Real-Time Scattering on Quantum Computers via Hamiltonian Truncation

TL;DR

This paper introduces a Hamiltonian Truncation method for simulating real-time scattering in quantum field theories on quantum computers, demonstrating initial experiments and discussing resource efficiency and challenges.

Contribution

The paper develops a Hamiltonian Truncation framework for quantum simulation of scattering, with experimental validation on ion-trap hardware, offering an alternative to lattice methods.

Findings

Successful state preparation via adiabatic evolution on IonQ hardware

Captured wavepacket dynamics, interference, and particle production

Hamiltonian Truncation reduces qubit requirements compared to lattice approaches

Abstract

We present a quantum computational framework using Hamiltonian Truncation (HT) for simulating real-time scattering processes in $(1+1)$-dimensional scalar $\phi^4$ theory. Unlike traditional lattice discretisation methods, HT approximates the quantum field theory Hilbert space by truncating the energy eigenbasis of a solvable reference Hamiltonian, significantly reducing the number of required qubits. Our approach involves preparing initial states as wavepackets through adiabatic evolution from the free-field theory to the interacting regime. We experimentally demonstrate this state preparation procedure on an IonQ trapped-ion quantum device and validate it through quantum simulations, capturing key phenomena such as wavepacket dynamics, interference effects, and particle production post-collision. Detailed resource comparisons highlight the advantages of HT over lattice approaches in terms of qubit efficiency, although we observe challenges associated with circuit depth scaling. Our findings suggest that Hamiltonian Truncation offers a promising strategy for quantum simulations of quantum field theories, particularly as quantum hardware and algorithms continue to improve.