Algebraic Quantum Codes: Linking Quantum Mechanics and Discrete Mathematics
Markus Grassl
TL;DR
This paper introduces a comprehensive framework for quantum error-correcting codes using algebraic coding theory, providing new methods for constructing and improving QECCs with potential applications in quantum computing.
Contribution
It presents a unified algebraic framework for QECCs and introduces secondary construction techniques to enhance code parameters.
Findings
Framework linking quantum mechanics and algebraic coding theory
New construction methods for QECCs
Propagation rules for QECC parameters
Abstract
We present a general framework of quantum error-correcting codes (QECCs) as a subspace of a complex Hilbert space and the corresponding error models. Then we illustrate how QECCs can be constructed using techniques from algebraic coding theory. Additionally, we discuss secondary constructions for QECCs, leading to propagation rules for the parameters of QECCs.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.