AI 中文总结
研究实时自旋动力学中量子优势评估，通过将量子比特自旋模型简化，以图协调为控制参数研究自旋星，推导连续时间\(1/d\)层次结构，给出相关渐近关系及数值测试结果，为评估量子优势提供新方法及验证阶梯。
AI 中文摘要
实时自旋动力学中的量子优势应与最强的相关经典替代物进行评估，而非仅针对微观系统的量子比特性质。我们通过将量子比特自旋模型简化为自旋 - 朗道 - 里夫希茨（LL）经典部分，并将剩余量子部分组织为可控修正，来为此边界开发一种基于物理的诊断方法。控制参数是图协调：我们研究具有\(d\)个叶和\(O(1/d)\)个中心 - 叶耦合的自旋星。其均匀形式为从LL可替代动力学向真正量子的离散部分干涉的转变提供基准；其完全驱动形式，具有随时间变化的场和双线性耦合，是树状和循环自旋结构的基本消息传递原语。对于相干态返回振幅，我们证明了精确的叶消除并推导了连续时间\(1/d\)层次结构。L0是驱动的单自旋弱平均场理论，而G1是将叶二次核与中心弱两点函数耦合的高斯非局部时间影响修正。在远离边界振幅零点的有界有限时间窗口上，层次结构给出\(\log\mathcal A - \log\mathcal A_{\rm L0}=O(1/d)\)和\(\log\mathcal A - \log\mathcal A_{\rm L0}-\Delta_{\rm G1}=O(1/d^2)\)；对完全驱动的各向异性系综的数值测试给出斜率\(-1.05\)和\(-2.03\)。静态、非均匀、对齐和完全驱动的星提供了验证阶梯，与时间矩阵乘积影响矩阵基线的比较描绘了互补区域。与Trotter网格上的秩压缩不同，层次结构由物理参数排序，以连续时间表述，每个截断级别本身就是一个物理理论，LL部分为高配位数极限。
英文摘要
Quantum advantage in real-time spin dynamics should be assessed against the strongest relevant classical substitutes, not merely against the qubit nature of the microscopic system. We develop a physics-based diagnostic for this boundary by reducing a qubit spin model to a spin-Landau--Lifshitz (LL) classical sector and organizing the residual quantum sector as controlled corrections. The control parameter is graph coordination: we study a spin star with \(d\) leaves and \(O(1/d)\) hub--leaf couplings. In its homogeneous form the star benchmarks the transition from LL-substitutable dynamics to genuinely quantum, discrete-sector interference; in its fully driven form, with time-dependent fields and bilinear couplings, it is the basic message-passing primitive for tree and loopy spin structures. For coherent-state return amplitudes we prove exact leaf elimination and derive a continuous-time \(1/d\) hierarchy. L0 is a driven one-spin weak-mean-field theory, while G1 is a Gaussian nonlocal-in-time influence correction coupling leaf two-time kernels to the hub weak two-point function. On bounded finite-time windows away from zeros of the boundary amplitudes, the hierarchy gives \(\log\mathcal A-\log\mathcal A_{\rm L0}=O(1/d)\) and \(\log\mathcal A-\log\mathcal A_{\rm L0}-Δ_{\rm G1}=O(1/d^2)\); numerical tests on fully driven anisotropic ensembles give slopes \(-1.05\) and \(-2.03\). Static, inhomogeneous, aligned, and fully driven stars provide validation rungs, and comparison with a temporal matrix-product influence-matrix baseline delineates complementary regimes. Unlike rank compression on a Trotter grid, the hierarchy is ordered by a physical parameter, formulated in continuous time, and each truncation level is itself a physical theory, with the LL sector as the high-coordination limit.
Comments36 pages, 10 figures
