Real-time quantum calculations of phase shifts using wave packet time delays

Erik Gustafson,Norbert M. Linke,Yingyue Zhu,Yannick Meurice,Patrick Dreher

doi:10.1103/physrevd.104.054507

Abstract

We present a method to extract the phase shift of a scattering process using the real-time evolution in the early and intermediate stages of the collision in order to estimate the time delay of a wave packet. This procedure is convenient when using noisy quantum computers for which the asymptotic out-state behavior is unreachable. We demonstrate that the challenging Fourier transforms involved in the state preparation and measurements can be implemented in $1+1$ dimensions with current trapped ion devices and IBM quantum computers. We compare quantum computation of the time delays obtained in the one-particle quantum mechanics limit and the scalable quantum field theory formulation with accurate numerical results. We discuss the finite volume effects in the Wigner formula connecting time delays to phase shifts. The results reported involve two- and four-qubit calculations, and we discuss the possibility of larger scale computations in the near future.

Highlights

In recent years, the idea of simulating quantum field theory with quantum computers has gained considerable interest [1]
For noisy intermediate-scale quantum (NISQ) devices with limited coherence time or gate-depth, using the information from the early stages of the collision is advantageous. We show that this idea can be implemented on both a quantum computer using superconducting transmon qubits and a trapped ion system operating at the University of Maryland [51]
The time delay ΔtW of a wave packet with a sharply defined momentum k is related to the derivative of the phase shift by the Wigner formula [44]: ΔtW 1⁄4 2δ0ðkÞ=ð∂E=∂kÞ; ð6Þ

Summary

INTRODUCTION

The idea of simulating quantum field theory with quantum computers has gained considerable interest [1]. In the context of high-energy and nuclear physics, a long term motivation is to develop quantum computing methods that perform real-time evolution for lattice quantum chromodynamics (QCD). This is an ab-initio, ultraviolet complete, theory of strong interactions which has been very successful in describing the static properties of hadrons and nuclei [2]. It can shown [52] that for finite range interactions, for instance involving only nearest neighbor degrees of freedom, the computing timescales like the size of the system

MODEL CALCULATIONS OF PHASE SHIFTS

TOWARD SCALABLE FIELD THEORY CALCULATIONS

Findings

CONCLUSIONS