发表机构
IBM Research; Massachusetts Institute of Technology（IBM 研究院; 麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究利用量子不可区分混淆构建经典可验证量子优势及BQP计算验证协议，首个公开可验证方案，并证明最坏到平均情况归约。
AI 中文摘要
我们利用量子不可区分混淆（qiO）构建了经典可验证量子优势以及BQP计算经典验证的协议。具体而言，给定qiO并假设BQP≠BPP的一个稍强版本，我们构造了一个两消息的量子优势协议，该协议可高效且公开验证。我们的结果可视为Aaronson和Zhang（arXiv:2404.14493）基于峰值随机电路采样的启发式量子优势提案的严格密码学基础。我们还构建了两个用于经典验证任意BQP计算的简单协议。第一个协议是私有可验证的，仅假设qiO的存在性。这提供了一个罕见的（量子）iO的非平凡密码学应用实例，该应用无需额外的计算硬度假设。第二个协议额外假设后量子单向函数，并且是公开可验证的。据我们所知，这是标准模型下基于计算假设的BQP计算经典验证的首个公开可验证协议。我们证明，当qiO仅针对无辅助幺正电路假设时，我们的所有结果均成立。作为支持该假设的证据，我们证明了对此类电路进行混淆的最坏情况到平均情况归约。该归约在Canetti、Chamon、Mucciolo和Ruckenstein（TCC 2024）的局部混合框架下，推广了其假设的量子类比。
英文摘要
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. As qiO is the basis for our results, we propose an approach to constructing qiO by adapting the local-mixing framework of Canetti--Chamon--Mucciolo--Ruckenstein.
