2025 CMS Winter Meeting

Toronto, Dec 5 - 8, 2025

Submission Form Plenary, Prize and Public Lectures By session By speaker Posters

Quantum Error Correction and Related Topics
Org: David Kribs and Rajesh Pereira (University of Guelph)
[PDF]

SERGE ADONSOU, University of Guelph Unified and Generalized Approach to Entanglement-Assisted Quantum Error Correction [PDF]: We introduce a framework for entanglement-assisted quantum error correcting codes that unifies the three original frameworks for such codes called entanglement-assisted quantum error correction, entanglement-assisted operator quantum error correction, and entanglement-assisted classical enhanced quantum error correction under a single umbrella. The unification is arrived at by viewing entanglement-assisted codes from the operator algebra quantum error correction perspective, and it is built upon a recently established extension of the stabilizer formalism to that setting. We denote the framework by entanglement-assisted operator algebra quantum error correction, and we prove a general error correction theorem for such codes, derived from the algebraic perspective, that generalizes each of the earlier results. This leads us to a natural notion of distance for such codes, and we derive a number of distance results for subclasses of the codes. We show how the classically enhanced codes form a proper subclass of the entanglement-assisted subspace codes defined by the general framework. We identify and construct new classes of entanglement-assisted subsystem codes and entanglement-assisted hybrid classical-quantum codes that are found outside of the earlier approaches, and we include a quantum communication application.
NINGPING CAO, National Research Council
GUILLAUME DAUPHINAIS, Xanadu Quantum Technologies
ALEXANDER FREI, University of Waterloo
SARAH HAGEN, University of Illinois at Urbana-Champaign
SOOYEONG KIM, University of Guelph
PRIYA NADKARNI, Xanadu Quantum Technologies
ANDREW NEMEC, University of Texas at Dallas
MUKESH TAANK, University of Guelph Generalized Knill–Laflamme theorem for families of isoclinic subspaces [PDF]: Isoclinic subspaces have been studied for over a century. Quantum error correcting codes were recently shown to define a subclass of families of isoclinic subspaces. The Knill–Laflamme theorem is a seminal result in the theory of quantum error correction, a central topic in quantum information. We show there is a generalized version of the Knill–Laflamme result and conditions that applies to all families of isoclinic subspaces. In the case of quantum stabilizer codes, the expanded conditions are shown to capture logical operators. We apply the general conditions to give a new perspective on a classical subclass of isoclinic subspaces defined by the graphs of anti-commuting unitary operators. We show how the result applies to recently studied mutually unbiased quantum measurements (MUMs), and we give a new construction of such measurements motivated by the approach.

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