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Identification Of Quantum Encoder Matrix From A Collection Of Pauli Errors

Gilles Burel 1, 2 Hugo Pillin 1, 2, 3 El-Houssaïn Baghious 1, 2 Paul Baird 3 Roland Gautier 1, 2
2 Lab-STICC_UBO_CACS_COM
IBNM - Institut Brestois du Numérique et des Mathématiques, Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
Abstract : Quantum information processing is a rapidly evolving field, due to promising applications in communications, cryptography, and computing. In this framework, there is a need to protect quantum information against errors, using quantum error-correcting codes. Efficient quantum codes, based on the stabilizer formalism (that exploits elements of the Pauli group), have been proposed. The stabilizer formalism allows one to simulate quantum codes and quantum errors using operations inside the Pauli group only, leading to huge gains in simulation time. However, to deeply study and simulate unconventional quantum errors and devices, there is a need to know the true quantum operator (represented by a unitary matrix). In this paper, we propose an algorithm, based on linear algebra, to identify the quantum encoder matrix from a collection of Pauli errors. The approach is two-steps. First, from a collection a Pauli errors whose matrix representation is diagonal, a search of common eigenvectors identifies the encoder matrix up to phase indeterminates. Second, additional Pauli errors with nondiagonal matrix representations are used to eliminate the remaining in-determinations. Simulation results are also provided to illustrate and validate the approach. Index Terms-quantum information, quantum error correction , Pauli errors, physical layer integrity
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https://hal.univ-brest.fr/hal-02455812
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Gilles Burel, Hugo Pillin, El-Houssaïn Baghious, Paul Baird, Roland Gautier. Identification Of Quantum Encoder Matrix From A Collection Of Pauli Errors. Asia-Pacific Conference on Communications (APCC 2019), Nov 2019, Ho Chi Minh city, Vietnam. ⟨hal-02455812⟩

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