# Oracles for Gauss's law on digital quantum computers

## TL;DR

This paper develops oracles that leverage local Gauss's law constraints to identify and correct errors in digital quantum simulations of Abelian lattice gauge theories, ensuring physical states are maintained.

## Contribution

It introduces a method to construct oracles that use local Gauss's law to distinguish physical from unphysical states in quantum simulations.

## Key findings

- Oracles successfully identify unphysical states violating Gauss's law.
- The approach enhances error detection in digital quantum simulations.
- Method applicable to Abelian lattice gauge theories.

## Abstract

Formulating a lattice gauge theory using only physical degrees of freedom generically leads to non-local interactions. A local Hamiltonian is desirable for quantum simulation, and this is possible by treating the Hilbert space as a subspace of a much larger Hilbert space in which Gauss's law is not automatic. Digital quantum simulations of this local formulation will wander into unphysical sectors due to errors from Trotterization or from quantum noise. In this work, oracles are constructed that use local Gauss law constraints to projectively distinguish physical and unphysical wave functions in Abelian lattice gauge theories. Such oracles can be used to detect errors that break Gauss's law.