ShadowNet for Data-Centric Quantum System Learning

TL;DR

This paper introduces ShadowNet, a data-centric quantum system learning framework combining classical shadows and neural networks to efficiently predict and analyze large quantum systems with limited data.

Contribution

It proposes a novel paradigm that leverages classical shadows and neural networks for scalable, generalizable quantum system learning, demonstrated on state tomography and fidelity estimation.

Findings

Effective prediction of unseen quantum systems with few state copies

Numerical analysis conducted on systems up to 60 qubits

Memory-efficient storage and faithful prediction enabled

Abstract

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.