arXiv:2606.19947quant-phcs.LG2026-06

用数学定理设计新正则化,让量子控制更抗环境噪声干扰。

QMaxCal: Path-Space Regularization for Open Quantum Control via Girsanov's Theorem

论文配图:QMaxCal: Path-Space Regularization for Open Quantum Control via Girsanov's Theorem
图 1 · 摘自论文原文
  • 基于吉尔萨诺夫定理,构建可微的轨迹分布差异估计器。
  • 在多量子比特系统上使最终态保真度提升最高50%,噪声不匹配时增益达27个百分点。
  • 适合需要高鲁棒性的量子控制任务,如真实硬件上的量子算法部署。

在退相干存在的情况下实现可靠的量子控制,需设计能对抗环境噪声影响的控制策略。受连续监测的开放量子系统会产生依赖于系统所经历噪声的古典测量记录;两条共享相同退相干通道的演化路径仅在漂移项上不同,据此可通过吉尔萨诺夫定理得到其轨迹分布之间KL散度的闭式、可微估计。我们以两种物理上合理的参考测度实例化该估计,得到两个正则化项:维纳KL(KL_W),在特定噪声模型下表现更优;以及漂移-方差正则化项(R_DV),适用于所有噪声模型。二者均与现有对控制幅度或平滑性的惩罚机制不同:它们惩罚的是控制对退相干通道的可观测影响,而非控制本身。在多种开放量子系统中,包括单/多量子比特基准测试及基于公开数据校准的IBM Kingston处理器多量子比特链,该正则化方法显著优于无正则化的梯度法和强化学习基线,在最终态保真度、对噪声模型失配的鲁棒性(训练噪声下增益+17个百分点,2.5倍噪声失配时达+27个百分点)以及禁止态占据率等方面均有提升。正则化使非保真度降低最多50%,在校准的IBM Kingston链上获得约16%的改进。

原文摘要 · Abstract (English)

Reliable quantum control in the presence of decoherence requires policies that combat the effect of environmental noise on the controlled dynamics. Open quantum systems under continuous monitoring generate classical measurement records whose drift depends on the noise experienced by the system; the records of two evolutions sharing the same decoherence channels differ only in this drift, so Girsanov's theorem yields a closed-form, differentiable estimator of the KL divergence between their trajectory distributions. We instantiate this estimator with two physically motivated reference measures, yielding two regularizers that both drive the system toward states where the effects of decoherence are minimal: the Wiener KL (KL_W), which is empirically more effective under certain conditions on the noise model, and the drift-variance regularizer (R_DV), which works for all noise models. Both are qualitatively distinct from existing penalties on control fluence or smoothness: they penalize the observable consequences of control on the decoherence channels rather than the control amplitude itself. The regularizers outperform unregularized gradient-based and reinforcement-learning baselines across a range of open quantum systems -- including single- and multi-qubit benchmarks and a multi-qubit chain calibrated to a published snapshot of the IBM Kingston processor -- along several axes of evaluation: final-state fidelity, robustness to mismatch in the assumed noise model (gains grow from +17 pp at training noise to +27 pp under 2.5x noise mismatch), and occupation of forbidden states. The regularizers reduce infidelity by up to 50%, with ~16% gains on the calibrated IBM Kingston chain.

量子控制退相干抑制正则化扩散模型

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