Verifiable Quantum Advantage and Computation via Quantum Circuit Obfuscation

2026-09-30

AI Summary

This study addresses the longstanding absence of public verification mechanisms for quantum computational advantage and the classical verifiability of BQP. To overcome this limitation, the authors construct protocols based on quantum indistinguishability obfuscation (qiO), post-quantum one-way functions, and quantum analog assumptions within a local hybrid framework. This work presents the first publicly verifiable protocol for BQP under computational assumptions in the standard model, establishing a worst-case to average-case reduction for ancilla-free circuit obfuscation. Furthermore, it develops an efficient two-message quantum advantage protocol alongside both private and public verification schemes for BQP. Collectively, these contributions lay a rigorous cryptographic foundation for demonstrating and verifying quantum computational advantage.

Abstract

We construct protocols for classically verifiable quantum advantage and classical verification of $\mathsf{BQP}$ computations using \emph{quantum indistinguishability obfuscation} (qiO). Specifically, given qiO and assuming a slightly stronger version of $\mathsf{BQP}\neq\mathsf{BPP}$, we construct a two-message quantum-advantage protocol that is efficiently and publicly verifiable. Our result can be viewed as a rigorous cryptographic foundation for the heuristic quantum advantage proposals based on \emph{peaked random circuit sampling} of Aaronson and Zhang (arXiv:2404.14493). We also construct two simple protocols for classically verifying arbitrary $\mathsf{BQP}$ computations. The first protocol is privately verifiable and assumes only the existence of qiO. This gives a rare example of a nontrivial cryptographic application of (quantum) iO that does not make additional computational hardness assumptions. The second protocol additionally assumes post-quantum one-way functions and is \emph{publicly verifiable}. To our knowledge, this is the first publicly verifiable protocol for classical verification of $\mathsf{BQP}$ computations under computational assumptions in the standard model. We show that all our results hold when qiO is assumed only for ancilla-free unitary circuits. As evidence supporting this assumption, we prove a worst-to-average-case reduction for obfuscating such circuits. This reduction extends the local-mixing framework of Canetti, Chamon, Mucciolo and Ruckenstein (TCC 2024) under quantum analogues of their assumptions.

Problem

• Verifiable Quantum Advantage
• Classical Verification of BQP
• Quantum Indistinguishability Obfuscation
• Random Circuit Sampling

Innovation

• Quantum Indistinguishability Obfuscation
• Verifiable Quantum Advantage
• Classical Verification of BQP
• Ancilla-Free Unitary Circuits
• Worst-to-Average-Case Reduction