Dynamical Decoupling and Zero-Noise Extrapolation Under Colored Noise

Zero-noise extrapolation (ZNE) is an established quantum error mitigation technique that infers noise-free expectation values by scaling circuit noise and extrapolating to the zero-noise limit. Standard ZNE formulations implicitly assume memoryless Markovian gate noise, where error rates scale linearly with circuit duration. In physical solid-state quantum processors dominated by colored 1/f^α environmental dephasing, this fundamental assumption fails: non-Markovian noise induces superlinear coherence decay χ(t) ∝ t1+α, causing standard polynomial extrapolation to diverge. In this work, we demonstrate how inserting dynamical decoupling (DD) sequences into idle circuit intervals spectrally filters low-frequency noise components, linearizing the effective decay profile into a Markovian regime χeff(t) ∝ t. We benchmark this combined DD–ZNE framework by reconstructing the order parameter across the quantum phase transition of a 1D Transverse-Field Ising Model (TFIM). Our results demonstrate that while standalone ZNE fails under non-Markovian dephasing, the combined DD–ZNE approach eliminates extrapolation divergence and reliably recovers ideal quantum observables. Key Highlights: Theoretical Breakdown: Analytical derivation showing why polynomial ZNE diverges under 1/f^α dephasing environments due to superlinear temporal scaling. Filter Function Engineering: Demonstration of spectator-qubit XY-4 pulse insertion as a high-pass spectral filter that suppresses low-frequency noise and restores linear decay dynamics. Phase Transition Benchmark: Validation on a 4-qubit 1D TFIM order parameter (σz⁽⁰⁾ σz⁽¹⁾) across g ∈ [0.1, 2.0], demonstrating a $>69%$ error reduction over unmitigated circuits and preventing non-physical polynomial divergence.