Pauli stabilizer codes are classified via algebraic L-theory, yielding a bulk-boundary map to Clifford QCAs and a structural comparison with continuum framed TQFTs.
Higher-group symmetry in finite gauge theory and stabilizer codes
6 Pith papers cite this work. Polarity classification is still indexing.
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Generalized symmetries generate exponentially many Krylov sectors in quantum many-body systems, showing that Hilbert space fragmentation does not by itself imply ergodicity breaking.
Extends n-dimensional topological stabilizer codes to Clifford hierarchy versions corresponding to non-Abelian gauge theories and constructs transversal gates at the (n+1)th Clifford level.
A homological framework identifies necessary and sufficient obstruction conditions for transversal logical diagonal gates in quantum CSS codes.
Automorphisms of gauge groups extend to higher or non-invertible symmetries in topological gauge theories and enable transversal non-Clifford gates in 2+1d Z_N qudit Clifford stabilizer models for N greater than or equal to 3.
Lecture notes that systematically introduce higher-form symmetries, SymTFTs, higher-group symmetries, and related concepts in QFT using gauge theory examples.
citing papers explorer
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The Classification of Pauli Stabilizer Codes: A Lattice and Continuum Treatise
Pauli stabilizer codes are classified via algebraic L-theory, yielding a bulk-boundary map to Clifford QCAs and a structural comparison with continuum framed TQFTs.
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Hilbert Space Fragmentation from Generalized Symmetries
Generalized symmetries generate exponentially many Krylov sectors in quantum many-body systems, showing that Hilbert space fragmentation does not by itself imply ergodicity breaking.
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Clifford Hierarchy Stabilizer Codes: Transversal Non-Clifford Gates and Magic
Extends n-dimensional topological stabilizer codes to Clifford hierarchy versions corresponding to non-Abelian gauge theories and constructs transversal gates at the (n+1)th Clifford level.
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Homological origin of transversal implementability of logical diagonal gates in quantum CSS codes
A homological framework identifies necessary and sufficient obstruction conditions for transversal logical diagonal gates in quantum CSS codes.
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Automorphism in Gauge Theories: Higher Symmetries and Transversal Non-Clifford Logical Gates
Automorphisms of gauge groups extend to higher or non-invertible symmetries in topological gauge theories and enable transversal non-Clifford gates in 2+1d Z_N qudit Clifford stabilizer models for N greater than or equal to 3.
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Lectures on Generalized Symmetries
Lecture notes that systematically introduce higher-form symmetries, SymTFTs, higher-group symmetries, and related concepts in QFT using gauge theory examples.