Quantum Convolutional Error Correcting Codes

Abstract

I report two general methods to construct quantum convolutional codes for $N$-state quantum systems. Using these general methods, I construct a quantum convolutional code of rate 1/4, which can correct one quantum error for every eight consecutive quantum registers.

arXiv commentMinor revisions and clarifications. To appear in Phys. Rev. A

References in corpus (8)

• Mixed State Entanglement and Quantum Error Correction
• Good Quantum Error-Correcting Codes Exist
• A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
• Quantum Error Correction and Orthogonal Geometry
• Simple Quantum Error Correcting Codes
• A nonadditive quantum code
• Five Quantum Register Error Correction Code For Higher Spin Systems
• Correcting Quantum Errors In Higher Spin Systems

Cited by in corpus (13)

• Quantum channels and memory effects
• Description of a quantum convolutional code
• Convolutional and tail-biting quantum error-correcting codes
• Tensor Networks and Quantum Error Correction
• Non-catastrophic Encoders and Encoder Inverses for Quantum Convolutional Codes
• Cyclic Quantum Error-Correcting Codes and Quantum Shift Registers
• The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure
• Constructions of Quantum Convolutional Codes
• Good Quantum Convolutional Error Correction Codes And Their Decoding Algorithm Exist
• Simple Rate-1/3 Convolutional and Tail-Biting Quantum Error-Correcting Codes
• Quantum resource theory of coding for error correction
• Removing correlations in signals transmitted over a quantum memory channel
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