Interactive proofs for BQP via self-tested graph states

TL;DR

This paper presents a method to verify quantum computations within BQP using interactive proofs with non-communicating quantum provers and a classical verifier, leveraging self-tested graph states for efficiency and generality.

Contribution

It introduces improved error bounds for self-testing graph states and extends measurement self-testing to adaptive measurements, enhancing verification techniques for quantum computations.

Findings

Polynomial scaling error bounds for self-tested graph states

Verification of all BQP languages with polynomial quantum provers

Extension of self-testing to adaptive measurement sets

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. In this regard we introduce two important improvements over previous work. Specifically, we derive new error bounds which scale polynomially with the size of the graph compared with exponential dependence on the size of the graph in previous work. We also extend the self-testing error bounds on measurements to a very general set which includes the adaptive measurements used for measurement-based quantum computation as a special case.