Disorder-blind Mpemba acceleration of quantum state preparation
Using the strong Mpemba effect to accelerate relaxation by initial-state design requires suppressing the slowest mode, which typically needs prior knowledge of the system. However, in disordered systems, this mode is sample-dependent, so a fixed preparation generally retains a slow-mode overlap. We show that a ``blind'' preparation, designed from the clean chain without knowledge of the disorder realisation or its distribution, can start farther from stationarity yet overtake a reference in typical samples of a dephased disordered XX chain. It requires only the chain geometry and the particle number. At strong dephasing, the density dynamics maps to a resistor chain, and an exact inverse-generator identity links the residual overlap to the spatial resistance profile. We find two distinct thresholds: a finite mean resistance suffices for diffusion, but the residual overlap decays as $L^{-1/2}$ with chain length $L$ only when the resistance variance is finite; rare weak links slow this decay. We predict the fraction of samples in which the blind preparation wins, which is an ensemble-level measure of its reliability. Finite-size calculations support both scaling regimes with interactions at strong dephasing. We give preparation circuits and a density readout for the residual overlap.