AI 中文总结
本研究提出精确常深度自适应协议，可制备任意Dicke态及对称态，通过均匀子集叠加态等基础模块实现，辅助量子比特开销为多项式级，并行重复可指数抑制失败概率。
AI 中文摘要
高效制备Dicke态及更一般的置换对称态对量子计量、量子网络和集体量子信息处理至关重要。测量与经典前馈可实现这些态的低深度制备，但需付出辅助量子比特的代价。本工作提出一种针对任意Dicke-(n,k)态及更一般对称态的精确常深度自适应制备协议。首先提供一种制备均匀子集叠加态的基础协议，采用常深度自适应电路，使用O(k²log²n)个辅助量子比特，成功概率至少为1/k，由此得到一种精确概率性常深度Dicke态制备协议，使用O(n² + k²log²n + kn log n log log n)个辅助量子比特。并行重复可指数级抑制失败概率且不增加量子深度。此外，均匀子集叠加态作为Johnson图的均匀顶点态、量子行走与拓扑数据分析算法中的紧致均匀子集态，具有独立研究价值。我们进一步建立通用提升框架，将干净幺正Dicke态制备电路与任意对称态制备相干结合，仅产生多项式级辅助开销。结合近期的常深度幺正Dicke态构造，可得到一种精确常深度制备任意n量子比特对称态的协议，使用O(n³√log n)个辅助量子比特。
英文摘要
Efficient preparation of Dicke states and, more generally, permutation-symmetric states is important for quantum metrology, quantum networking, and collective quantum information processing. Measurements and classical feedforward enable low-depth preparations of these states, with a cost of ancillary qubits. In this work, we introduce an exact constant-depth adaptive preparation protocol for arbitrary Dicke-$(n,k)$ states and further symmetric states. We first provide a protocol preparing the uniform subset superposition state, as a primitive, using constant-depth adaptive circuit with $O(k^2\log^2 n)$ ancillary qubits and success probability at least $1/k$. This yields an exact, probabilistic, constant-depth Dicke-state preparation protocol using $O\left(n^2+k^2\log^2 n+kn\log n\log\log n\right)$ ancillary qubits. Parallel repetition suppresses the failure probability exponentially without increasing the quantum depth. Moreover, the uniform subset superposition state is also of independent interest as the uniform vertex state of the Johnson graph and as the compact uniform subset state appearing in quantum-walk and topological-data-analysis algorithms. We further establish a general lifting framework that coherently combines clean unitary Dicke-state preparation circuits to prepare arbitrary symmetric states with only polynomial ancillary overhead. Combined with recent constant-depth unitary Dicke-state constructions, this gives an exact constant-depth preparation protocol for arbitrary $n$-qubit symmetric states using $O(n^3\sqrt{\log n})$ ancillary qubits.
Comments19 pages, 2 figures, 4 tables. Comments are welcome!
