Asymmetric Quantum LDPC Codes
Pradeep Kiran Sarvepalli, Martin Roetteler, Andreas Klappenecker
TL;DR
This paper introduces systematic methods for constructing asymmetric quantum LDPC codes that leverage error probability asymmetries in quantum channels, using a CSS approach with BCH and finite geometry LDPC codes.
Contribution
It presents a novel CSS-based construction method for asymmetric quantum stabilizer codes utilizing BCH and finite geometry LDPC codes.
Findings
Provides systematic construction techniques for asymmetric quantum codes.
Exploits error asymmetry in quantum channels like amplitude damping.
Enhances quantum error correction efficiency for specific error models.
Abstract
Recently, quantum error-correcting codes were proposed that capitalize on the fact that many physical error models lead to a significant asymmetry between the probabilities for bit flip and phase flip errors. An example for a channel which exhibits such asymmetry is the combined amplitude damping and dephasing channel, where the probabilities of bit flips and phase flips can be related to relaxation and dephasing time, respectively. We give systematic constructions of asymmetric quantum stabilizer codes that exploit this asymmetry. Our approach is based on a CSS construction that combines BCH and finite geometry LDPC codes.
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