Relativistic verifiable delegation of quantum computation

The importance of being able to verify quantum computation delegated to remote servers increases with recent development of quantum technologies. In some of the proposed protocols for this task, a client delegates her quantum computation to non-communicating servers. The fact that the servers do not communicate is not physically justified and it is essential for the proof of security of such protocols. For the best of our knowledge, we present in this work the first verifiable delegation scheme where a classical client delegates her quantum computation to two entangled servers that are allowed to communicate, but respecting the plausible assumption that information cannot be propagated faster than speed of light. We achieve this result by proposing the first one-round two-prover game for the Local Hamiltonian problem where provers only need polynomial time quantum computation and access to copies of the groundstate of the Hamiltonian.