arXiv subjects

Krishna Bhatia

Publications and source records attributed to Krishna Bhatia.

10 recordsLinked to original sources

arXiv2026

Partial-Moment PINNs for Caldeira--Leggett Parameter Learning in Quantum Brownian Motion

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.

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arXiv2026

Quantum Reservoir Computing with Physics-Informed Correction for Reduced-Order PDE Forecasting

We study a hybrid proposal--correction architecture for reduced-order PDE forecasting in which a pure-state quantum reservoir computer (QRC) predicts latent coefficient dynamics and a PINN-based physics-informed corrector (PIC) refines local rollout windows. The method is evaluated on Burgers and Kuramoto--Sivashinsky (KS), with KS as the primary chaotic benchmark. On KS, QRC+PIC consistently improves over QRC alone in RMSE, NRMSE, and PDE residual, while Burgers highlights a regime in which simple baselines remain strong. These results suggest that QRC proposals with local physics-informed correction are a viable benchmark-dependent reduced-order forecasting strategy.

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arXiv2026

Physics-Guided Linear Mapper for Quantum Error Mitigation

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.

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arXiv2026

Quantum-Logic Tsetlin Machines: Interpretable Quantum Machine Learning with Commuting Projector Clauses

Tsetlin Machines (TMs) learn interpretable Boolean clauses using finite-state automata. We introduce the Quantum-Logic Tsetlin Machine (QL-TM), which replaces Boolean literals with quantum propositions represented by projectors while retaining classical include/exclude automata. Clauses are restricted to commuting measurement contexts and activate through the Born probability of their joint projector. We prove an exact reduction to ordinary Boolean TM clauses in diagonal computational-basis contexts and connect Pauli-projector clauses to stabilizer and syndrome semantics. Controlled experiments on Bell states, phase-flip syndromes, randomized 16-class stabilizer tasks, mixed literal pools, context-budget ablations, and finite-shot noise show that correct non-diagonal contexts recover physically meaningful clauses, while diagonal or wrong contexts lose the relevant phase/syndrome information. The context-budget results closely follow the predicted separability ladder 2^(b-k) as true stabilizer generators are removed. The contribution is a controlled bridge between Tsetlin clause learning and quantum logic, not a claim of quantum advantage.

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arXiv2026

Continuous Quantum Feedback Control via Kraus-Parameterized Belief Reinforcement Learning

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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arXiv2026

Hybrid LLM-Guided Search for Quantum Reservoir Architecture Design

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.

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arXiv2026

Kraus Constrained Sequence Learning For Quantum Trajectories from Continuous Measurement

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.

cs.LG↗

arXiv2025

Sustained Performance and Energy Accounting for Nonlinear Forecasting Across Classical and Simulated Quantum Models

Energy-efficient AI should be evaluated across the full application pipeline, not only by lowest error or shortest training time. We study this through nonlinear time-series forecasting using simulated quantum reservoir computing (QRC) as an emerging-computing case study. Our evaluation spans 33 forecasting configurations and 825 completed runs on NARMA-10, NARMA-20, Mackey--Glass, Lorenz-63, and Santa Fe laser data. The core benchmark includes 775 fully instrumented runs across statistical, linear, reservoir, neural, continuous-variable Gaussian QRC, and gate-based statevector QRC models, with 50 additional variational QNN runs extending the trainable-quantum comparison. We measure NRMSE, RMSE, MAE, wall time, inference latency, peak CPU/GPU memory, parameter count, operational energy, and carbon. Since a fixed QRC encoder can generate reusable features for multiple readouts, we report both cold-start and amortized costs. We also use a Sustainable Forecasting Score (SFS), a diagnostic geometric mean of normalized predictive skill and log-scaled carbon efficiency, while retaining raw measurements and Pareto analyses. The best mean NRMSE is achieved by continuous-variable QRC with a Transformer readout (0.332), followed closely by classical TCN (0.341) and QRC+TCN (0.340). However, ESN and ridge-lag deliver the strongest sustained efficiency, with average amortized carbon of 0.014 and 0.012 gCO2 per run and SFS values of 0.814 and 0.805. Larger QRC feature maps increase cost without improving average accuracy, while gate-based statevector simulation is not competitive. These results support three practices for emerging AI systems: expose stage-level energy, use reuse-aware accounting boundaries, and co-design the feature generator or accelerator with the classical readout.

quant-ph↗

arXiv2025

Domain-Aware Probability Sampling for Hybrid Quantum Systems using Bayesian Optimization

We study the problem of probability distribution matching and sampling on near-term quantum computers, aiming to construct parameterized circuits that generate samples from a target distribution while minimizing resource overhead. This task arises naturally in hybrid quantum-classical workflows, where measurement-driven objectives replace full state reconstruction, and is central to applications in generative modeling and variational inference. However, it remains challenging due to hardware noise, limited circuit depth, and a high-dimensional, non-convex parameter space. We propose CircuitTree, a surrogate-guided optimization framework based on Bayesian Optimization with tree-based models for scalable, domain-aware distribution matching. Our approach introduces a structured, layerwise decomposition aligned with the variational circuit architecture, enabling distributed and sample-efficient optimization within hybrid loops with theoretical convergence guarantees. Across representative distribution-matching tasks, CircuitTree achieves up to 2-3x lower total variation distance while using 40-60% fewer gates than prior approaches. These results demonstrate its effectiveness as a practical building block for end-to-end hybrid quantum sampling.

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arXiv2022

Hybrid Quantum Generative Adversarial Networks for Molecular Simulation and Drug Discovery

In molecular research, the modelling and analysis of molecules through simulation is an important part that has a direct influence on medical development, material science and drug discovery. The processing power required to design protein chains with hundreds of peptides is huge. Classical computing techniques, including state-of-the-art machine learning models being deployed on classical computing machines, have proven to be inefficient in this task, though they have been successful in a limited way. Moreover, current practical implementations, as opposed to purely theoretical modelling, are often infeasible in terms of both time and cost. One of the major areas where quantum machine learning is expected to have a profound advantage over classical algorithms is drug discovery. Quantum generative models have given some promising benefits in recent studies. This paper introduces three novel quantum generative adversarial network (QGAN) architecture variants resulting from different configurations, various quantum circuit layers and patched ansatz. A quantum simulator from Xanadu's PennyLane was utilized for executing the QGAN models trained on the QM9 dataset. Upon evaluation, one of the models, namely the QWGAN-HG-GP (Wasserstein distance with gradient penalty) model, outperformed the other QGAN models in different drug molecule property metrics.

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