Reflection and Transmission Amplitudes in a Digital Quantum Simulation

TL;DR

This paper presents a quantum simulation protocol to measure reflection and transmission amplitudes in 1D scattering problems using an ancillary qubit, enabling efficient tomography of complex scattering data.

Contribution

It introduces a novel method coupling a particle with an ancillary spin-1/2 to reconstruct scattering amplitudes in digital quantum simulations.

Findings

Protocol successfully reconstructs complex scattering amplitudes

Efficient measurement using only one qubit readout

Applicable to various potential scattering scenarios

Abstract

In this paper we show how to measure in the setting of digital quantum simulations the reflection and transmission amplitudes of the one-dimensional scattering of a particle with a short-ranged potential. The main feature of the protocol is the coupling between the particle and an ancillary spin-1/2 degree of freedom. This allows us to reconstruct tomographically the scattering amplitudes, which are in general complex numbers, from the readout of one qubit. Applications of our results are discussed.