Investigation of tunneling dynamics on a quantum computer

Abstract

The potential tunneling of a particle is one of the most representative examples that appear every quantum mechanics textbook. The tunneling phenomenon is very quantum mechanical without any classical analogue and becomes a foundation of modern electronics. Despite its straightforward description with Schrödinger equation, the tunneling dynamics presents a long-standing problem which still remains as an unsolved mystery: a time for a particle to pass through the potential barrier. Many speculations have been proposed so far, including phase time, Larmor time, Landauer time, Hartman effect and so on, but no consensus has been arrived yet. In an attempt to understand the so-called “tunneling time”, we carry out a tunneling simulation of a particle on IBM quantum computer. By designing a 2-qubit quantum circuit, we obtained the tunneling probability (PT) as a function of time. PT is found to show a well-defined periodicity as the potential varies. The periodicity shows the tendency of Hartman effect stating that a particle tunnels a wall faster as the potential barrier increases.