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Quantum Error Correcting Codes From The Compression Formalism

Man-Duen Choi·David W. Kribs·Karol Zyczkowski
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Abstract

We solve the fundamental quantum error correction problem for bi-unitary channels on two-qubit Hilbert space. By solving an algebraic compression problem, we construct qubit codes for such channels on arbitrary dimension Hilbert space, and identify correctable codes for Pauli-error models not obtained by the stabilizer formalism. This is accomplished through an application of a new tool for error correction in quantum computing called the ``higher-rank numerical range''. We describe its basic properties and discuss possible further applications.

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Man-Duen Choi, David W. Kribs, Karol Zyczkowski. 2006-05-12. Quantum Error Correcting Codes From The Compression Formalism. https://doi.org/10.1016/s0034-4877(06)80041-8

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