Symmetry criteria for quantum simulability of effective interactions

TL;DR

This paper establishes symmetry-based criteria to determine if a quantum device can simulate specific effective interactions, enhancing understanding of quantum simulation capabilities beyond traditional Lie algebra methods.

Contribution

It introduces symmetry criteria for quantum simulability, enabling decision-making without explicit algebra determination and linking symmetries to resource theories.

Findings

Symmetry criteria effectively decide simulability of target interactions.

Conserved quantities from symmetries form a resource theory for simulation.

Applications include entanglement invariants and unitary gate problems.

Abstract

What can one do with a given tunable quantum device? We provide complete symmetry criteria deciding whether some effective target interaction(s) can be simulated by a set of given interactions. Symmetries lead to a better understanding of simulation and permit a reasoning beyond the limitations of the usual explicit Lie closure. Conserved quantities induced by symmetries pave the way to a resource theory for simulability. On a general level, one can now decide equality for any pair of compact Lie algebras just given by their generators without determining the algebras explicitly. Several physical examples are illustrated, including entanglement invariants, the relation to unitary gate membership problems, as well as the central-spin model.