一维两轮CHSH问题的无条件量子优势
Unconditional quantum advantage from a two-round CHSH problem in one dimension
- Kangwon National University（江原国立大学）
- Korea Institute of Science and Technology (KIST)（韩国科学技术院）
- Kyung Hee University（庆熙大学）
- Korea Institute for Advanced Study（韩国高等研究院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
通过构造一维两轮CHSH问题，证明仅用深度为八的相邻门量子电路即可实现无条件量子优势，而经典电路需对数深度，且无需完美成功概率。
AI中文摘要：
我们引入了一个由Clauser-Horne-Shimony-Holt（CHSH）博弈构造的关系问题，称之为两轮一维CHSH问题。其两轮结构确保了CHSH问题仅在相关的Pauli框架数据被确定之后才被提供，从而排除了当所有输入同时提供时能完美解决相应问题的简单经典策略。我们构造了一个作用于$2N$个量子比特的量子电路，该电路仅使用相邻的两量子比特门，操作深度至多为八，并达到了CHSH的最优量子成功概率，该概率严格小于一。我们证明，对于每一个固定的$0\leq\delta<(\sqrt{2}-1)/4$，任何具有固定布线和有界门扇入的随机经典电路，若其平均成功概率至少为$(2+\sqrt{2})/4-\delta$，则在第二轮问题提供之后需要深度$\Omega(\log N)$。这产生了无条件的分离，尽管量子电路被限制在一维几何结构中，而经典电路没有几何局域性限制。该结果表明，完美的量子成功概率对于浅电路的元条件量子优势并非必要。
英文摘要：
We introduce a relation problem constructed from the Clauser--Horne--Shimony--Holt (CHSH) game, which we call the two-round one-dimensional CHSH problem. Its two-round structure ensures that the CHSH questions are supplied only after the relevant Pauli-frame data have been fixed, thereby ruling out a simple classical strategy that solves the corresponding problem perfectly when all inputs are supplied simultaneously. We construct a quantum circuit on $2N$ qubits that uses only adjacent two-qubit gates, has operational depth at most eight, and achieves the optimal quantum success probability of CHSH, which is strictly smaller than one. We prove that, for every fixed $0\leqδ<(\sqrt{2}-1)/4$, any randomized classical circuit with fixed wiring and bounded gate fan-in that achieves an average success probability of at least $(2+\sqrt{2})/4-δ$ requires depth $Ω(\log N)$ after the questions of the second round are supplied. This yields an unconditional separation even though the quantum circuit is restricted to a one-dimensional geometry, whereas the classical circuit has no geometric locality restriction. The result shows that perfect quantum success is not necessary for unconditional quantum advantage with shallow circuits.
