LEGO_HQEC: Automating the Analysis, Construction, and Decoding of Holographic Quantum Codes
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912798679760896 |
|---|---|
| author | Fan, Junyu Steinberg, Matthew Jahn, Alexander Cao, Chunjun Sarkar, Aritra Feld, Sebastian |
| author_facet | Fan, Junyu Steinberg, Matthew Jahn, Alexander Cao, Chunjun Sarkar, Aritra Feld, Sebastian |
| contents | Quantum error correction (QEC) is a crucial prerequisite for future large-scale quantum computation. Finding and analyzing new QEC codes, along with efficient decoding and fault-tolerance protocols, is central to this effort. Holographic codes are a recent class of generalized concatenated codes derived from holographic bulk/boundary dualities. In addition to exploring the physics of such dualities, these codes possess useful QEC properties such as tunable encoding rates, distance scaling competitive with other well-studied code classes,and excellent recovery thresholds. To allow for a comprehensive analysis of holographic code constructions, we introduce LEGO_HQEC, a software package utilizing the quantum LEGO formalism. This package allows for the construction and analysis of holographic codes on regular hyperbolic tilings, computing their stabilizer generators and logical operators for a specified number of seed codes and layers. Three decoders are included: an erasure decoder based on Gaussian elimination; an integeroptimization decoder; and a tensor-network decoder. With these tools, LEGO_HQEC enables systematic studies of both previously known holographic codes and novel variants. As a demonstration, we provide new numerical results on the holographic blackhole pentagon code, establishing its threshold behavior under the erasure channel as a benchmark example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22861 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | LEGO_HQEC: Automating the Analysis, Construction, and Decoding of Holographic Quantum Codes Fan, Junyu Steinberg, Matthew Jahn, Alexander Cao, Chunjun Sarkar, Aritra Feld, Sebastian Quantum Physics Quantum error correction (QEC) is a crucial prerequisite for future large-scale quantum computation. Finding and analyzing new QEC codes, along with efficient decoding and fault-tolerance protocols, is central to this effort. Holographic codes are a recent class of generalized concatenated codes derived from holographic bulk/boundary dualities. In addition to exploring the physics of such dualities, these codes possess useful QEC properties such as tunable encoding rates, distance scaling competitive with other well-studied code classes,and excellent recovery thresholds. To allow for a comprehensive analysis of holographic code constructions, we introduce LEGO_HQEC, a software package utilizing the quantum LEGO formalism. This package allows for the construction and analysis of holographic codes on regular hyperbolic tilings, computing their stabilizer generators and logical operators for a specified number of seed codes and layers. Three decoders are included: an erasure decoder based on Gaussian elimination; an integeroptimization decoder; and a tensor-network decoder. With these tools, LEGO_HQEC enables systematic studies of both previously known holographic codes and novel variants. As a demonstration, we provide new numerical results on the holographic blackhole pentagon code, establishing its threshold behavior under the erasure channel as a benchmark example. |
| title | LEGO_HQEC: Automating the Analysis, Construction, and Decoding of Holographic Quantum Codes |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2410.22861 |