AI 中文总结
本文针对多项式单正交哈密顿量等构成的连续监测系统，推导了其任意有限阶正交矩条件动力学的精确有限维随机表示，提供了一种高效的非线性零差轨迹研究方法。
AI 中文摘要
非线性随机主方程的模拟通常需要对大希尔伯特空间密度矩阵进行轨迹级演化，这使得强非线性连续监测系统的计算极具挑战性。本文确定了一类可精确求解的连续监测系统，其由多项式单正交哈密顿量、线性阻尼以及同一正交的零差测量构成。对于高斯初始态，我们通过条件动量层级的闭合，推导出了任意有限阶正交矩⟨Q^mP^n⟩的条件动力学的精确有限维随机表示。所得系数方程仅依赖于哈密顿量阶数和矩阶数，计算复杂度为O(C_{d,n}T)，与希尔伯特空间维度无关。该方法无需福克空间截断、高斯近似或矩闭合近似。数值模拟表明其与直接随机主方程演化结果一致，为研究这类连续监测系统中的非线性零差轨迹提供了一种高效的精确方法。
英文摘要
Simulation of nonlinear stochastic master equations generally requires trajectory-level evolution of large Hilbert-space density matrices, making strongly nonlinear continuously monitored systems computationally challenging. Here we identify an exactly solvable class centered on polynomial Hamiltonians of commuting quadratures with linear damping and homodyne measurement of those same quadratures. For initial states with a Gaussian measured-quadrature marginal and polynomial conditional-momentum sections, we derive an exact finite stochastic representation through any fixed momentum order. The result extends to interacting multimode systems, arbitrary measurement efficiency, and finite thermal occupation. Its computational cost is linear in trajectory length and independent of Hilbert-space dimension, requiring no Fock-space truncation, Gaussian approximation, or approximate moment closure. As an application, we derive an exact causal filter for monitored cubic-phase gates that uses the homodyne record to determine the variance-minimizing momentum displacement. Numerical simulations validate the representation against direct stochastic-master-equation evolution, demonstrate substantial speedups over converged Fock-space propagation, and show that this record-conditioned recentering can efficiently recover nonlinear squeezing otherwise lost through trajectory averaging.
Comments15 pages, 5 figures
