Simulating Many-Body Quantum Systems: Quantum Algorithms and Experimental Realisation

Abstract

The simulation of many-body quantum systems is an extensive field of research which has a large number of applications and has motivated numerous experimental, theoretical and computational studies. It hopes to answer fundamental questions about physical phenomena and aid in the development of new and exciting materials. At the frontiers of research, classical simulations grapple with increasingly large and complex systems which quantum simulators hope to alleviate. Even within quantum simulation there is great diversity as to the hardware used to perform calculations and whether simulations are implemented in an analogue or digital manner. In this thesis we explore elements from across the field. We investigate the limits of classical simulation and the quantum resources that are required to outperform it. We include analysis of the behaviour of errors when the simulation is Trotterised which motivates an alternate perspective for the implications of this scheme. The execution of digital quantum simulation will be implemented on quantum hardware. Here, we present results of experiments on superconducting qubits of both the ‘traditonal’ transmon type and a novel superconductor-semiconductor implementation of the transmon called the gatemon. We explore experiments aimed at increasing the connectivity of these qubits by use of a superconducting bus. A new realisation of these qubits is reported which enables them to be fabricated scalably and Bayesian inference is employed to efficiently characterise superconducting qubits.