No voltage is required as the resistance is zero. This is for static conditions only. In order to change the current, i.e. ac condition, a voltage is needed due to inductance, since v = L * di/dt. When a superconductor connects a power source, which is generally constant voltage, to a load resistance, then the current is simply Vsource/Rload, with all the voltage dropped across the load, and none dropped across the superconductor. In the ac domain, however, the superconductor contributes some inductance. There is a non-zero voltage due to inductance.