Explicit decoders using fixed-point amplitude amplification based on QSVT
This paper presents two explicit quantum circuit decoders—the generalized Yoshida-Kitaev decoder and a Petz-like decoder—that utilize fixed-point amplitude amplification based on quantum singular value transformation to reliably recover quantum information from arbitrary noisy channels when the decoupling condition is satisfied, thereby achieving communication rates arbitrarily close to the quantum capacity with significantly reduced computational complexity compared to previous methods.