On Calculating the Dynamics of Very Large Quantum Systems

TL;DR

This paper introduces a symbolic algebra-based method to model the dynamics of large quantum systems, enabling the calculation of observable quantities without approximation despite exponential state space growth.

Contribution

The authors develop a novel approach combining a symbolic non-commutative algebra engine with Ehrenfest theorem to analyze large quantum systems without initial entanglement constraints.

Findings

Able to determine dynamics of observable quantities in large quantum systems

Removes previous constraints like initial entanglement restrictions

Applicable to quantum machines, emergent behavior, and quantum chemistry

Abstract

Due to the exponential growth of the state space of coupled quantum systems it is not possible, in general, to numerically store the state of a very large number of quantum systems within a classical computer. We demonstrate a method for modelling the dynamical behaviour of measurable quantities for very large numbers of interacting quantum systems. Our approach makes use of a symbolic non-commutative algebra engine that we have recently developed in conjunction with the well-known Ehrenfest theorem. Here we show the possibility of determining the dynamics of experimentally observable quantities, without approximation, for very large numbers of interacting harmonic oscillators. Our analysis removes a large number of significant constraints present in previous analysis of this example system (such as having no entanglement in the initial state). This method will be of value in simulating the operation of large quantum machines, emergent behaviour in quantum systems, open quantum systems and quantum chemistry to name but a few.