Minimal-memory, non-catastrophic, polynomial-depth quantum convolutional encoders

Abstract

Quantum convolutional coding is a technique for encoding a stream of quantum information before transmitting it over a noisy quantum channel. Two important goals in the design of quantum convolutional encoders are to minimize the memory required by them and to avoid the catastrophic propagation of errors. In a previous paper, we determined minimal-memory, non-catastrophic, polynomial-depth encoders for a few exemplary quantum convolutional codes. In this paper, we elucidate a general technique for finding an encoder of an arbitrary quantum convolutional code such that the encoder possesses these desirable properties. We also provide an elementary proof that these encoders are non-recursive. Finally, we apply our technique to many quantum convolutional codes from the literature.

Continuation and expansion of arXiv:1011.5535; 21 pages, 2 figures; v2 includes an elementary proof that the encoders in this paper are non-recursive in addition to being non-catastrophic; v3, accepted into IEEE Transactions on Information Theory

References in corpus (10)

• Correcting Quantum Errors with Entanglement
• Optimal Entanglement Formulas for Entanglement-Assisted Quantum Coding
• Non-catastrophic Encoders and Encoder Inverses for Quantum Convolutional Codes
• On the logical operators of quantum codes
• Quantum Convolutional BCH Codes
• Constructions of Quantum Convolutional Codes
• Unified Quantum Convolutional Coding
• Extra Shared Entanglement Reduces Memory Demand in Quantum Convolutional Coding
• Minimal-memory realization of pearl-necklace encoders of general quantum convolutional codes
• Examples of minimal-memory, non-catastrophic quantum convolutional encoders

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• Transforming Collections of Pauli Operators into Equivalent Collections of Pauli Operators over Minimal Registers