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We present a theory of the subgap tails of the density of states in adiffusive superconductor containing magnetic impurities. We show that thesubgap tails have two contributions: one arising from mesoscopic gapfluctuations, previously discussed by Lamacraft and Simons, and the otherassociated to the long-wave fluctuations of the concentration of magneticimpurities. We study the latter both in small superconducting grains and inbulk systems [$d=1,2,3$], and establish the dimensionless parameter thatcontrols which of the two contributions dominates the subgap tails. We observethat these contributions are related to each other by dimensional reduction. Weapply the theory to estimate the effects of a weak concentration of magneticimpurities [$\approx 1 {\rm p.p.m}$] on the phase coherence of Josephsonqubits. We find that at these typical concentrations, magnetic impurities arerelevant for the dephasing in large qubits, designed around a $10 {\rm \mu m}$scale, where they limit the quality factor to be $Q<10^4-10^5$.Comment: 13 pages, 1 figur

Subgap states in dirty superconductors and their effect on dephasing in Josephson qubits