来自混沌哈密顿量微扰时间演化的酉设计
Unitary designs from perturbed time evolutions of a chaotic Hamiltonian
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- International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料中心）
- Wilczek Quantum Center, Shanghai Institute for Advanced Studies, University of Science and Technology of China（中国科学院大学上海高等研究院吴文俊亚洲数学中心）
- Hefei National Laboratory（合肥国家实验室）
- Beijing Key Laboratory of Quantum Devices, Peking University（北京大学量子器件北京市重点实验室）
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中文总结 AI 辅助
研究提出基于含中间酉微扰的混沌哈密顿量时间演化生成酉设计的协议，推导其框架势，指出中间系综满足特定条件即可，还表明多哈密顿量时间协议可被单哈密顿量协议取代。
中文摘要 AI 辅助
酉设计在量子信息处理、随机测量和多体量子动力学中为哈尔随机酉矩阵提供了有效的替代方案。我们提出了一种基于具有中间酉微扰的单个混沌哈密顿量时间演化的协议来生成酉设计。我们推导了所得系综的框架势，它依赖于中间系综的框架势。中间系综本身不必是哈尔随机的或近似酉设计；只要其框架势增长相对于最大可能缩放保持良好抑制即可。非平凡泡利集和克利福德系综是满足此标准的简单示例，而固定大小的系综通常不满足。我们进一步表明，在框架势层面，多哈密顿量时间协议可以递归地被与固定迹抑制微扰交错的单哈密顿量协议所取代。
英文摘要
Unitary designs provide efficient substitutes for Haar-random unitaries in quantum information processing, randomized measurements, and many-body quantum dynamics. We propose a protocol based on time evolutions of a single chaotic Hamiltonian interleaved with unitary perturbations to generate unitary designs. We derive the frame potential of the resulting ensemble in terms of those of the intermediate ensemble. The intermediate ensemble need not itself be Haar random or exhibit Haar-level frame potentials, provided that its trace moments and frame-potential growth are sufficiently suppressed. The nontrivial Pauli set and the Clifford ensemble are simple examples, whereas ensembles whose cardinality does not grow with the Hilbert-space dimension generally fail. We further establish a frame-potential correspondence between multi-Hamiltonian temporal protocols and one-Hamiltonian protocols interleaved with repeated fixed trace-suppressed perturbations, showing that two perturbations suffice to recover Haar-level frame potentials. For local Hamiltonians, we derive a lower bound on the space--depth control resource, while more generally we establish a universal finite-window bound that constrains the required temporal sampling range. Together, these results identify complementary spatial and temporal resource requirements for perturbation-assisted randomness generation.
