Quantum Simulation of Simple Many-Body Dynamics

TL;DR

This paper presents a quantum algorithm for simulating the time evolution of many-body Coulombic systems, demonstrating its effectiveness through numerical tests that align with analytical solutions.

Contribution

It introduces a general quantum simulation algorithm for non-relativistic many-body systems and details its implementation and validation.

Findings

Numerical simulations agree with analytical solutions.

The algorithm effectively simulates small many-body quantum systems.

Detailed operator constructions enable practical implementation.

Abstract

Quantum computers could potentially simulate the dynamics of systems such as polyatomic molecules on a much larger scale than classical computers. We investigate a general quantum computational algorithm that simulates the time evolution of an arbitrary non-relativistic, Coulombic many-body system in three dimensions, considering only spatial degrees of freedom. We use a simple discretized model of Schrodinger evolution and discuss detailed constructions of the operators necessary to realize the scheme of Wiesner and Zalka. The algorithm is simulated numerically for small test cases, and its outputs are found to be in good agreement with analytical solutions.