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We give a quantum interactive proof system for the local Hamiltonian problemon n qubits in which (i) the verifier has a single round of interaction withfive entangled provers, (ii) the verifier sends a classical message on O(log n)bits to each prover, who reply with a constant number of qubits, and (iii)completeness and soundness are separated by an inverse polynomial in n. As thesame class of proof systems, without entanglement between the provers, isincluded in QCMA, our result provides the first indication that quantummultiprover interactive proof systems with entangled provers may be strictlymore powerful than unentangled-prover interactive proof systems. Adistinguishing feature of our protocol is that the completeness propertyrequires honest provers to share a large entangled state, obtained as theencoding of the ground state of the local Hamiltonian via an error-correctingcode. Our result can be interpreted as a first step towards a multiprovervariant of the quantum PCP conjecture.

A multiprover interactive proof system for the local Hamiltonian problem