Quantum simulations of a particle in one-dimensional potentials using NMR

TL;DR

This paper demonstrates quantum simulation of a single particle in one-dimensional potentials using a five-qubit NMR system, effectively mimicking quantum dynamics with high fidelity.

Contribution

It presents the first experimental realization of simulating Schrödinger dynamics for 1D potentials on a small-scale NMR quantum computer.

Findings

Successfully simulated wave-function spreading, potential-well evolution, and barrier reflection.

Achieved accurate measurement of spatial probabilities matching theoretical predictions.

Demonstrated feasibility of quantum simulation for simple quantum systems using NMR.

Abstract

A classical computer simulating Schrodinger dynamics of a quantum system requires resources which scale exponentially with the size of the system, and is regarded as inefficient for such purposes. However, a quantum computer made up of a controllable set of quantum particles has the potential to efficiently simulate other quantum systems of matching dimensions. In this work we studied quantum simulations of single particle Schrodinger equation for certain one-dimensional potentials. In particular, we report the following cases: (i) spreading of wave-function of a free-particle, (ii) evolution of a particle in a potential-well, and (iii) reflection of a particle from a potential-barrier. Using a five-qubit NMR system, we achieve space discretization with four qubits, and the other qubit is used for preparation of initial states as well as measurement of spatial probabilities. The experimental relative probabilities compare favorably with the theoretical values, thus effectively mimicking a small-scale quantum simulator.