Kraus Constrained Sequence Learning For Quantum Trajectories from Continuous Measurement

Priyanshi Singh, Krishna Bhatia

Keywords: Physics-Informed Machine Learning, Quantum State Estimation, Inductive Bias, Gated Recurrence, State-Space Models, Stochastic Differential Equations, Stiefel Manifold

Abstract:

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.

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Journal Notes: We will extend the workshop paper into a more rigorous study of physically constrained neural quantum filtering by isolating the contribution of the Kraus/CPTP layer from the contribution of recursive state initialization. The journal version will add matched recursive baselines with access to ρ0, soft-constraint baselines, controlled hardware/runtime comparisons, latency and memory benchmarking against adaptive SME solvers, and robustness experiments under more realistic settings such as imperfect efficiency and non-Markovian/drifting dynamics. A smaller scaling study beyond the current single-qubit setting will also be included if feasible. The main constraints are QR/Kraus memory cost, fairness of matched training setups, and the practical difficulty of extending to higher-dimensional systems within current compute limits.

Submission Number: 113