Robustness of QMA against witness noise

TL;DR

This paper proves that the complexity class QMA remains unchanged under constant noise on witness qubits using concatenated stabilizer coding, with implications for physical implementations and complexity class relationships.

Contribution

It demonstrates the robustness of QMA against specific levels of noise, extending understanding of quantum verification protocols under realistic conditions.

Findings

QMA is robust against 27% dephasing noise.

QMA is robust against 18% depolarizing noise.

The result links noise resilience to complexity class stability.

Abstract

Using the tool of concatenated stabilizer coding, we prove that the complexity class QMA remains unchanged even if every witness qubit is disturbed by constant noise. This result may not only be relevant for physical implementations of verifying protocols but also attacking the relationship between the complexity classes QMA, QCMA and BQP, which can be reformulated in this unified framework of a verifying protocol receiving a disturbed witness. While QCMA and BQP are described by fully dephasing and depolarizing channels on the witness qubits, respectively, our result proves QMA to be robust against 27% dephasing and 18% depolarizing noise.