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

• Digital quantum simulation of a particle in 1D potentials using a 5-qubit NMR quantum simulator.
• Direct read out of spatio-temporal probabilities from the ancilla spectral lines without tomography.
• Use of optimal control methods to realize Schrödinger dynamics.

A quantum computer made up of a controllable set of quantum particles has the potential to efficiently simulate other quantum systems. In this work we studied quantum simulations of single particle Shrödinger equation for certain one-dimensional potentials. 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 favourably with the theoretical expectations, thus effectively mimicking a small scale quantum simulator.