Boolean Functions, Projection Operators and Quantum Error Correcting Codes
arXiv:cs/0610159 · doi:10.1109/TIT.2008.917720
Abstract
This paper describes a fundamental correspondence between Boolean functions and projection operators in Hilbert space. The correspondence is widely applicable, and it is used in this paper to provide a common mathematical framework for the design of both additive and non-additive quantum error correcting codes. The new framework leads to the construction of a variety of codes including an infinite class of codes that extend the original ((5,6,2)) code found by Rains [21]. It also extends to operator quantum error correcting codes.
Submitted to IEEE Transactions on Information Theory, October 2006, to appear in IEEE Transactions on Information Theory, 2008
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- Codeword Stabilized Quantum Codes
- Efficient Representation of Topologically Ordered States with Restricted Boltzmann Machines
- Codeword stabilized quantum codes: algorithm and structure
- Nonbinary Codeword Stabilized Quantum Codes
- Non-Additive Quantum Codes from Goethals and Preparata Codes
- Clustered Error Correction of Codeword-Stabilized Quantum Codes
- Structured Error Recovery for Codeword-Stabilized Quantum Codes
- Encoders and Decoders for Quantum Expander Codes Using Machine Learning
- On the Construction for Quantum Code ((n,K, d))p via Logic Function over Fp
- Logic Functions and Quantum Error Correcting Codes