Learning the tensor network model of a quantum state using a few single-qubit measurements

TL;DR

This paper introduces a scalable, efficient method to learn tensor network models of quantum states using minimal single-qubit measurements, addressing the exponential complexity of traditional quantum tomography.

Contribution

The authors develop a constructive, numerically efficient protocol that applies PAC learning theory to model quantum states with limited measurements, improving scalability over existing methods.

Findings

The method successfully learns tensor network models from few measurements.

It demonstrates scalability to larger quantum systems.

The approach offers a practical alternative to full quantum tomography.

Abstract

The constantly increasing dimensionality of artificial quantum systems demands for highly efficient methods for their characterization and benchmarking. Conventional quantum tomography fails for larger systems due to the exponential growth of the required number of measurements. The conceptual solution for this dimensionality curse relies on a simple idea - a complete description of a quantum state is excessive and can be discarded in favor of experimentally accessible information about the system. The probably approximately correct (PAC) learning theory has been recently successfully applied to a problem of building accurate predictors for the measurement outcomes using a dataset which scales only linearly with the number of qubits. Here we present a constructive and numerically efficient protocol which learns a tensor network model of an unknown quantum system. We discuss the limitations and the scalability of the proposed method.