Oracles for Gauss's law on digital quantum computers

Understand

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.