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Subsystem Codes

Salah A. Aly·Andreas Klappenecker·Pradeep Kiran Sarvepalli
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Abstract

We investigate various aspects of operator quantum error-correcting codes or, as we prefer to call them, subsystem codes. We give various methods to derive subsystem codes from classical codes. We give a proof for the existence of subsystem codes using a counting argument similar to the quantum Gilbert-Varshamov bound. We derive linear programming bounds and other upper bounds. We answer the question whether or not there exist [[n,n-2d+2,r>0,d]] q subsystem codes. Finally, we compare stabilizer and subsystem codes with respect to the required number of syndrome qudits.

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Salah A. Aly, Andreas Klappenecker, Pradeep Kiran Sarvepalli. 2006-10-18. Subsystem Codes. https://arxiv.org/abs/quant-ph/0610153

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