A multiprover interactive proof system for the local Hamiltonian problem

TL;DR

This paper introduces a quantum multiprover interactive proof system for the local Hamiltonian problem, demonstrating potential advantages of entangled provers over unentangled systems and advancing towards a quantum PCP conjecture variant.

Contribution

It presents the first quantum multiprover proof system with entangled provers for the local Hamiltonian problem, highlighting increased computational power over unentangled systems.

Findings

Verifiers interact with five entangled provers in a single round.

The protocol achieves inverse polynomial completeness-soundness gap.

Entangled provers share a large encoded ground state of the Hamiltonian.

Abstract

We give a quantum interactive proof system for the local Hamiltonian problem on n qubits in which (i) the verifier has a single round of interaction with five 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 the same class of proof systems, without entanglement between the provers, is included in QCMA, our result provides the first indication that quantum multiprover interactive proof systems with entangled provers may be strictly more powerful than unentangled-prover interactive proof systems. A distinguishing feature of our protocol is that the completeness property requires honest provers to share a large entangled state, obtained as the encoding of the ground state of the local Hamiltonian via an error-correcting code. Our result can be interpreted as a first step towards a multiprover variant of the quantum PCP conjecture.