We introduce coherent-state propagation, a computational framework for simulating bosonic systems. We focus on bosonic circuits composed of displaced linear optics augmented by Kerr nonlinearities, a universal model of bosonic quantum computation that is also physically motivated by driven Bose-Hubbard dynamics. The method works in the Schrödinger picture representing the evolving state as a sparse superposition of coherent states. We develop approximation strategies that keep the simulation cost tractable in physically relevant regimes, notably when the number of Kerr gates is small or the Kerr nonlinearities are weak, and prove rigorous guarantees for both observable estimation and sampling. In particular, bosonic circuits with logarithmically many Kerr gates admit quasi-polynomial-time classical simulation at exponentially small error in trace distance. We further identify a weak-nonlinearity regime in which the runtime is polynomial for arbitrarily small constant precision. We complement these results with numerical benchmarks on the Bose-Hubbard model with all-to-all connectivity. The method reproduces Fock-basis and matrix-product-state reference data, suggesting that it offers a useful route to the classical simulation of bosonic systems.

翻译：我们提出相干态传播，一种用于模拟玻色子系统的计算框架。重点关注由位移线性光学与克尔非线性增强构成的玻色子电路——后者是玻色子量子计算的通用模型，同时其物理动机源于受驱动玻色-哈伯德动力学。该方法在薛定谔绘景中运行，将演化态表示为相干态的稀疏叠加。我们发展了近似策略，使得在物理相关区域（尤其是当克尔门数量较少或克尔非线性较弱时）的模拟成本可控，并给出了可观测量估计和采样的严格保证。特别地，包含对数数量级克尔门的玻色子电路，能够在迹距离指数级小误差下实现准多项式时间的经典模拟。我们进一步识别出一个弱非线性区域，在该区域中，对于任意小的常数精度，运行时均为多项式级。我们通过全连通玻色-哈伯德模型的数值基准测试补充了这些结果。该方法可复现福克基和矩阵乘积态的参考数据，表明其为玻色子系统经典模拟提供了一条有效途径。