Quantum proofs can be verified using only single qubit measurements

TL;DR

This paper demonstrates that quantum proofs can be verified using only single qubit measurements, significantly reducing the verifier's quantum resource requirements while still verifying QMA problems.

Contribution

It proves that QMA verification is possible with minimal quantum resources, using only single qubit measurements, without quantum memory or multiqubit operations.

Findings

Verification of QMA problems with single qubit measurements is possible.

Two independent proofs are provided, based on measurement-based quantum computation and local Hamiltonian problem.

The approach also applies to QMA₁, with one-sided error.

Abstract

QMA (Quantum Merlin Arthur) is the class of problems which, though potentially hard to solve, have a quantum solution which can be verified efficiently using a quantum computer. It thus forms a natural quantum version of the classical complexity class NP (and its probabilistic variant MA, Merlin-Arthur games), where the verifier has only classical computational resources. In this paper, we study what happens when we restrict the quantum resources of the verifier to the bare minimum: individual measurements on single qubits received as they come, one-by-one. We find that despite this grave restriction, it is still possible to soundly verify any problem in QMA for the verifier with the minimum quantum resources possible, without using any quantum memory or multiqubit operations. We provide two independent proofs of this fact, based on measurement based quantum computation and the local Hamiltonian problem, respectively. The former construction also applies to QMA$_1$, i.e., QMA with one-sided error.