Entanglement-Assisted Quantum Quasi-Cyclic LDPC Codes with Transversal Logical Operators
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908623561555968 |
|---|---|
| author | Kumar, Pavan Sharma, Abhi Kumar Garani, Shayan Srinivasa |
| author_facet | Kumar, Pavan Sharma, Abhi Kumar Garani, Shayan Srinivasa |
| contents | We derive two families of EA-QC quantum LDPC (EA-QC-QLDPC) codes by tiling permutation matrices of prime and composite orders. The unassisted portion of the Tanner graphs corresponding to these codes, constructed from two distinct classical QC-LDPC codes, exhibits girth greater then 4 an essential property for effective error correction. We analytically derive the exact code rate of the proposed constructions. Remarkably, one of these families requires only a single Bell pair to be shared between the quantum transmitter and receiver. Furthermore, two additional families of EA-QC-QLDPC codes are constructed based on a single classical code, whose Tanner graphs exhibit girths exceeding six, thereby further enhancing the error-correction capability. For one of these families, we explicitly determine the transversal logical operators an aspect that is typically non-trivial for random quasi-cyclic codes. The performance of the proposed codes is assessed under both random and burst error models under the depolarizing and Markovian noise actions. Employing a modified sum-product decoding algorithm over a quaternary alphabet, we demonstrate that correlated Pauli errors can be effectively addressed within the decoding framework. Simulation results reveal nearly an order of improvement in error-correction performance with the quaternary decoder compared to the binary decoder over both depolarizing and Markovian channels. Further, the proposed codes are compared with existing ones, demonstrating significant improvement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07363 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Entanglement-Assisted Quantum Quasi-Cyclic LDPC Codes with Transversal Logical Operators Kumar, Pavan Sharma, Abhi Kumar Garani, Shayan Srinivasa Information Theory We derive two families of EA-QC quantum LDPC (EA-QC-QLDPC) codes by tiling permutation matrices of prime and composite orders. The unassisted portion of the Tanner graphs corresponding to these codes, constructed from two distinct classical QC-LDPC codes, exhibits girth greater then 4 an essential property for effective error correction. We analytically derive the exact code rate of the proposed constructions. Remarkably, one of these families requires only a single Bell pair to be shared between the quantum transmitter and receiver. Furthermore, two additional families of EA-QC-QLDPC codes are constructed based on a single classical code, whose Tanner graphs exhibit girths exceeding six, thereby further enhancing the error-correction capability. For one of these families, we explicitly determine the transversal logical operators an aspect that is typically non-trivial for random quasi-cyclic codes. The performance of the proposed codes is assessed under both random and burst error models under the depolarizing and Markovian noise actions. Employing a modified sum-product decoding algorithm over a quaternary alphabet, we demonstrate that correlated Pauli errors can be effectively addressed within the decoding framework. Simulation results reveal nearly an order of improvement in error-correction performance with the quaternary decoder compared to the binary decoder over both depolarizing and Markovian channels. Further, the proposed codes are compared with existing ones, demonstrating significant improvement. |
| title | Entanglement-Assisted Quantum Quasi-Cyclic LDPC Codes with Transversal Logical Operators |
| topic | Information Theory |
| url | https://arxiv.org/abs/2501.07363 |