Insights from Quantum Information into Fundamental Physics

Abstract

This thesis is split into two parts, which are united in the sense that they involve applying ideas from quantum information to fundamental physics. The first part is focused on examining discrete-time models in quantum computation (discrete-time quantum walks and quantum cellular automata) as discretized models of relativistic systems. One of the results here is a theorem demonstrating that a large class of discrete-time quantum walks have relativistic dynamics in the continuum limit. Additionally, the problem of fermion doubling for these models is investigated, and it is seen that the problem can be circumvented in two dimensional space. This was already known for one dimensional systems. Another result involves taking the limits of causal free field theories in discrete spacetime to recover continuum field theories, something that is not straightforward because of the nontrivial nature of the vacuum in quantum field theory. Additionally, it is shown that general systems of fermions evolving causally in discrete spacetime can be represented by quantum cellular automata, which makes them efficiently simulable by quantum computers. A related result is that quantum cellular automata composed of fermions are equivalent to regular quantum cellular automata. In the second part of this thesis, the focus is on the foundations of statistical physics. The main result of this part is a general bound on the time it takes a quantum system to effectively reach equilibrium. The discussion also includes a practical definition of equilibration that takes our measurement capabilities into account. Finally, the nature of the equilibrium state is also discussed, with a focus on initial state independence, which relates to the important question of when the equilibrium state is a Gibbs state.

Ph.D. thesis, originally submitted in December 2014; 194 pages, 35 figures; identical to final thesis except that acknowledgments have been omitted

References in corpus (13)

• Quantum many-body systems out of equilibrium
• Alternatives to Eigenstate Thermalization
• Absence of Thermalization in Nonintegrable Systems
• Thermalization in Nature and on a Quantum Computer
• A quantum central limit theorem for non-equilibrium systems: Exact local relaxation of correlated states
• Many-body localisation implies that eigenvectors are matrix-product states
• Diverging equilibration times in long-range quantum spin models
• Canonical thermalization
• On the time scales in the approach to equilibrium of macroscopic quantum systems
• Spectra and eigenstates of spin chain Hamiltonians
• Convergence to equilibrium under a random Hamiltonian
• The complexity of energy eigenstates as a mechanism for equilibration
• Thermalization under randomized local Hamiltonians

Cited by in corpus (7)

• A review of Quantum Cellular Automata
• Quantum walks in external gauge fields
• A quantum cellular automaton for one-dimensional QED
• Quantum cellular automata and quantum field theory in two spatial dimensions
• Quantum walk on a graph of spins: magnetism and entanglement
• Discretizing quantum field theories for quantum simulation
• An overview of Quantum Cellular Automata