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Multivariate Bicycle Codes
- Publication Year :
- 2024
-
Abstract
- 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-4 and weight-5 TB-QLDPC codes which promise to be more amenable to near-term experimental setups. We show that our TB-QLDPC codes up to weight-6 have a bi-planar structure. Further, most of our new codes can also be arranged in a two-dimensional toric layout, and have 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 30 physical qubits with weight-5 check measurements, while a surface code with these parameters requires 100 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.<br />Comment: 4 + 14 pages, 17 figures
- Subjects :
- Quantum Physics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2406.19151
- Document Type :
- Working Paper