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

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, $(KL_{\mathrm{W}})$ which is empirically more effective under certain conditions on the noise model, and the drift-variance regularizer $(R_{\mathrm{DV}})$, 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 $2.5\times$ noise mismatch), and occupation of forbidden states. The regularizers reduce infidelity by up to 50\%, with $\sim$16\% gains on the calibrated IBM Kingston chain.