Asymmetric Quantum Codes on Toric Surfaces
This work provides domain-specific solutions for quantum computing by developing new asymmetric quantum codes, though it appears incremental as it builds on existing Calderbank-Shor-Steane constructions.
The paper tackled the problem of constructing asymmetric quantum error-correcting codes for biased quantum channels, resulting in families of toric surfaces and codes that address qubit-flip and phase-shift errors with potentially different probabilities.
Asymmetric quantum error-correcting codes are quantum codes defined over biased quantum channels: qubit-flip and phase-shift errors may have equal or different probabilities. The code construction is the Calderbank-Shor-Steane construction based on two linear codes. We present families of toric surfaces, toric codes and associated asymmetric quantum error-correcting codes.