Good quantum-convolutional error-correction codes and their decoding algorithm exist

Abstract

A quantum-convolutional code was introduced recently as an alternative way to protect vital quantum information. To complete the analysis of the quantum-convolutional code, I report a way to decode certain quantum-convolutional codes based on the classical Viterbi decoding algorithm. This decoding algorithm is optimal for a memoryless channel. I also report three simple criteria to test if decoding errors in a quantum-convolutional code will terminate after a finite number of decoding steps whenever the Hilbert space dimension of each quantum register is a prime power. Finally, I show that certain quantum-convolutional codes are in fact stabilizer codes. And hence, these quantum stabilizer convolutional codes have fault-tolerant implementations. ©1999 The American Physical Society.