Interactive proofs for BQP via self-tested graph states (extended abstract)

TL;DR

This paper presents a method for verifying quantum computations in BQP using interactive proofs with multiple non-communicating quantum provers and a classical verifier, leveraging self-tested graph states.

Contribution

It introduces a novel approach combining measurement-based quantum computation and self-tested graph states to verify quantum proofs with minimal quantum effort from provers.

Findings

Interactive proofs for all BQP languages with polynomial quantum provers

Provers perform only a single measurement in honest execution

Verification of provers' honesty via self-tested graph states

Abstract

Using the measurement-based quantum computation model, we construct interactive proofs with non-communicating quantum provers and a classical verifier. Our construction gives interactive proofs for all languages in BQP with a polynomial number of quantum provers, each of which, in the honest case, performs only a single measurement. Our techniques use self-tested graph states which allow us to test the provers for honesty, establishing that they hold onto a particular graph state and measure it in specified bases. In this extended abstract we give an overview of the construction and proofs.