Generalized symmetries generate exponentially many Krylov sectors in quantum many-body systems, showing that Hilbert space fragmentation does not by itself imply ergodicity breaking.
Higher-group symmetry of (3+1)D fermionicZ 2 gauge theory: logical CCZ, CS, and T gates from higher symmetry
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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.
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.
citing papers explorer
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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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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.
- Sixteen-Fold Way for Fermionic Topological Orders