Prospects for Simulating a Qudit Based Model of (1+1)d Scalar QED

TL;DR

This paper develops a gauge-invariant digitization of (1+1)d scalar QED suitable for qudit quantum computers, demonstrating cost-effective encoding and initial state simulation on current hardware.

Contribution

It introduces a novel gauge-invariant digitization method for scalar QED on qudit-based quantum computers, including a Trotter operator construction and cost analysis.

Findings

Qutrit encoding reduces resource costs compared to qubit encoding.

A simple initial state can be simulated on current noisy qutrit hardware.

The method is adaptable for arbitrary spin truncations in scalar QED.

Abstract

We present a gauge invariant digitization of $(1+1)$d scalar quantum electrodynamics for an arbitrary spin truncation for qudit-based quantum computers. We provide a construction of the Trotter operator in terms of a universal qudit-gate set. The cost savings of using a qutrit based spin-1 encoding versus a qubit encoding are illustrated. We show that a simple initial state could be simulated on current qutrit based hardware using noisy simulations for two different native gate set.