Intrinsic Geometric Filtering in Symmetry-Locked Metric-Degenerate Quantum Logic

We introduce a geometric paradigm for two-qubit logic based on controllable exchange degeneracy. The resulting Li–iSWAP(ρ) family interpolates between identity and iSWAP through a degeneracy parameter ρ, with the half-degenerate gate
U_Li-HALF = √iSWAP emerging as a native entangling primitive.

We show that U_Li-HALF is symmetry-locked: it commutes with SWAP and preserves the decomposition of the two-qubit Hilbert space into symmetric and antisymmetric sectors. This locking induces an intrinsic protected manifold where entanglement activation is suppressed under exchange-symmetric (SWAP-commuting) geometric noise.

Numerical simulations reveal (i) a geometric filtering effect — an extended near-zero entanglement region in state-space scans for certain noise configurations — and (ii) a symmetry-protected spatial isolation (firewall) against correlated crosstalk.

For product-state inputs, entanglement activation largely follows a one-parameter scaling relation governed by

x_eff = Λ(ρ) (1 − s), s = |⟨φ | χ⟩|²,

where s is the local overlap invariant. The different ρ-families exhibit an approximate collapse onto a common activation curve when plotted against x_eff. Breaking exchange symmetry reduces the regularity of both the filtering plateau and the scaling collapse, indicating their predominantly symmetry-enhanced geometric origin.