Quantum simulation of quantum mechanical system with spatial noncommutativity

TL;DR

This paper demonstrates the quantum simulation of a noncommutative quantum mechanical system using a novel group theoretical approach and analyzes how noncommutativity influences the simulation accuracy and Trotter error.

Contribution

It introduces a method to simulate noncommutative quantum systems on a quantum computer by mapping to ordinary Hamiltonians and studies the effects of noncommutativity on simulation errors.

Findings

Successful mapping of noncommutative Hamiltonian to ordinary form

Impact of noncommutativity parameter on Trotter error analyzed

Sizable noncommutativity affects simulation accuracy

Abstract

Quantum simulation has become a promising avenue of research that allows one to simulate and gain insight into the models of High Energy Physics whose experimental realizations are either complicated or inaccessible with current technology. We demonstrate the quantum simulation of such a model, a quantum mechanical system with spatial noncommutativity, which is inspired by the works in Noncommutative Geometry and Noncommutative Field theory for a universal quantum computer. We use the novel group theoretical formalism to map the Hamiltonian of such a noncommutative quantum system into the ordinary quantum mechanical Hamiltonian and then carry out the quantum simulation using the Trotter-Suzuki product formula. Furthermore, we distinguish the impact of the noncommutativity parameter on the quantum simulation, especially on the Trotter error, and point out how its sizable value affects the simulation.