The classical-quantum divergence of complexity in modelling spin chains

The minimal memory required to model a given stochastic process - known as the statistical complexity - is a widely adopted quantifier of structure in complexity science. Here, we ask if quantum mechanics can fundamentally change the qualitative behaviour of this measure. We study this question in the context of the classical Ising spin chain. In this system, the statistical complexity is known to grow monotonically with temperature. We evaluate the spin chain's quantum mechanical statistical complexity by explicitly constructing its provably simplest quantum model, and demonstrate that this measure exhibits drastically different behaviour: it rises to a maximum at some finite temperature then tends back towards zero for higher temperatures. This demonstrates how complexity, as captured by the amount of memory required to model a process, can exhibit radically different behaviour when quantum processing is allowed.Comment: 9 pages, 3 figures, comments are welcom

Surveying structural complexity in quantum many-body systems

Quantum many-body systems exhibit a rich and diverse range of exotic behaviours, owing to their underlying non-classical structure. These systems present a deep structure beyond those that can be captured by measures of correlation and entanglement alone. Using tools from complexity science, we characterise such structure. We investigate the structural complexities that can be found within the patterns that manifest from the observational data of these systems. In particular, using two prototypical quantum many-body systems as test cases - the one-dimensional quantum Ising and Bose-Hubbard models - we explore how different information-theoretic measures of complexity are able to identify different features of such patterns. This work furthers the understanding of fully-quantum notions of structure and complexity in quantum systems and dynamics.Comment: 9 pages, 5 figure

CLASSICAL-QUANTUM DIVERGENCES IN STRUCTURAL COMPLEXITIES OF MANY-BODY SYSTEMS

Ph.DDOCTOR OF PHILOSOPH

Stochastic boundary conditions for molecular dynamics simulations.

At present, the cutting edge molecular dynamics simulation can be performed fr a system of approximately 10$^{10}$ to 10$^{11}$ particles over about 10$^{3}$ nodes. Nevertheless, such systems are still profoundly undersized compared to a real physical systems that contains particle number at the order of 10$^{23}$. As a result, finite size effect can undermine the validity of studies of physical system. In minimizing the finite size effects, periodic boundary conditions have been widely used in molecular dynamics simulations. However, due to the artifical correlation caused by the time reversal invariance of the periodic boundary conditions, the periodic boundary conditions has very limited applications. Therefore, we strive to develop stochastic boundary conditions that will not only rid such artificial correlation, but also has a wide area of applications. By using the statistics gathered from the periodic boundary condition simulation, we perform a numerical cumulative distribution transform and implement the first order stochastic boundary conditions into our system. Henceforth, the thermodynamical properties of the system is calculated and compared to the existing canonical and grand canonical ensemble properties. It is shown in our project that our system does not belong to the canonical ensemble but more data is required to compare our system to the grand canonical ensemble more accurately.Bachelor of Science in Physic

Quantum-inspired algorithm for vehicle sharing problem

Singapore National Research Foundation under Corp Lab @ University National Research Foundation (NRF) Singapor