Toward extracting scattering phase shift from integrated correlation functions on quantum computers

TL;DR

This work addresses extracting infinite-volume elastic scattering phase shifts $\delta(\epsilon)$ from a few-body system trapped in a potential using quantum computing. It builds on a relation that connects the integrated trap correlation functions $C(t)$ and $C_0(t)$ to $\delta(\epsilon)$ via $C(t)-C_0(t) \to \frac{it}{\pi}\int_0^{\infty} d\epsilon\,\delta(\epsilon)\,e^{-i\epsilon t}$, enabling a trap-based route to scattering information. The Hamiltonian and two-particle operators are mapped to quantum registers in the trap basis, with the integrated correlator computed by an ancilla-based circuit and trotterized time evolution; a simple 1+1D contact-interacting fermion model serves as a proof of principle. Data processing to mitigate finite-volume oscillations—via short-time averaging—followed by fitting a parameterized $\delta(\epsilon)$ to the integral, demonstrates a viable path to obtaining infinite-volume phase shifts from quantum simulations. The approach offers a quantum-computing avenue to real-time scattering information beyond traditional sign-problem-laden classical methods.

Abstract

Based on a established relation in Refs.~\cite{Guo:2023ecc,Guo:2024zal,Guo:2024pvt} that relates the integrated correlation functions for a trapped system to the infinite volume scattering phase shifts through a weighted integral, we propose to extract the infinite volume scattering phase shifts through quantum simulation of the integrated correlation functions of trapped two-particle systems on quantum computers. The integrated correlation function can be computed by an ancilla-based algorithm proposed in Ref.~\cite{PhysRevA.64.022319}. The proposal is demonstrated with a simple contact interaction fermion model.

Figures (3)

• Figure 1: Demo of quantum circuit for computing the integrated two-particle correlation function $C(t)$.
• Figure 2: Demo plots of real part of $\triangle C(t)$ (black) vs. its infinite volume limit given by the right-hand side of Eq.(\ref{['dCtinflimit']}) (red) with parameters: $V_0=2.5$, $\mu =1$, $L = 90$ and $N=300$.
• Figure 3: Demo plots of real part of $\triangle C_{avg}(t)$ (black) vs. its infinite volume limit given by the right-hand side of Eq.(\ref{['dCtinflimit']}) (red) with parameters: $V_0=2.5$, $\mu =1$, $L = 90$, $N=1000$, $t_0=2$ and $N_t=20$.