Encoding of Nonbinary Entanglement-Unassisted and Assisted Stabilizer Codes

• Published in: IEEE transactions on quantum engineering Vol. 2; pp. 1 - 22
• Main Authors: Nadkarni, Priya J., Garani, Shayan Srinivasa
• Format: Journal Article
• Language: English
• Published: New York IEEE 2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Coders; Communications systems; Computer architecture; Encoding; Encoding architecture; entanglement-assisted (EA) codes; Error correction; First principles; Generators; nonbinary codes; Quantum computing; Quantum entanglement; quantum error correction; Quantum state; Quantum system; Qubits (quantum computing); qudit stabilizer codes; Tensors
• ISSN: 2689-1808; 2689-1808
• DOI: 10.1109/TQE.2021.3050848

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 <inline-formula><tex-math notation="LaTeX">\mathbb {F}_{p^k}</tex-math></inline-formula>, with <inline-formula><tex-math notation="LaTeX">p</tex-math></inline-formula> prime and <inline-formula><tex-math notation="LaTeX">k \geq 1</tex-math></inline-formula> from first principles, generalizing prior works on qubit-based codes and codes that work over <inline-formula><tex-math notation="LaTeX">\mathbb {F}_p</tex-math></inline-formula>. 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.