Testing quantum circuits and detecting insecure encryption

TL;DR

This paper demonstrates that testing quantum circuit behavior and detecting insecure quantum encryption are computationally hard problems, establishing their QMA-completeness and highlighting challenges in quantum cryptography verification.

Contribution

It proves the QMA-hardness of testing quantum circuits and detecting insecure quantum encryption, and provides a QMA protocol for the latter, advancing understanding of quantum cryptographic security.

Findings

Testing quantum circuits is QMA-hard.

Detecting insecure quantum encryption is QMA-complete.

Provides a QMA protocol for quantum encryption insecurity detection.

Abstract

We show that computational problem of testing the behaviour of quantum circuits is hard for the class of problems known as QMA that can be verified efficiently with a quantum computer. This result is a generalization of the techniques previously used to prove the hardness of other problem on quantum circuits. We use this result to show the QMA-hardness of a weak version of the problem of detecting the insecurity of a symmetric-key quantum encryption system, or alternately the problem of determining when a quantum channel is not private. We also give a QMA protocol for the problem of detecting insecure encryption to show that it is QMA-complete.