Quantum simulations of a particle in one-dimensional potentials 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.

7 pages, 8 figures

References in corpus (5)

• Polynomial-time quantum algorithm for the simulation of chemical dynamics
• Quantum simulation of the single-particle Schrodinger equation
• Experimental simulation of quantum tunneling in small systems
• Quantum Simulation of Tunneling in Small Systems
• Writing electronic ferromagnetic states in a high-temperature paramagnetic nuclear spin system

Cited by in corpus (3)

• Experimentally Probing Topological Order and Its Breakdown via Modular Matrices
• Estimating Franck-Condon factors using an NMR quantum processor
• Self-Consistent Determination of Single-Impurity Anderson Model Using Hybrid Quantum-Classical Approach on a Spin Quantum Simulator