内容：
Circuit depth is a fundamental proxy for computational time. As has long been studied in the classical field, a similar question central in quantum complexity is: Does each additional layer of gates really increase computational power? We answer this question in the affirmative within the quantum complexity class $\mathsf{QNC}^0$ by establishing a robust, worst-case depth hierarchy. For any integer $d$ greater than or equal to 12, we explicitly construct problems where any depth-$(d-1)$ quantum circuit fails to achieve near-perfect success, while slightly deeper circuits succeed perfectly. Moreover, all bounded fan-in classical circuits of sublogarithmic depth (in the input size) fail to achieve perfect success on these tasks for every $d$, hence demonstrating unconditional quantum advantage of $\mathsf{QNC}^0$ over $\mathsf{NC}^0$. To circumvent the scarcity of quantum lower-bound techniques, we apply a group-theoretic approach and develop a systematic framework to analyse how depth affects a circuit’s ability to generate nonlocal correlations in a fine-grained manner. Our work represents the first explicit, unconditional, and genuinely quantum depth hierarchy in computation. Beyond structural complexity, these depth-sensitive tasks also provide a concrete mechanism to certify coherence times and validate non-Clifford resources on near-term quantum computing platforms.
Research article information: //arxiv.org/abs/2606.16425
