Lift-Connected Surface Codes
- URL: http://arxiv.org/abs/2401.02911v1
- Date: Fri, 5 Jan 2024 17:22:49 GMT
- Title: Lift-Connected Surface Codes
- Authors: Josias Old, Manuel Rispler and Markus M\"uller
- Abstract summary: We use the recently introduced lifted product to construct a family of Quantum Low Density Parity Check Codes (QLDPC codes)
The codes we obtain can be viewed as stacks of surface codes that are interconnected, leading to the name lift-connected surface (LCS) codes.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We use the recently introduced lifted product to construct a family of
Quantum Low Density Parity Check Codes (QLDPC codes). The codes we obtain can
be viewed as stacks of surface codes that are interconnected, leading to the
name lift-connected surface (LCS) codes. LCS codes offer a wide range of
parameters - a particularly striking feature is that they show interesting
properties that are favorable compared to the standard surface code already at
moderate numbers of physical qubits in the order of tens. We present and
analyze the construction and provide numerical simulation results for the
logical error rate under code capacity and phenomenological noise. These
results show that LCS codes attain thresholds that are comparable to
corresponding (non-connected) copies of surface codes, while the logical error
rate can be orders of magnitude lower, even for representatives with the same
parameters. This provides a code family showing the potential of modern product
constructions at already small qubit numbers. Their amenability to 3D-local
connectivity renders them particularly relevant for near-term implementations.
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