Variational method for learning Quantum Channels via Stinespring Dilation on neutral atom systems

Abstract: Real-world quantum systems interact with their environments, leading to the irreversible dynamics described by the Lindblad equation. Solutions to the Lindblad equation give rise to quantum channels $\Phi_t$ that characterize the evolution of density matrices as $\rho(t) = \Phi_t(\rho_0)$. In many quantum experiments, the observation windows are limited by experimental instability or technological constraints. Nevertheless, extending the evolution of the state beyond this window may be valuable for identifying sources of decoherence and dephasing or determining the steady state of the evolution. In this work, we propose a method to approximate an arbitrary target quantum channel by variationally constructing equivalent unitary operations on an extended system, leveraging the Stinespring dilation theorem. We also present an experimentally feasible approach to extrapolate the quantum channel in discrete time steps beyond the period covered by the training data. Our approach takes advantage of the unique capability of neutral-atom quantum computers to spatially transport entangled qubits, an essential feature for implementing our method. The approach demonstrates significant predictive power for approximating non-trivial quantum channels.