PhD Defense Dylan Harley

Analogue quantum simulation and perturbation theory

Abstract

Analogue quantum simulation is the general technique of encoding the behaviour of one physical system of interest into a different simulator system which is experimentally accessible. In this way, the system of interest can be indirectly studied by observing the natural evolution of a artificial simulator system. This leads to a natural yet subtle question: when can one family of Hamiltonians simulate another? This question has been studied from two directions: the experimental perspective, in order to characterise the expressive power of physically realisable devices; and the complexity-theoretic perspective, where the hardness of problems in physics and chemistry can be related through the simulation of hard instances. In the study of the latter perspective, a wide toolbox of techniques involving perturbation theory have been developed and applied to show that very simple families of Hamiltonian (restricted in both geometry and the types of interactions they contain) suffice to simulate all others. These conclusions are not easy to connect to the former perspective, however: perturbative simulations generically require enormous interaction strengths which are experimentally unrealistic.
  In this thesis, we examine this tension and explore the conditions under which these unrealistic features are necessary for analogue simulations, and when they can be avoided by working outside of the usual perturbation theory framework. We first do this by generalising previous notions of local Hamiltonian simulation and establishing a no-go result which rules out locality reduction without strong interactions. We also describe a way to circumvent this theorem using dissipative dynamics. In the final part of this thesis, we show how classical postprocessing techniques can be used to reduce the overhead of analogue simulators by extrapolating the properties of inaccurate simulations with weaker interactions to the perturbative limit.

Advisor

Matthias Christandl, University of Copenhagen

Assessment Committee

Chair, Professor Søren Fournais, University of Copenhagen 
Professor Dorit Aharonov, Hebrew University, Israel
Rahul Trivedi, Max Planck Institute for Quantum Optics Garching, Germany