Crowley, PJD; (2017) Entanglement and Thermalization in Many Body Quantum Systems. Doctoral thesis , UCL (University College London).

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Abstract

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.

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