AI 中文总结
该研究以Kitagawa-Ueda单轴扭曲模型为对象，通过双重极限推导有限N修正，揭示封闭多体系统可产生涌现非马尔可夫退相位，为量子计算硬件的非马尔可夫噪声提供微观实现。
AI 中文摘要
开放系统描述通常通过将量子系统耦合到外部环境来引入，本文表明，一个封闭的相互作用多体系统自身可通过对非线性平均场极限的有限尺寸修正，生成作用于约化非线性量子比特的受控非马尔可夫量子通道。我们利用Kitagawa-Ueda单轴扭曲模型（哈密顿量H=χJ_z²，这是集体自旋动力学、自旋压缩及两分量玻色-爱因斯坦凝聚的范例模型）演示这一现象。尽管该模型的大N regime已被广泛研究，但传统固定χ标度并未产生非平凡的动力学大N极限。本文中，我们研究从双重极限N→∞与χ→O(g/N)（其中g为耦合常数）得到的互补大N公式，推导该极限下的主导有限N修正，并表明这些修正对应于涌现的非马尔可夫退相位过程，产生布洛赫矢量相干性的高斯衰减，其特征时标t_φ≥√N/(2g)。精确的有限N计算表明，该有效开放系统描述对包含约一百个量子比特的系统而言在定量上准确。所得框架提供了由封闭多体系统内在产生的非马尔可夫退相位的微观实现，并能有效模拟超越幺正平均场理论的集体量子动力学。这些结果将原子系综与玻色-爱因斯坦凝聚中长期研究的相位扩散现象，与量子计算硬件中对非马尔可夫、超越Lindblad噪声的日益增长的表征努力联系起来，提供了此类噪声通道源自微观动力学而非现象学拟合的罕见案例。
英文摘要
Open-system descriptions are typically introduced by coupling a quantum system to an external environment. Here we show that a closed interacting many-body system can itself generate a controlled non-Markovian quantum channel acting on a reduced nonlinear qubit through finite-size corrections to a nonlinear mean-field limit. We demonstrate this using the Kitagawa-Ueda one-axis twisting model, $H=χJ_z^2$, a paradigmatic model of collective spin dynamics, spin squeezing, and two-component Bose-Einstein condensates. Although the large-$N$ regime of this model has been extensively studied, the conventional fixed-$χ$ scaling does not yield a nontrivial dynamical large-$N$ limit. In this paper, we investigate a complementary large-$N$ formulation obtained from the double limit $N\rightarrow\infty$ and $χ\rightarrow O(g/N)$, where $g$ is a coupling constant. We derive the leading finite-$N$ corrections to this limit and show that they correspond to an emergent non-Markovian dephasing process, producing a Gaussian decay of the Bloch-vector coherence with characteristic timescale $t_φ\geq\sqrt{N}/(2g)$. Exact finite-$N$ calculations demonstrate that this effective open-system description becomes quantitatively accurate for systems containing on the order of one hundred qubits. The resulting framework provides a microscopic realization of non-Markovian dephasing generated intrinsically by a closed many-body system and enables efficient simulation of collective quantum dynamics beyond unitary mean-field theory. These results link the long-studied phenomenon of phase diffusion in atomic ensembles and Bose-Einstein condensates to the growing effort to characterize non-Markovian, beyond-Lindblad noise in quantum computing hardware, providing a rare case in which such a noise channel is derived from microscopic dynamics rather than fit phenomenologically.
