Hamiltonian Property Testing

Understand

Locality is a fundamental feature of many physical time evolutions.

• Assumptions on locality and related structural properties also underlie recently proposed procedures for learning an unknown Hamiltonian from access to the induced time evolution.
• However, no protocols to rigorously test whether an unknown Hamiltonian is local were known.
• We investigate Hamiltonian locality testing as a property testing problem, where the task is to determine whether an unknown $n$-qubit Hamiltonian $H$ is $k$-local or $\varepsilon$-far from all $k$-local Hamiltonians, given access to the time evolution along $H$.