Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.19151 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909502648877056 |
|---|---|
| author | Voss, Lukas Xian, Sim Jian Haug, Tobias Bharti, Kishor |
| author_facet | Voss, Lukas Xian, Sim Jian Haug, Tobias Bharti, Kishor |
| contents | Quantum error correction suppresses noise in quantum systems to allow for high-precision computations. In this work, we introduce Multivariate Bicycle (MB) Quantum Low-Density Parity-Check (QLDPC) codes, via an extension of the framework developed by Bravyi et al. [Nature, 627, 778-782 (2024)] and particularly focus on Trivariate Bicycle (TB) codes. Unlike the weight-6 codes proposed in their study, we offer concrete examples of weight-5 TB-QLDPC codes which promise to be more amenable to near-term experimental setups. We show that TB-QLDPC codes up to weight-6 have a bi-planar structure and often posses a two-dimensional toric layout. Under circuit level noise, we find substantially better encoding rates than comparable surface codes while offering similar error suppression capabilities. For example, we can encode $4$ logical qubits with distance $5$ into $60$ physical qubits using weight-5 check measurements of circuit depth 7, while a surface code with these parameters requires $200$ physical qubits. The high encoding rate and compact layout make our codes highly suitable candidates for near-term hardware implementations, paving the way for a realizable quantum error correction protocol. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19151 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multivariate Bicycle Codes Voss, Lukas Xian, Sim Jian Haug, Tobias Bharti, Kishor Quantum Physics Quantum error correction suppresses noise in quantum systems to allow for high-precision computations. In this work, we introduce Multivariate Bicycle (MB) Quantum Low-Density Parity-Check (QLDPC) codes, via an extension of the framework developed by Bravyi et al. [Nature, 627, 778-782 (2024)] and particularly focus on Trivariate Bicycle (TB) codes. Unlike the weight-6 codes proposed in their study, we offer concrete examples of weight-5 TB-QLDPC codes which promise to be more amenable to near-term experimental setups. We show that TB-QLDPC codes up to weight-6 have a bi-planar structure and often posses a two-dimensional toric layout. Under circuit level noise, we find substantially better encoding rates than comparable surface codes while offering similar error suppression capabilities. For example, we can encode $4$ logical qubits with distance $5$ into $60$ physical qubits using weight-5 check measurements of circuit depth 7, while a surface code with these parameters requires $200$ physical qubits. The high encoding rate and compact layout make our codes highly suitable candidates for near-term hardware implementations, paving the way for a realizable quantum error correction protocol. |
| title | Multivariate Bicycle Codes |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2406.19151 |