Quantum Logspace Computations are Verifiable

TL;DR

This paper demonstrates that quantum logspace computations can be efficiently and securely verified by classical logspace algorithms using streaming proofs, ensuring correctness with minimal randomness and unconditional security.

Contribution

It introduces a method for classical logspace verifiers to verify quantum logspace computations with information-theoretic security and streaming proofs.

Findings

Quantum logspace computations are verifiable by classical logspace algorithms.

Verifiers use only O(log n) random bits for verification.

The verification process is information-theoretically secure.

Abstract

In this note, we observe that quantum logspace computations are verifiable by classical logspace algorithms, with unconditional security. More precisely, every language in BQL has an (information-theoretically secure) streaming proof with a quantum logspace prover and a classical logspace verifier. The prover provides a polynomial-length proof that is streamed to the verifier. The verifier has a read-once one-way access to that proof and is able to verify that the computation was performed correctly. That is, if the input is in the language and the prover is honest, the verifier accepts with high probability, and, if the input is not in the language, the verifier rejects with high probability even if the prover is adversarial. Moreover, the verifier uses only $O(\log n)$ random bits.