A graph-based approach to entanglement entropy of quantum error correcting codes
arXiv:2501.06407 · doi:10.1103/jc6b-txy9
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.
20 pages, 7 figures
References in corpus (11)
- Black holes as mirrors: quantum information in random subsystems
- High-threshold and low-overhead fault-tolerant quantum memory
- Bipartite entanglement and entropic boundary law in lattice spin systems
- Ground state entanglement and geometric entropy in the Kitaev's model
- Symmetry restoration and quantum Mpemba effect in symmetric random circuits
- On the logical operators of quantum codes
- An entanglement asymmetry study of black hole radiation
- Entanglement properties of topological color codes
- Constructions and performance of hyperbolic and semi-hyperbolic Floquet codes
- Minimal instances for toric code ground states
- How much entanglement is needed for quantum error correction?