AUTHOR=Michelogiannakis George , Butko Anastasiia , Gonzalez-Guerrero Patricia , Vasudevan Dilip , Bautista-Jurney Meriam Gay , Grace Carl , Zarkos Panagiotis , Shalf John TITLE=Unconventional compute methods and future challenges for superconducting digital computing JOURNAL=Frontiers in Materials VOLUME=Volume 12 - 2025 YEAR=2025 URL=https://www.frontiersin.org/journals/materials/articles/10.3389/fmats.2025.1618615 DOI=10.3389/fmats.2025.1618615 ISSN=2296-8016 ABSTRACT=Superconducting digital computing (SDC) based on Josephson junctions (JJs) offers significant potential for enhancing compute throughput and reducing energy consumption compared to conventional room-temperature CMOS-based approaches. Current superconducting logic families exhibit diverse characteristics in clocking strategies, power management, and information encoding techniques. This paper reviews recent advancements in unconventional computing methods specifically designed for superconducting digital circuits, emphasizing temporal computing and pulse-train representations. Notable techniques include race logic (RL), temporal pulse train computing (U-SFQ), and temporal multipliers, each offering unique performance and area advantages suited to superconducting implementations. Additionally, this paper reviews innovations in superconducting coarse-grain reconfigurable architectures (CGRA), superconducting-specific on-chip communication architectures, cryogenic sensor interfaces, and quantum computing control electronics. Finally, we highlight research challenges that should be addressed to facilitate the widespread adoption of superconducting digital computing.