Suppression of Non-Markovian Drift in Dual-Rail Superconducting Qubits via Real-Time Topological Frame Rotation

Description / Abstract Abstract Current Quantum Error Correction (QEC) protocols, such as the Surface Code, are typically optimized for Markovian noise models where errors are independent and identically distributed. We demonstrate that superconducting qubit architectures are susceptible to a specific class of non-Markovian correlated drift that remains undetectable by standard stabilizer measurements until it induces a catastrophic coherence collapse. We analytically derive this failure mode as a Fisher Information Horizon Limit, proving that an estimator optimizing solely for instantaneous gate fidelity experiences a divergence in variance regarding long-term structural drift. We model this "Hyper-Stable" regime as a system approaching an Exceptional Point (EP) in its effective non-Hermitian Hamiltonian. To mitigate this, we propose a control architecture utilizing a Systolic Drift Monitor (SDM) that integrates the geometric Berry phase of the noise history. By implementing a periodic Frame Update Unitary (conceptually isomorphic to basis rotation) on a dual-rail encoded subspace, we convert latent non-Markovian drift into observable execution variance, allowing for real-time suppression of the spectral singularity. Implementation Details The proposed architecture is designed for deployment on FPGA-based quantum control stacks (e.g., Xilinx RFSoC). Simulation results demonstrate a significant improvement in effective coherence times under 1/{f^alpha} noise conditions (alpha = 0.95) by preventing the system from entering the null space of the stabilizer code. The hardware logic is estimated to operate with a feedback latency of < 200 ns, well within the coherence time of standard transmon qubits. Keywords Quantum Error Correction, Superconducting Qubits, Non-Markovian Noise, Exceptional Points, Non-Hermitian Physics, FPGA Control, Dual-Rail Encoding, Fisher Information, Cramér-Rao Bound, Control Theory, Systolic Drift Monitor