用物理约束的神经网络提升量子态实时重建精度
Kraus Constrained Sequence Learning For Quantum Trajectories from Continuous Measurement
- 在序列模型输出层引入克劳斯算符结构，保证量子态更新符合物理规律
- 在参数漂移场景下，Kraus-LSTM使状态估计准确率提升7%，且预测始终物理合法
- 适用于需要高可靠性量子控制的实验系统，如量子计算与传感
从连续测量记录中实时重构条件量子态是量子反馈控制的基本需求，但标准随机主方程求解器需精确已知系统参数，对参数失配敏感。尽管神经序列模型可拟合此类随机动力学，但无约束预测可能违反物理性（如正定性、迹为1），导致推演不稳定和非物理解。本文提出克劳斯结构输出层，将通用序列骨干的隐状态转换为完全正定保迹（CPTP）量子操作，从而保证状态更新的物理合法性。我们在RNN、GRU、LSTM、TCN、ESN和Mamba等多种骨干网络上实现该结构，以神经微分方程作为对比基准，评估其在参数漂移的随机轨迹上的表现。结果揭示门控机制、线性递归与全局注意力间的权衡。所有模型中，Kraus-LSTM表现最优，在非平稳环境下相较无约束版本提升状态估计质量7%，且始终保证物理合法性。
原文摘要 · Abstract (English)
Real-time reconstruction of conditional quantum states from continuous measurement records is a fundamental requirement for quantum feedback control, yet standard stochastic master equation (SME) solvers require exact model specification, known system parameters, and are sensitive to parameter mismatch. While neural sequence models can fit these stochastic dynamics, the unconstrained predictors can violate physicality such as positivity or trace constraints, leading to unstable rollouts and unphysical estimates. We propose a Kraus-structured output layer that converts the hidden representation of a generic sequence backbone into a completely positive trace preserving (CPTP) quantum operation, yielding physically valid state updates by construction. We instantiate this layer across diverse backbones, RNN, GRU, LSTM, TCN, ESN and Mamba; including Neural ODE as a comparative baseline, on stochastic trajectories characterized by parameter drift. Our evaluation reveals distinct trade-offs between gating mechanisms, linear recurrence, and global attention. Across all models, Kraus-LSTM achieves the strongest results, improving state estimation quality by 7% over its unconstrained counterpart while guaranteeing physically valid predictions in non-stationary regimes.
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