ShadowNet for Data-Centric Quantum System Learning
Yuxuan Du Yibo Yang Tongliang Liu Zhouchen Lin Bernard Ghanem Dacheng Tao
Understanding the dynamics of large quantum systems is hindered by the curse
of dimensionality. Statistical learning offers new possibilities in this regime
by neural-network protocols and classical shadows, while both methods have
limitations: the former is plagued by the predictive uncertainty and the latter
lacks the generalization ability. Here we propose a data-centric learning
paradigm combining the strength of these two approaches to facilitate diverse
quantum system learning (QSL) tasks. Particularly, our paradigm utilizes
classical shadows along with other easily obtainable information of quantum
systems to create the training dataset, which is then learnt by neural networks
to unveil the underlying mapping rule of the explored QSL problem. Capitalizing
on the generalization power of neural networks, this paradigm can be trained
offline and excel at predicting previously unseen systems at the inference
stage, even with few state copies. Besides, it inherits the characteristic of
classical shadows, enabling memory-efficient storage and faithful prediction.
These features underscore the immense potential of the proposed data-centric
approach in discovering novel and large-scale quantum systems. For
concreteness, we present the instantiation of our paradigm in quantum state
tomography and direct fidelity estimation tasks and conduct numerical analysis
up to 60 qubits. Our work showcases the profound prospects of data-centric
artificial intelligence to advance QSL in a faithful and generalizable manner.