-called toric code by repulsive long-range interactions between anyons and show that this makes the code stable against thermal fluctuations. Furthermore, we investigate incoherent effects of quenched disorder in the toric code and similar systems

Searching for New Physics using Classical and Quantum Machine Learning

The development of machine learning (ML) has provided the High Energy Physics (HEP) community with new methods of analysing collider and Monte-Carlo generated data. As experiments are upgraded to generate an increasing number of events, classical techniques can be supplemented with ML to increase our ability to find signs of New Physics in the high-dimensional event data. This thesis presents three methods of performing supervised and unsupervised searches using novel ML methods. The first depends on the use of an autoencoder to perform an unsupervised anomaly detection search. We demonstrate that this method allows you to carry out a data-driven, model-independent search for New Physics. Furthermore, we show that by extending the model with an adversary we can account for systematic errors that may arise from experiments. The second method develops a form of quantum machine learning to be applied to a supervised search. Using a variational quantum classifier (a neural network style model built from quantum information principles) we demonstrate a quantum advantage arises when compared to a classical network. Finally, we make use of the continuous-variable (CV) paradigm of quantum computing to build an unsupervised method of classifying events stored as graph data. Gaussian boson sampling provides an example of a quantum advantage unique to the CV method of quantum computing and allows our events to be used in an anomaly detector model built using the Q-means clustering algorithm

Quantum information dynamics in many-body systems

The study of quantum information provides a common lens to our investigation of quantum mechanical phenomena in various fields, including condensed matter, high energy, and gravitational physics. This thesis is a collection of theoretical and numerical studies of the dynamics of quantum information in quantum many-body systems, focused on characterizing the scrambling of information and entanglement dynamics in generic dynamical setups. In the first part of the thesis I study out-of-time-ordered correlators (OTOCs) as a probe for quantum information scrambling. By computing OTOCs in disordered quantum spin systems we find that disorder leads to distinct patterns of scrambling, and can arrest the information propagation significantly for high enough values of disorder. I also study the generic features of finite temperature OTOCs in gapped local systems and their relation to the temperature bound on chaos, using a combination of numerical and analytical approaches. In the second part of the thesis, I study analytically tractable models of measurement-induced entanglement transition. Frequent measurements in a quantum circuit lead to distinct entanglement phases of the prepared quantum state. Using these models, we find effective field theories describing the entanglement patterns and the entanglement phase transitions. By considering generalizations of these models, we find that long-range interactions in the quantum circuit lead to novel entanglement phases with efficient emergent error-correcting properties. In the last part of the thesis, I study tensor network states defined on generic sparse graphs. Using the intuition that generic graphs are locally tree-like, I develop efficient numerical methods to access local information of such states, which serve as a pathway for studying quantum many-body physics on sparse graphs beyond lattices

A journey into the world of inverse problems in quantum mechanics

Technology has come a long way since the birth of quantum mechanics. The science has led to computers, and now, the scientists are pushing the fundamentals further to eventually be able to construct a quantum computer from the bottom up. Quantum tomography has a vital role in this ambitious endeavour: it’s the study of how one can retrieve the values describing a quantum state, like finding coordinates on a map for a given position. The challenge that the quantum tomographer faces lies in the shear number of these values, which grows exponentially with the components of quantum system. This is the curse of dimensionality and cannot be avoided with classical means. Therefore, the tomographer is forced to come up with algorithms that scale well with the number of components, either via prior information or by reducing the problem to its simplest form. In this thesis, we devise algorithms for retrieving quantum states using a little of both approaches. We develop a direct way of retrieving quantum state-vector values by assuming that the state is pure, which is often the case in optics. In addition, we show that a simple optimisation technique, projected gradient descent, can outperform all other methods for retrieving general quantum states. Our contribution to the field is thus to provide tools that enable the tomographer to work on larger quantum states and that hopefully help her create the building blocks of a quantum computer. We touch on other somewhat related subjects such as image denoising and imaging quantum correlations

Entanglement and Thermalization in Many Body Quantum Systems

In this thesis we study problems relating the the structure and simulation of entangled many body quantum systems, their utility in adiabatic quantum computation, and the influence of the environment in thermalizing the system and degrading the usefulness of quantum dynamics in this setting. We then study a particular strongly coupled many body quantum system in order to better understand when quantum systems do not thermalize in this manner. In chapter 2 of this thesis we study the properties of quantum dynamics restricted to an efficiently representable sub-manifold of quantum states both the finite and infinite chain of spin- 1=2 subsystems. We investigate the trade-off between gains in efficiency due to this restriction against losses in fidelity. We find the integration to be very stable and shows significant gains in efficiency compared to the naively related matrix product states. However, much of this advantage is offset by a significant reduction in fidelity. We investigate the effect of explicit symmetry breaking in the ansatz and formulate the principles for determining when correlator product states may be a useful tool. We find that scaling with overlap/bond order may be more stable with correlator product states allowing a more efficient extraction of critical exponents and present an example in which the use of correlator product states is orders of magnitude quicker than matrix product states. In chapters 3, 4 and 5 we extend this picture to allow for the study of the dissipative and decohering dynamics of a quantum system interacting with a bath, and pay particular reference to its effect on adiabatic quantum computation. In chapter 3 we consider a system of mutually interacting superconducting flux qubits coupled to a thermal bath that generalises the dissipative model of Landau-Lifschitz-Gilbert to the case of anisotropic bath couplings. We show that the dissipation acts to bias the quantum trajectories towards a reduced phase space. We study the model in the context of the D-Wave computing device and recover dynamics closely related to several models proposed on phenomenological grounds. In chapter 4 we extend this analysis to study explicitly the influence of dissipative dynamics on the lifetime of entanglement. In chapter 5 we apply this understanding to develop a methodology for benchmarking the quantum correlations harnessed by an adiabatic computation and apply this process to the D-Wave Vesuvius machine. Further developing this interest in the effect of thermalisation of quantum dynamics in chapter 6 we consider systems which fail to thermalise even in the presence of strong coupling to their surroundings. This many body localised behaviour has been recently established to be a robust phase of matter in the presence of strong disorder in one dimension. Here we show the the low lying energy states of a many body system contain immobile excitations, this immobility results in an transition in the character of low lying eigenstates at arbitrarily weak disorder. This represents a novel appearance of localising behaviour in many body systems. Finally we consider possible avenues for future work stemming from this thesis