qSeq: Full Algorithmic and Tool Support for Synthesizing Sequential Circuits in Superconducting SFQ Technology

Synthesizing general nonlinear sequential circuits in superconducting Single Flux Quantum (SFQ) technology is a challenging task involving the proper leveling of cyclic digraphs, handling nested feedback loops, and ensuring the full path balancing property throughout the synthesis process. This paper presents a precise definition of the level of a node in a cyclic digraph and a polynomial time algorithm for the corresponding level assignment and full path balancing in sequential SFQ circuits, including SFQ Finite State Machines (FSMs). A case study is conducted on a 3-bit counter, as an FSM, which has a power consumption of $44. 7 \mu W$ and $1. 4 \mu W$ using rapid SFQ and energy-efficient rapid RSFQ cells, respectively, with the local clock frequency of 55GHz (throughput of 11GHz) which is significantly higher than the typical CMOS clock frequencies. More results on larger SFQ circuits are also presented.