Systems and methods for determining critical timing paths in a superconducting circuit design including Josephson junctions are provided. An example method includes providing timing information concerning a plurality of source terminals of at least one logic gate coupled with a first sink terminal of the at least one logic gate. The method further includes using a processor, determining whether, in view of the timing information, the first sink terminal is reachable by a single flux quantum (SFQ) pulse within a predetermined range of arrival time based on an assigned first phase to the at least one logic gate.