Encoding of Nonbinary Entanglement-Unassisted and Assisted Stabilizer Codes

Quantum coding schemes over qudits using preshared entanglement between the encoder and decoder can provide better error correction capability than without it. In this article, we develop procedures for constructing encoding operators for entanglement-unassisted and entanglement-assisted qudit stabilizer codes over
$\mathbb {F}_{p^k}$
, with
$p$
prime and
$k \geq 1$
from first principles, generalizing prior works on qubit-based codes and codes that work over
$\mathbb {F}_p$
. We also provide quantum encoding architectures based on the proposed encoding procedures using one and two qudit gates, useful toward realizing coded quantum computing and communication systems using qudits.