Good Quantum Convolutional Error Correction Codes And Their Decoding Algorithm Exist

Abstract

Quantum convolutional code was introduced recently as an alternative way to protect vital quantum information. To complete the analysis of 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.

Minor changes, to appear in PRA

References in corpus (6)

• Unconditional Security Of Quantum Key Distribution Over Arbitrarily Long Distances
• A Theory of Fault-Tolerant Quantum Computation
• Error correction for continuous quantum variables
• Analog quantum error correction
• A nonadditive quantum code
• Quantum Convolutional Error Correcting Codes

Cited by in corpus (10)

• Quantum channels and memory effects
• Description of a quantum convolutional code
• Convolutional and tail-biting quantum error-correcting codes
• Non-catastrophic Encoders and Encoder Inverses for Quantum Convolutional Codes
• The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure
• Constructions of Quantum Convolutional Codes
• Quantum Coding with Entanglement
• Simple Rate-1/3 Convolutional and Tail-Biting Quantum Error-Correcting Codes
• On Quantum and Classical Error Control Codes: Constructions and Applications
• Quantum serial turbo-codes