MPS Classification of Modulated Symmetry-Protected Topological Phases and LSM Constraints

MPS framework classifies 1D SPT phases under modulated symmetries via H²(G,U(1)) cohomology, confirming the crystalline equivalence principle and proving Lieb-Schultz-Mattis constraints for modulated and non-invertible Kramers-Wannier symmetries.

#TopologicalPhases #QuantumMatter #Research

Non-Clifford Symmetry-Protected Topological Higher-Order Cluster States for Multi-Qubit Measurement-Based Quantum Computation

Using CCZ/CNZ gates to build cluster states creates (2N+1)-body entangled systems with 2²ᴺ-fold degenerate edges, enabling N-qubit input/output in measurement-based quantum computation via non-Clifford symmetry-protected topological phases.

#QuantumComputing #TopologicalPhases #ClusterStates