Kraus Constrained Sequence Learning For Quantum Trajectories from Continuous Measurement
This work provides a method for quantum engineers and physicists to achieve more robust and physically consistent real-time quantum state estimation, which is essential for quantum feedback control, especially in scenarios with parameter drift.
This paper addresses the challenge of real-time reconstruction of conditional quantum states from continuous measurement records, which is crucial for quantum feedback control but often hindered by the sensitivity of standard solvers to model and parameter inaccuracies. The authors propose a Kraus-structured output layer that ensures physically valid state updates by converting the hidden representation of a sequence model into a completely positive trace preserving (CPTP) quantum operation. Their Kraus-LSTM model improves state estimation quality by 7% over its unconstrained version while maintaining physical validity in non-stationary conditions.
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.