Multivariate Bicycle Codes
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 p...
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Zusammenfassung: | 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. |
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DOI: | 10.48550/arxiv.2406.19151 |