Quantum Simulation of Two Interacting Schrödinger Particles

Abstract

In this paper, we examine whether a quantum computer can efficiently simulate time evolution of two Schrödinger particles. We consider particles interacting with each other and with an external potential. In order to solve the Schrödinger equation in the quantum register, we use an algorithm based on the quantum Fourier transform.

Bulletin of the Polish Academy of Sciences: Technical Sciences

“…In our previous work [20] we examined only the elastic collision of the Schrödinger particles. Here, for the first time, we simulate an inelastic scattering and return of the shield to the ground state by the photon emission.…”

“…In our earlier works we have shown that also rectangular potentials (like thresholds and wells) can be simulated using this method. This provides the ability to examine other interesting processes, such as the tunnel effect [19] and scattering of two Schrödinger particles to each other [20]. The present study also makes use of this kind of potential to simulate interaction between Schrödinger particle and shield.…”