Josephson junction based logic devices and methods for their use are described. An example Josephson junction based logic device includes a two-input OR/AND (OA2) gate. The OA2 gate includes a first input node inductively coupled to a first input source and a second input node inductively coupled to a second input source. The first and second input sources are configured to provide single-flux-quantum (SFQ) pulses. The OA2 gate also includes first plurality of inductors coupled between the first input node and one of: a first output node or a second output node. The OA2 gate additionally includes a second plurality of inductors coupled between the second input node and one of: the first or the second output nodes. The OA2 gate also includes Josephson junctions coupled between a common node and one of: the first or the second input node, or the first or the second output node.