Simulating Schwinger model dynamics with quasi-one-dimensional qubit arrays

TL;DR

This paper proposes a method to simulate the real-time dynamics of the Schwinger model, relevant to particle physics, using quasi-one-dimensional qubit arrays, enabling studies of non-perturbative phenomena beyond classical computational reach.

Contribution

It introduces a novel encoding of the Schwinger model into quantum spin lattices and establishes the optimal array geometry for accurate real-time simulations.

Findings

Optimal array is a quasi-one-dimensional ribbon with polynomial length and polylogarithmic width.

The method enables simulation of wave packet collisions and string fragmentation.

Implementation with Rydberg atom arrays is feasible for near-term quantum simulators.

Abstract

Real-time dynamics of the Schwinger model provide an effective description of quark confinement out of equilibrium, routinely employed to model hadronization processes in particle-physics event generators. Ab-initio simulations of such non-perturbative processes are far beyond the reach of existing computational tools, and remain an outstanding open quest for quantum simulators to date. In this work we develop a general strategy to run Schwinger model dynamics on synthetic quantum spin lattices, such as neutral-atom or superconducting-qubit arrays. Our construction encodes the constrained fermionic and bosonic degrees of freedom of the model into the geometric shape of a magnetic interface. We show that global magnetic field patterns can drive coherent quantum dynamics of the interface equivalent to the lattice Schwinger Hamiltonian. We rigorously establish that the optimal array required for simulating real-time wave packet collisions and string fragmentation processes with accuracy $\epsilon$ in the continuum field-theory limit, is a quasi-one-dimensional ribbon with polynomial length and polylogarithmic width in $\epsilon^{-1}$. We finally discuss a concrete advantageous implementation using a state-of-the-art dual-species Rydberg atom array. This work opens up a path for near-term quantum simulators to address questions of immediate relevance to particle physics.