We study parameter recovery in the Caldeira--Leggett (quantum Brownian) oscillator from partial moment traces. Our model is a moment-level PINN that predicts the five first/second moments and enforces the linear CL/HPZ ODEs by automatic differentiation. Physical structure is imposed through a PSD (Cholesky) covariance head, high-temperature CL assumptions with $D_{xp}\approx0$, and fluctuation--dissipation ties between $D_{pp}$ and $\gamma$. On synthetic CL data with channels ${\mu_x,\sigma_{xx},\sigma_{xp}}$, the constrained variant recovers $(\omega,\gamma)$ accurately, stabilizes $D_{pp}$, and achieves low rollout error compared to finite differences and Kalman--EM (expectation--maximization) with exact Van Loan discretization. Fisher-style checks confirm that diffusion needs at least one variance observable, and sparse $\sigma_{pp}$ ``anchors''restore conditioning. We also show that the same PINN can learn time-varying HPZ coefficients.
Quantum reservoir computing (QRC) uses fixed quantum dynamics as a high-dimensional temporal feature map and trains only a lightweight classical readout. QRC is attractive for near-term quantum machine learning, but its performance depends strongly on architecture choices such as input encoding, reservoir depth, entanglement topology, measurement features, state-reset policy, feature construction, and readout regularization. We introduce \method, a simulator-based benchmark that formulates QRC design as constrained black-box architecture search and evaluates whether large language models can act as proposal controllers for this search problem. The benchmark compares five policies under identical evaluation budgets: random search, evolutionary search, Bayesian/TPE optimization, a feedback-based LLM agent, and \hybrid, which combines LLM proposals with memory, mutation, crossover, duplicate avoidance, and exploration. On NARMA10, Mackey-Glass forecasting, and temporal parity, \hybrid{} is the most consistent policy: it ranks first on NARMA10 and temporal parity and second on Mackey-Glass, narrowly behind evolutionary search. Under a 25-evaluation budget and three seeds, \hybrid{} improves over random search on all tasks, including a 23.6\% relative reduction in Mackey-Glass error. The results do not show that LLMs are universal QRC optimizers; rather, they show that generative models can be useful high-level controllers when embedded inside validated, reproducible hybrid search loops.
We introduce a novel physics-guided linear mapper (PGLM) for quantum error mitigation that uses seven distinct interpretable features derived from circuit complexity and device calibration data. The goal is to provide a data-efficient, interpretable, and low-latency alternative to the black-box machine learning for quantum error mitigation in noisy-intermediate scale quantum devices. Evaluated on 52 simulated benchmark circuits (1--4 qubits), PGLM demonstrates strong performance in noise-accumulation regimes: 50.1% RMSE reduction on 3-qubit circuits and 32.3% on 4-qubit circuits, while single-qubit circuits show degraded performance. A circuit-size-aware deployment policy achieves 32.6% aggregate improvement. Sub-millisecond inference enables integration into variational algorithms, and analysis of learned coefficients reveals that circuit depth and CNOT count dominate error prediction, consistent with decoherence mechanisms. Results are simulator-based with idealized noise models; hardware validation remains essential future work.
Tulsi Chaudhari, Krish Bhatia, Shalini Devendrababu et al.· 0 citations
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