MANY-BODY LOCALIZED EIGENSTATES AND SCALABLE QUANTUM COMPUTATION OF HAMILTONIAN SPECTRA

Abstract

This thesis investigates applications of near-term and fault-tolerant quantum computers in physics and chemistry, and the properties of disordered many-body localized systems. In the first part of the thesis, we propose and study an application of quantum linear system problem (QLSP) solvers to prepare highly excited eigenstates of physical Hamiltonians. This is enabled by the efficient computation of inverse expectation values, taking advantage of the QLSP solvers' exponentially better scaling in problem size without concealing exponentially costly pre/post-processing steps that usually accompanies it. We detail implementations of this scheme for both fault-tolerant and near-term quantum computers, analyse their efficiency and implementability, and discuss applications and simulation results in many-body physics and quantum chemistry that demonstrate its superior effectiveness and scalability over existing approaches. In the second part of the thesis, we study the phenomenon of many-body localization from a quantum information perspective through the quantum Fisher information (QFI). From numerical simulations, we obtain indications that the scaling and dynamics of the QFI, a measure of multipartite entanglement, can distinguish between the ergodic and localized phases of a disordered system.