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

• URL: http://arxiv.org/abs/2501.06407v2
• Date: Fri, 21 Feb 2025 13:05:40 GMT
• Title: A graph-based approach to entanglement entropy of quantum error correcting codes
• Abstract summary: We develop a graph-based method to study the entanglement entropy of Calderbank-Shor-Steane quantum codes.<n>We illustrate the method by calculating the von Neumann entropy of subsystems in toric codes and a special type of quantum low-density-parity check codes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 a special type of quantum low-density-parity check codes, known as bivariate bicycle codes, and by comparing the scaling behavior of entanglement entropy with respect to subsystem size. Our method provides a new perspective for understanding the entanglement structure in quantum many-body systems.

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