The Pauli Lightcone: Information-Theoretic Error Mitigation Beyond the Autocorrelation

Abstract

We introduce the wavemap: a spatial portrait of noise effects that assigns each site a per-noise-level arrival delay l_\gamma (v) and cross-entropy loss L_\gamma(v). These observables are exact at the lightcone frontier, where bond dimension \chi is small and the simulation is most faithful. Eigenvalue analysis of the composed gate-plus-noise Pauli transfer matrices confirms that the studied noise is pure amplitude damping: the spatial propagation pattern is entirely determined by the gate, making the wavemap a model-free noise diagnostic. We apply the multi-product formula (MPF) to recover the noiseless Pauli weight field from the noisy samples, subject to the Lieb-Robinson causal constraint nMPF<= nnl . Fitting time-adaptive coefficients \alpha(t) over the frontier recovers up to 55% of the information loss relative to the best noisy sample, exploiting the fact that the frontier is where truncation error is smallest. On an IBM heavy-hex lattice with heterogeneous hardware noise the method identifies an information-starved regime, pointing to calibrated synthetic noise as the next required experiment.