A proof of quantumness is an efficiently verifiable interactive test that an efficient quantum computer can pass, but all efficient classical computers cannot (under some cryptographic assumption). Such protocols play a crucial role in the certification of quantum devices. Existing single-round protocols (like asking the quantum computer to factor a large number) require large quantum circuits, whereas multi-round ones use smaller circuits but require experimentally challenging mid-circuit measurements. As such, current proofs of quantumness are out of reach for near-term devices. In this work, we construct efficient single-round proofs of quantumness based on existing knowledge assumptions. While knowledge assumptions have not been previously considered in this context, we show that they provide a natural basis for separating classical and quantum computation. Specifically, we show that multi-round protocols based on Decisional Diffie-Hellman (DDH) or Learning With Errors (LWE) can be "compiled" into single-round protocols using a knowledge-of-exponent assumption or knowledge-of-lattice-point assumption, respectively. We also prove an adaptive hardcore-bit statement for a family of claw-free functions based on DDH, which might be of independent interest. Previous approaches to constructing single-round protocols relied on the random oracle model and thus incurred the overhead associated with instantiating the oracle with a cryptographic hash function. In contrast, our protocols have the same resource requirements as their multi-round counterparts without necessitating mid-circuit measurements, making them, arguably, the most efficient single-round proofs of quantumness to date. Our work also helps in understanding the interplay between black-box/white-box reductions and cryptographic assumptions in the design of proofs of quantumness.

翻译：量子优越性证明是一种高效可验证的交互式测试，高效量子计算机能够通过该测试，而所有高效经典计算机均无法通过（基于某些密码学假设）。此类协议在量子设备认证中起着关键作用。现有的单轮协议（例如要求量子计算机分解大整数）需要大规模量子电路，而多轮协议虽使用较小电路，却需要实验上具有挑战性的中途测量。因此，当前的量子优越性证明尚无法在近期设备上实现。本研究中，我们基于现有知识假设构建了高效的单轮量子优越性证明。尽管知识假设此前未在此领域被考虑，我们证明其能为经典与量子计算分离提供自然基础。具体而言，我们证明基于判定性迪菲-赫尔曼（DDH）或容错学习（LWE）的多轮协议，可分别通过指数知识假设或格点知识假设"编译"为单轮协议。我们还证明了基于DDH的无爪函数族自适应硬核比特声明，该结论可能具有独立研究价值。先前构建单轮协议的方法依赖于随机预言机模型，因此需承担用密码学哈希函数实例化预言机带来的开销。相比之下，我们的协议在保持与多轮协议相同资源需求的同时，无需中途测量，使其成为迄今为止最高效的单轮量子优越性证明。本研究亦有助于理解黑盒/白盒归约与密码学假设在量子优越性证明设计中的相互作用。