Driven Quantum Stars as Controlled Primitives for Real-Time Spin Dynamics

• URL: http://arxiv.org/abs/2607.10899v1
• Date: Sun, 12 Jul 2026 19:58:56 GMT
• Title: Driven Quantum Stars as Controlled Primitives for Real-Time Spin Dynamics
• Abstract summary: Quantum advantage in real-time spin dynamics should be assessed against the strongest relevant classical substitutes.<n>We develop a physics-based diagnostic for this boundary by reducing a qubit spin model to a spin-Landau--Lifshitz (LL) classical sector.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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