Eliminating Metric Time in Quantum Computation through Geometric Degeneracy

We introduce a geometric quantum computation framework in which logical operations arise from metric degeneracy mappings rather than time-evolution under Hamiltonians. A continuous family of geometric exchange gates, termed Li-SWAP, interpolates between identity and SWAP through a degeneracy parameter $\rho$. We demonstrate that a half-degenerate Li-SWAP acts as an entangling gate, enabling universal quantum computation when combined with single-qubit rotations. Entanglement generation is governed by a geometric correction law controlled by input-state symmetry defects and degeneracy strength. Numerical simulations reveal symmetry-locking for exchange-symmetric states and exact collapse behavior for specific input subspaces. This framework effectively eliminates the metric distance between remote qubits at the level of an effective circuit model, enabling metric-independent logical exchange operations without requiring long-range dynamical propagation, while respecting no-signalling.