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Due to the exponential growth of the state space of coupled quantum systemsit is not possible, in general, to numerically store the state of a very largenumber of quantum systems within a classical computer. We demonstrate a methodfor modelling the dynamical behaviour of measurable quantities for very largenumbers of interacting quantum systems. Our approach makes use of a symbolicnon-commutative algebra engine that we have recently developed in conjunctionwith the well-known Ehrenfest theorem. Here we show the possibility ofdetermining the dynamics of experimentally observable quantities, withoutapproximation, for very large numbers of interacting harmonic oscillators. Ouranalysis removes a large number of significant constraints present in previousanalysis of this example system (such as having no entanglement in the initialstate). This method will be of value in simulating the operation of largequantum machines, emergent behaviour in quantum systems, open quantum systemsand quantum chemistry to name but a few.

On Calculating the Dynamics of Very Large Quantum Systems