Kraus Constrained Sequence Learning For Quantum Trajectories from Continuous Measurement

TL;DR

This paper introduces a Kraus-structured neural network layer that ensures physically valid quantum state updates during continuous measurement trajectory reconstruction, improving accuracy and stability over traditional methods.

Contribution

It proposes a novel Kraus-structured output layer for neural sequence models that guarantees completely positive trace preserving quantum operations, enhancing quantum state estimation.

Findings

Kraus-LSTM outperforms unconstrained models with 7% better state estimation.

The method guarantees physically valid predictions in non-stationary regimes.

Different neural architectures exhibit trade-offs in modeling quantum trajectories.

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.