Computing Quantum Resources using Tensor Cross Interpolation

TL;DR

This paper introduces a versatile tensor cross interpolation method for efficiently computing various quantum information quantifiers in complex systems, demonstrated on Ising models.

Contribution

It presents a general tensor cross interpolation framework that is system- and quantifier-independent for quantum resource computation.

Findings

Successfully computed non-stabilizerness Rényi entropy and Relative Entropy of Coherence.

Demonstrated the method's versatility on 1D and 2D Ising models.

Provides a generic approach for exploring quantum information measures.

Abstract

Quantum information quantifiers are indispensable tools for analyzing strongly correlated systems. Consequently, developing efficient and robust numerical methods for their computation is crucial. We propose a general procedure based on the family of Tensor Cross Interpolation (TCI) algorithms to address this challenge in a fully general framework, independent of the system or the quantifier under consideration. To substantiate our approach, we compute the non-stabilizerness R\'{e}nyi entropy (SRE) and Relative Entropy of Coherence (REC) considering the 1D and 2D ferromagnetic Ising models with minimal modifications to the numerical procedure. This method not only demonstrates its versatility, but also provides a generic framework for exploring other quantum information quantifiers in complex systems.