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

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.