Quantum state reconstruction in a noisy environment via deep learning

Abstract Quantum noise is currently limiting efficient quantum information processing and computation, impacting on the fidelity and reliability of quantum states. In this work, we consider the tasks of reconstructing and classifying quantum states corrupted by the action of an unknown noisy channel using classical feed-forward neural networks. By framing reconstruction as a regression problem, we show how such an approach can be used to recover with fidelities exceeding 99% the noiseless density matrices of quantum states of up to three qubits undergoing noisy evolution, and we test its performance with both single-qubit (bit-flip, phase-flip, depolarizing, and amplitude damping) and two-qubit quantum channels (correlated amplitude damping). Furthermore, a critical aspect of our investigation involves also a comprehensive comparison between mean squared error and infidelity as loss functions. Our findings reveal that these two metrics yield comparable results in the context of state reconstruction. Moreover, we also consider the task of distinguishing between different quantum noisy channels, and show how a neural network-based classifier is able to solve such a classification problem with perfect accuracy.