Dynamical Entanglement Preservation via Graded Floquet Attractors on Superconducting Transmon Chains

We report the observation of long-range dynamical protection and coherent transport of two-qubit entangled states across discrete 1D lattice chains on a 156-qubit superconducting quantum processor (ibm_marrakesh). By combining an affine geometric phase gradient with periodic CPMG dynamical decoupling and Hermitian conjugate frame unwinding, we suppress continuous dephasing, spatial wavepacket dispersion, and accumulative cross-resonance errors. The protocol achieves an unmitigated Bell state fidelity of 97.92% +/- 0.10% across 512 physical SWAP gates (1,536 native two-qubit hardware operations) and maintains an unmitigated fidelity of 97.93% +/- 0.22% (Tr(rho^2) = 0.9591) through 1,024 physical SWAPs (3,072 native pulses), contrasting with bare unmitigated transport decay (F < 1%). We demonstrate spatial transport scaling across up to 101 contiguous transmons (89.06% fidelity across 198 SWAPs), confirm the attractor basin geometry under continuous 3D Bloch sphere parameter sweeps (theta in [0, 2pi]), and validate sensitivity to intentional single-qubit phase and bit-flip defect injections.