Kraus Constrained Sequence Learning For Quantum Trajectories from Continuous Measurement
2026-03-05 • Machine Learning
Machine Learning
AI summaryⓘ
The authors address the challenge of accurately tracking quantum states in real-time, even when the system parameters can change and are not perfectly known. They introduce a special output layer based on Kraus operators that ensures the predicted quantum states are always physically valid. This new approach was tested with various neural network models and showed better and more stable predictions than traditional methods, particularly with a Kraus-structured LSTM model. Their work helps improve quantum state estimation while respecting fundamental quantum rules.
quantum statesstochastic master equationKraus operatorsneural networksLSTMquantum feedback controlcontinuous measurementcompletely positive trace preserving (CPTP)parameter drift
Authors
Priyanshi Singh, Krishna Bhatia
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.