Analogue quantum simulation and perturbation theory

PhD defence by Dylan Keir Harley

Assessment Committee

Professor Søren Fournais, Mathematical Sciences, University of Copenhagen (Chairperson)
Professor Dorit Aharonov, Hebrew University Jerusalem
Research group leader(tenured) Rahul Trivedi, Max Planck Institute for Quantum Optics, Garching

Supervisors

Professor Matthias Christandl

Department

Department of Mathematical Sciences

Place

The defence is conducted as a hybrid defence.

To attend the defence in person:
Building: Vibenshuset, 4th floor, Lyngbyvej 2, 2100 København Ø

To attend the defence online:
Please follow the link to attend the defence online: https://ucph-ku.zoom.us/j/2020738479?omn=67597545279
MeetingID, if relevant: 202 073 8479

Email address to gain access to the thesis: dylan.harley@gmail.com.
You will either receive a copy of the thesis or be informed where you can read a physical copy.
Recipients of copies of the thesis are not allowed to share or distribute it due to copyright compliance.

Short description of the thesis

Analogue quantum simulation is the 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 an artificial simulator system. This leads to a natural yet subtle question: when can one family of Hamiltonians simulate another?

In this thesis, we approach this question by studying and generalising the toolbox of so-called perturbative gadgets, which give modular constructions of analogue simulator Hamiltonians. We prove no-go theorems, demonstrating that certain kinds of simulations cannot be performed without access to very high-energy systems. Finally, we demonstrate how the cost of perturbative simulation may be reduced via classical postprocessing inspired by error mitigation techniques.