发表机构
Fudan University; Tsinghua University; Peking University（复旦大学; 清华大学; 北京大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出了一种稀疏对易量子电路系综，可在恒定深度下实现高精度量子投影设计，所需量子资源极低，适用于随机表征、量子计量等多个领域。
AI 中文摘要
随机量子对象是量子信息处理的强大资源，但精确的Haar随机性成本高昂且通常不必要。我们在n个量子比特上引入了一个显式的稀疏对易电路系综，该系综在严格的相对误差意义上可重现低阶Haar矩。该电路由一个稀疏Clifford相位层和独立的单量子比特Clifford门组成。作用于简单乘积态时，所得系综在相对误差下形成ε近似投影2-设计和3-设计，所需的对数相互作用度在该电路族内是渐近最优的。它可在全连通架构上实现无辅助量子比特的量子深度O(log(n/ε))，也可使用O(nlog(n/ε))个辅助量子比特实现自适应恒定深度（实际上是深度7）的实现。与现有的浅设计范式不同，我们的分析利用了对易相位电路的固有矩结构；在三阶时，这需要一种新的块分解和组合分析，这也为高阶浅设计提供了一条途径。我们的结果表明，精确的类Haar统计可从稀疏对易动力学中以极低的量子资源出现，可应用于随机表征、量子计量学、量子算法和多体物理学。
英文摘要
Random quantum objects are powerful resources for quantum information processing, yet exact Haar randomness is costly and typically unnecessary. We introduce an explicit sparse commuting circuit ensemble on $n$ qubits that reproduces low-order Haar moments in the stringent relative-error sense. The circuit consists of a sparse Clifford phase layer followed by independent single-qubit Clifford gates. Acting on a simple product state, the resulting ensemble forms $ε$-approximate projective $2$- and $3$-designs in relative error, with the required logarithmic interaction degree being asymptotically optimal within this circuit family. It admits an ancilla-free implementation of quantum depth $O(\log(n/ε))$ on an all-to-all architecture, as well as an adaptive constant-depth implementation---in fact, depth seven---using $O(n\log(n/ε))$ ancilla qubits. Departing from existing shallow-design paradigms, our analysis exploits the intrinsic moment structure of commuting phase circuits; at third order, this requires a new block decomposition and combinatorial analysis that also suggests a route toward higher-order shallow designs. Our results show that precise Haar-like statistics can emerge from sparse commuting dynamics with remarkably low quantum resources, with applications to randomized characterization, quantum metrology, quantum algorithms, and many-body physics.
Comments9+35 pages, 3 figures
