用几何约束的神经网络实现更稳定的量子反馈控制。
Continuous Quantum Feedback Control via Kraus-Parameterized Belief Reinforcement Learning
- 用斯特费尔流形约束的循环编码器生成合法量子态估计。
- 控制信念保真度达0.77-0.80，方差比基线低得多。
- 适合需要物理可解释性的量子控制研究者。
量子反馈控制需在无法直接观测量子态的情况下，基于噪声的连续测量信号进行决策。本文提出基于克劳斯参数化的信念强化学习方法：利用受限于斯特费尔流形的循环编码器生成保证半正定且迹归一的密度矩阵估计，将量子态几何结构直接嵌入学习过程；再通过近端策略优化（PPO）策略将这些物理有效的信念状态映射为连续控制动作。在模拟持续监测的量子比特上，该策略实现了稳定反馈控制，测量条件下的信念保真度维持在0.77至0.80之间，并在正常与分布外条件下均显著降低回报方差，优于参数匹配的LSTM历史基线。尽管目标保真度提升有限，但几何约束确保了物理可解释的信念表示，在测量效率低下和动态突变情况下表现出明显更优的稳定性。结果表明，物理信息引导的神经记忆是实现可靠量子反馈控制的有效归纳偏置。
原文摘要 · Abstract (English)
Quantum feedback control requires acting on noisy continuous measurement records without direct access to the underlying quantum state. We propose Kraus-Parameterized Belief Reinforcement Learning, a pipeline in which a recurrent encoder, constrained to the Stiefel manifold, produces density-matrix estimates that are guaranteed positive-semidefinite and trace-normalized by construction, embedding quantum state geometry directly into the learning loop. A Proximal Policy Optimization (PPO) actor then maps these physically valid belief states to continuous control actions. On a simulated continuously monitored qubit, the resulting policy achieves stable feedback control, maintaining a measurement-conditioned belief fidelity of approximately 0.77-0.80 and exhibiting substantially lower return variance than a parameter-matched LSTM-history baseline across both nominal and out-of-distribution conditions. Although gains in raw target fidelity are modest, the geometric constraint guarantees a physically valid, interpretable belief representation and yields markedly more stable control under measurement inefficiency and abrupt dynamics switches. These results indicate that physics-informed neural memory is a practical inductive bias for reliable quantum feedback control.
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