Non-Clifford symmetry protected topological hyper-cluster states and multi-qubit universal measurement-based quantum computation
The research explores non-Clifford cluster states generated by higher-order gates like CCZ and CN Z, creating entangled states with five-body or general (2N+1)-body interactions. These states possess a 2xZ even x odd symmetry that protects ground state degeneracies for open chains, providing robust logical qubits for measurement-based quantum computation.