Stabilizer Formalism for Operator Algebra Quantum Error Correction

• URL: http://arxiv.org/abs/2304.11442v2
• Date: Thu, 15 Feb 2024 18:54:30 GMT
• Title: Stabilizer Formalism for Operator Algebra Quantum Error Correction
• Authors: Guillaume Dauphinais, David W. Kribs and Michael Vasmer
• Abstract summary: We introduce a stabilizer formalism for the general quantum error correction framework called operator algebra quantum error correction (OAQEC) We formulate a theorem that fully characterizes the Pauli errors that are correctable for a given code. We show how some recent hybrid subspace code constructions are captured by the formalism.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a stabilizer formalism for the general quantum error correction framework called operator algebra quantum error correction (OAQEC), which generalizes Gottesman's formulation for traditional quantum error correcting codes (QEC) and Poulin's for operator quantum error correction and subsystem codes (OQEC). The construction generates hybrid classical-quantum stabilizer codes and we formulate a theorem that fully characterizes the Pauli errors that are correctable for a given code, generalizing the fundamental theorems for the QEC and OQEC stabilizer formalisms. We discover hybrid versions of the Bacon-Shor subsystem codes motivated by the formalism, and we apply the theorem to derive a result that gives the distance of such codes. We show how some recent hybrid subspace code constructions are captured by the formalism, and we also indicate how it extends to qudits.

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