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We demonstrate that shunting of Superconductor-Insulator-SuperconductorJosephson junctions by Superconductor-Insulator-Normal metal (S-I-N) structureshaving pronounced non-linear I-V characteristics can remarkably modify theJosephson dynamics. In the regime of Josephson generation the phase behaves asan overdamped coordinate, while in the superconducting state the damping andcurrent noise are strikingly small, that is vitally important for applicationof such junctions for readout and control of Josephson qubits. SuperconductingNb/AlO${_x}$/Nb junction shunted by Nb/AlO${_x}$/AuPd junction of S-I-N typewas fabricated and, in agreement with our model, exhibited non-hysteretic I-Vcharacteristics at temperatures down to at least 1.4 K.Comment: 4 pages incl. 3 figure

Josephson junctions with nonlinear damping for rapid single-flux-quantum - qubit circuits