We propose and analyze a novel interactive protocol for demonstrating quantum computational advantage, which is efficiently classically verifiable. Our protocol relies upon the cryptographic hardness of trapdoor claw-free functions (TCFs). Through a surprising connection to Bell's inequality, our protocol avoids the need for an adaptive hardcore bit, with essentially no increase in the quantum circuit complexity and no extra cryptographic assumptions. Crucially, this expands the set of compatible TCFs, and we propose two new constructions: one based upon the decisional Diffie-Hellman problem and the other based upon Rabin's function, $x^2 \bmod N$. We also describe two independent innovations which improve the efficiency of our protocol's implementation: (i) a scheme to discard so-called "garbage bits", thereby removing the need for reversibility in the quantum circuits, and (ii) a natural way of performing post-selection which significantly reduces the fidelity needed to demonstrate quantum advantage. These two constructions may also be of independent interest, as they may be applicable to other TCF-based quantum cryptography such as certifiable random number generation. Finally, we design several efficient circuits for $x^2 \bmod N$ and describe a blueprint for their implementation on a Rydberg-atom-based quantum computer.
翻译:我们提出并分析一种新的互动协议,以展示量子计算优势,这在古典中是有效的可核实的。我们的协议依赖于陷阱门无爪功能(TCF)的加密硬度。通过与贝尔不平等的惊人联系,我们的协议避免了对适应性硬核部分的需要,而量子电路的复杂性基本上没有增加,也没有额外的加密假设。关键的是,这扩大了一套兼容的TCF,我们建议了两个新的结构:一个基于Diffie-Hellman决定问题,另一个基于Rabin的功能,$x%2\bmod N。我们还描述了提高我们协议执行效率的两种独立创新:(一) 放弃所谓的“塑料比部分”的计划,从而消除了量子电路的可逆性需求,以及(二) 进行后选的自然方式,这大大降低了显示量子优势所需要的真实性。这两种建筑也可能具有独立的兴趣,因为它们可能适用于其他基于TCF$的量子2\bmod N。我们描述其高效型的计算机成本设计,从而可以将它作为数字,我们用来描述成一个高效的计算机的智能路段。