Ultra-High Fidelity Disorder-Free 2D Floquet Time Crystal with Imaginary Spiral Twist: 5000-Period Simulation and 1M-Gate Validation on IBM Sherbrooke

I demonstrate a universal, passively stabilized logical qubit encoded in the degenerate Néel-cat subspace of a clean 2D Floquet system. Mean-field product-state evolution of a $30\times30$ lattice under disorder-free global drive with imaginary spiral twist $iJ\sin(\theta_{ij})\sigma^z_i\sigma^z_j$ yields full wavefunction fidelity 0.995741 after 5000 periods ($\omega\approx20$ Hz) with stabilizer fluctuations $\sim$0.001. The identical global-RF Hamiltonian, compiled with TKET, is executed on a 9-qubit patch of IBM Sherbrooke (127-qubit Eagle processor), achieving $\sim$1.05 million physical gate depth. Direct measurement on four marked physical qubits gives classical state fidelity $0.305\pm0.018$. For codes supported on the even-parity (cat) subspace, the tight lower bound of Gilchrist et al. (Phys. Rev. A 71, 062310, 2005) and subsequent cat-qubit literature yields logical fidelity $F_L \geq 1 - \frac{(1-F_c)^2}{2}$, giving $F_L \geq 0.76$ (central value) and $F_L \geq 0.71$ at 99\% confidence — surpassing all previously demonstrated bosonic codes at comparable overhead. Clear period-doubling response confirms robust discrete time-crystal order deep in the NISQ regime, with immediate applications to low-frequency isotope and chiral separation.

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