On Information-Theoretic Classical Verification of Quantum Computers

TL;DR

This paper explores the limitations of classical verification protocols for quantum computations, showing they require very powerful provers and suggesting potential directions for protocols with weaker provers like quantum computers.

Contribution

It introduces a family of verification protocols for quantum computations and proves their inherent requirement for powerful provers, extending previous known protocols.

Findings

Any protocol in this family requires an extremely powerful prover.

The analysis suggests possible approaches for protocols with weaker provers, such as quantum computers.

The work generalizes existing protocols like AAV13 and AG17.

Abstract

Quantum inspired protocols e.g. [AAV13,AG17] attempt to achieve a single-prover interactive protocol where a classical machine can verify quantum computations in an information-theoretically secure manner. We define a family of protocols which seem natural for verifying quantum computations and generalizes such known protocols, namely those of [AAV13,AG17]. We show that any protocol from this family is bound to require an extremely powerful prover, much like the classical protocols of [LFKN92] and [Sha92]. Using our analysis, we also hint at possible ways one might try to realize a protocol where the prover can be weaker, namely a quantum computer (i.e. a BQP machine).