Neural-Shadow Quantum State Tomography

TL;DR

Neural-shadow quantum state tomography (NSQST) introduces a neural network method utilizing classical shadows and infidelity loss for efficient, noise-robust quantum state reconstruction applicable to a broad class of states.

Contribution

NSQST proposes a novel neural network-based quantum state tomography approach using infidelity and classical shadows, overcoming limitations of basis-dependent methods and broadening applicability.

Findings

NSQST outperforms traditional NNQST in learning phases of quantum states.

NSQST demonstrates robustness against noise without error mitigation.

NSQST surpasses direct shadow estimation in efficiency.

Abstract

Quantum state tomography (QST) is the art of reconstructing an unknown quantum state through measurements. It is a key primitive for developing quantum technologies. Neural network quantum state tomography (NNQST), which aims to reconstruct the quantum state via a neural network ansatz, is often implemented via a basis-dependent cross-entropy loss function. State-of-the-art implementations of NNQST are often restricted to characterizing a particular subclass of states, to avoid an exponential growth in the number of required measurement settings. To provide a more broadly applicable method for efficient state reconstruction, we present "neural-shadow quantum state tomography" (NSQST)-an alternative neural network-based QST protocol that uses infidelity as the loss function. The infidelity is estimated using the classical shadows of the target state. Infidelity is a natural choice for training loss, benefiting from the proven measurement sample efficiency of the classical shadow formalism. Furthermore, NSQST is robust against various types of noise without any error mitigation. We numerically demonstrate the advantage of NSQST over NNQST at learning the relative phases of three target quantum states of practical interest, as well as the advantage over direct shadow estimation. NSQST greatly extends the practical reach of NNQST and provides a novel route to effective quantum state tomography.