ShadowNet for Data-Centric Quantum System Learning

Understanding the dynamics of large quantum systems is hindered by the curse of dimensionality. Statistical learning offers new possibilities in this regime through neural network protocols and classical shadows, while both methods have limitations: the former suffers from incompatible dataset construction rules, resulting in substantial computational demands for data collection when addressing different tasks; the latter lacks the ability to distill knowledge from prior data to enhance subsequent learning endeavors. In this study, we propose a data-centric learning paradigm combining the strengths of these two approaches to advance quantum system learning (QSL). Central to our paradigm lies a unified dataset construction rule, achieved by classical shadows along with other easily obtainable information of quantum systems. To illustrate our approach, we present ShadowNet, implemented under both convolutional and attention mechanisms, to efficiently and faithfully tackle two pivotal QSL tasks: quantum state tomography (QST) and direct fidelity estimation (DFE). Numerical simulations on QST and DFE up to 60 qubits validate the efficacy of our proposal, showcasing how ShadowNet advances classical shadows with limited state copies, and highlighting how the varied neural networks impact the performance. Our work underscores the immense potential of a data-centric approach in comprehending novel and large quantum systems.