Scattering phase shift in quantum mechanics on quantum computers

TL;DR

This paper explores extracting scattering phase shifts in quantum mechanics using quantum computers, verifying a formalism with simple models, and testing on IBM hardware, highlighting current limitations and potential solutions.

Contribution

It demonstrates the feasibility of using quantum circuits to compute scattering phase shifts and discusses methods to mitigate errors in current quantum hardware.

Findings

Good agreement with two qubits on IBM hardware

Failure with three qubits due to gate errors

Proposes post-data analysis methods for oscillatory functions

Abstract

We investigate the feasibility of extracting infinite volume scattering phase shift on quantum computers in a simple one-dimensional quantum mechanical model, using the formalism established in Ref.~\cite{Guo:2023ecc} that relates the integrated correlation functions (ICF) for a trapped system to the infinite volume scattering phase shifts through a weighted integral. The system is first discretized in a finite box with periodic boundary conditions, and the formalism in real time is verified by employing a contact interaction potential with exact solutions. Quantum circuits are then designed and constructed to implement the formalism on current quantum computing architectures. To overcome the fast oscillatory behavior of the integrated correlation functions in real-time simulation, different methods of post-data analysis are proposed and discussed. Test results on IBM hardware show that good agreement can be achieved with two qubits, but complete failure ensues with three qubits due to two-qubit gate operation errors and thermal relaxation errors.