A graph-based approach to entanglement entropy of quantum error correcting codes

TL;DR

This paper introduces a graph-based method to analyze the entanglement entropy in quantum error correcting codes, providing new insights and computational tools for quantum information science.

Contribution

It presents a novel graph-theoretical approach to interpret and compute entanglement entropy in quantum codes, including toric and LDPC codes.

Findings

Calculated von Neumann entropy for toric and LDPC codes.

Revealed the scaling behavior of entanglement entropy with subsystem size.

Provided a new perspective on entanglement in quantum many-body systems.

Abstract

We develop a graph-based method to study the entanglement entropy of Calderbank-Shor-Steane quantum codes. This method offers a straightforward interpretation for the entanglement entropy of quantum error correcting codes through graph-theoretical concepts, shedding light on the origins of both the local and long-range entanglement. Furthermore, it inspires an efficient computational scheme for evaluating the entanglement entropy. We illustrate the method by calculating the von Neumann entropy of subsystems in toric codes and two types of quantum low-density-parity check codes, and by comparing the scaling behavior of the entanglement entropy with respect to the subsystem size. Our method provides a new perspective for understanding the entanglement structure in quantum many-body systems.