🤖 AI Summary
本文提出一种新的动态期望值估计方法，通过结合状态和可观测量的联合影响来指导近似，使用耦合损失函数算法，显著减少了估计误差。
📝 Abstract
Computing dynamical expectation values typically relies on approximations optimized for the state or observable separately, without accounting for how their errors combine in the final expression.This work explores an alternative approach in which each approximation is guided by both the state and the observable, accounting for how they jointly determine the target expectation value. This idea is implemented through a sweep algorithm with coupled loss functions for forward state and backward observable updates. Exact error relations provide an analytical rationale for how the proposed losses can improve the accuracy. Numerical tests on 30-qubit random circuits show errors two to three orders of magnitude smaller than those of variational state compression at equal bond dimensions. These results motivate further exploration of joint state and observable approximation for dynamical expectation value estimation.