Molecular Optimization for Classical and Quantum Condensed Phase Systems

Abstract

Condensed phase phenomena remain a theoretical challenge to thoroughly understand and elucidate due to the close interactions among large number of microscopic degrees of freedom. Such deviation from the non-interacting ideality necessitates an effective resolution of the constrained fluctuations and strong correlations in condensed phase systems, which can be methodically achieved using non-Euclidean optimization tools. This thesis is devoted to the optimization-based development of molecular simulations that facilitate our understanding of the static and dynamical properties of many-body systems.

Chapter 1 introduces the background on simulating condensed phase systems and sets up the overall scope of the thesis. Chapter 2 provides a primary exposure to a few fundamental connections between functional minimization on manifolds and essential properties, for example statistical and spectral, of many-body systems.

Chapter 3 considers methods adept at treating representative classical condensed-phase systems. We start with phenomenological spin models on a lattice and turn our attention to atomistic interfaces including aqueous electrolyte-electrode and polymer-protein composite. We discuss proficient schemes to implement and process our molecular simulations, allowing us to elucidate (a)typical structural-dynamical fluctuations to heterogeneities native to these classical systems.

Chapter 4 considers methods capable of studying correlated quantum condensed-phase systems. In particular, we explore the theoretical and numerical underpinnings behind non-parametric simulation schemes that utilize the error-mitigating technique of quantum subspace expansion. We focus on the emergent scenario in which the sub- space is generated by a real-time evolution implemented efficiently on quantum hardware. The practical advantages of the schemes are highlighted through demonstration of their fast and accurate extraction of spectral information.