{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T12:22:27Z","timestamp":1767183747633,"version":"3.37.3"},"reference-count":44,"publisher":"IOP Publishing","issue":"1","license":[{"start":{"date-parts":[[2024,2,23]],"date-time":"2024-02-23T00:00:00Z","timestamp":1708646400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,2,23]],"date-time":"2024-02-23T00:00:00Z","timestamp":1708646400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Neuromorph. Comput. Eng."],"published-print":{"date-parts":[[2024,3,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Conventional semiconductor-based integrated circuits are gradually approaching fundamental scaling limits. Many prospective solutions have recently emerged to supplement or replace both the technology on which basic devices are built and the architecture of data processing. Neuromorphic circuits are a promising approach to computing where techniques used by the brain to achieve high efficiency are exploited. Many existing neuromorphic circuits rely on unconventional and useful properties of novel technologies to better mimic the operation of the brain. One such technology is single flux quantum (SFQ) logic\u2014a cryogenic superconductive technology in which the data are represented by quanta of magnetic flux (fluxons) produced and processed by Josephson junctions embedded within inductive loops. The movement of a fluxon within a circuit produces a quantized voltage pulse (SFQ pulse), resembling a neuronal spiking event. These circuits routinely operate at clock frequencies of tens to hundreds of gigahertz, making SFQ a natural technology for processing high frequency pulse trains. This work harnesses thermal stochasticity in superconducting synapses to emulate stochasticity in biological synapses in which the synapse probabilistically propagates or blocks incoming spikes. The authors also present neuronal, fan-in, and fan-out circuitry inspired by the literature that seamlessly cascade with the synapses for deep neural network construction. Synapse weights and neuron biases are set with bias current, and the authors propose multiple mechanisms for training the network and storing weights. The network primitives are successfully demonstrated in simulation in the context of a rate-coded multi-layer XOR neural network which achieves a wide classification margin. The proposed methodology is based solely on existing SFQ technology and does not employ unconventional superconductive devices or semiconductor transistors, making this proposed system an effective approach for scalable cryogenic neuromorphic computing.<\/jats:p>","DOI":"10.1088\/2634-4386\/ad207a","type":"journal-article","created":{"date-parts":[[2024,1,19]],"date-time":"2024-01-19T22:20:41Z","timestamp":1705702841000},"page":"014005","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":8,"title":["Harnessing stochasticity for superconductive multi-layer spike-rate-coded neuromorphic networks"],"prefix":"10.1088","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7050-3151","authenticated-orcid":false,"given":"Alexander J","family":"Edwards","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3022-0368","authenticated-orcid":true,"given":"Gleb","family":"Krylov","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9847-4455","authenticated-orcid":false,"given":"Joseph S","family":"Friedman","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5549-7160","authenticated-orcid":false,"given":"Eby G","family":"Friedman","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2024,2,23]]},"reference":[{"key":"ncead207abib1","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1038\/s43588-021-00184-y","article-title":"Opportunities for neuromorphic computing algorithms and applications","volume":"2","author":"Schuman","year":"2022","journal-title":"Nat. Comput. Sci."},{"key":"ncead207abib2","doi-asserted-by":"publisher","first-page":"2454","DOI":"10.1109\/TC.2012.142","article-title":"Overview of the spinnaker system architecture","volume":"62","author":"Furber","year":"2013","journal-title":"IEEE Trans. Comput."},{"key":"ncead207abib3","doi-asserted-by":"publisher","first-page":"1537","DOI":"10.1109\/TCAD.2015.2474396","article-title":"Truenorth: design and tool flow of a 65 mw 1 million neuron programmable neurosynaptic chip","volume":"34","author":"Akopyan","year":"2015","journal-title":"IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst."},{"key":"ncead207abib4","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1109\/MM.2018.112130359","article-title":"Loihi: a neuromorphic manycore processor with on-chip learning","volume":"38","author":"Davies","year":"2018","journal-title":"IEEE Micro"},{"key":"ncead207abib5","doi-asserted-by":"publisher","DOI":"10.1063\/5.0027997","article-title":"Superconducting neural networks with disordered Josephson junction array synaptic networks and leaky integrate-and-fire loop neurons","volume":"129","author":"Goteti","year":"2021","journal-title":"J. Appl. Phys."},{"key":"ncead207abib6","doi-asserted-by":"publisher","DOI":"10.1109\/TASC.2012.2228531","article-title":"Pseudo sigmoid function generator for a superconductive neural network","volume":"23","author":"Yamanashi","year":"2013","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ncead207abib7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.82.011914","article-title":"Josephson junction simulation of neurons","volume":"82","author":"Crotty","year":"2010","journal-title":"Phys. Rev. E"},{"key":"ncead207abib8","doi-asserted-by":"publisher","first-page":"934","DOI":"10.1038\/s41598-020-57892-0","article-title":"Synaptic weighting in single flux quantum neuromorphic computing","volume":"10","author":"Schneider","year":"2020","journal-title":"Sci. Rep."},{"key":"ncead207abib9","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.1701329","article-title":"Ultralow power artificial synapses using nanotextured magnetic Josephson junctions","volume":"4","author":"Schneider","year":"2018","journal-title":"Sci. Adv."},{"key":"ncead207abib10","doi-asserted-by":"publisher","DOI":"10.1063\/5.0025168","article-title":"Fan-out and fan-in properties of superconducting neuromorphic circuits","volume":"128","author":"Schneider","year":"2020","journal-title":"J. Appl. Phys."},{"key":"ncead207abib11","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.95.032220","article-title":"Synchronization dynamics on the picosecond time scale in coupled Josephson junction neurons","volume":"95","author":"Segall","year":"2017","journal-title":"Phys. Rev. E"},{"key":"ncead207abib12","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/j.physb.2014.07.048","article-title":"Phase-flip bifurcation in a coupled Josephson junction neuron system","volume":"455","author":"Segall","year":"2014","journal-title":"Physica B"},{"key":"ncead207abib13","doi-asserted-by":"publisher","DOI":"10.1063\/1.5042425","article-title":"Tutorial: high-speed low-power neuromorphic systems based on magnetic Josephson junctions","volume":"124","author":"Schneider","year":"2018","journal-title":"J. Appl. Phys."},{"article-title":"Single flux quantum based ultrahigh speed spiking neuromorphic processor architecture","year":"2020","author":"Bozbey","key":"ncead207abib14"},{"key":"ncead207abib15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TASC.2023.3270766","article-title":"JJ-Soma: towards a spiking neuromorphic processor architecture","volume":"33","author":"Karamuftuoglu","year":"2023","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ncead207abib16","doi-asserted-by":"publisher","DOI":"10.1063\/5.0118287","article-title":"Perspectives on nanoclustered magnetic Josephson junctions as artificial synapses","volume":"121","author":"Ju\u00e9","year":"2022","journal-title":"Appl. Phys. Lett."},{"key":"ncead207abib17","doi-asserted-by":"publisher","first-page":"8059","DOI":"10.1021\/acs.nanolett.0c03057","article-title":"Superconducting nanowire spiking element for neural networks","volume":"20","author":"Toomey","year":"2020","journal-title":"Nano Lett."},{"key":"ncead207abib18","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6668\/ac4cd2","article-title":"Supermind: a survey of the potential of superconducting electronics for neuromorphic computing","volume":"35","author":"Schneider","year":"2022","journal-title":"Supercond. Sci. Technol."},{"key":"ncead207abib19","doi-asserted-by":"publisher","first-page":"781","DOI":"10.1016\/S0893-6080(01)00057-0","article-title":"Probabilistic synaptic weighting in a reconfigurable network of vlsi integrate-and-fire neurons","volume":"14","author":"Goldberg","year":"2001","journal-title":"Neural Netw."},{"key":"ncead207abib20","doi-asserted-by":"publisher","first-page":"241","DOI":"10.3389\/fnins.2016.00241","article-title":"Stochastic synapses enable efficient brain-inspired learning machines","volume":"10","author":"Neftci","year":"2016","journal-title":"Front. Neurosci."},{"key":"ncead207abib21","doi-asserted-by":"publisher","first-page":"2219","DOI":"10.1109\/JPROC.2015.2496679","article-title":"To spike or not to spike: that is the question","volume":"103","author":"Maass","year":"2015","journal-title":"Proc. IEEE"},{"key":"ncead207abib22","article-title":"Dynamic stochastic synapses as computational units","volume":"vol 10","author":"Maass","year":"1997"},{"key":"ncead207abib23","doi-asserted-by":"publisher","DOI":"10.3389\/fnsys.2021.629436","article-title":"Stochasticity versus determinacy in neurobiology: from ion channels to the question of the free will","volume":"15","author":"Braun","year":"2021","journal-title":"Front. Syst. Neurosci."},{"key":"ncead207abib24","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevApplied.18.064014","article-title":"Stochastic synapses made of magnetic domain walls","volume":"18","author":"Wang","year":"2022","journal-title":"Phys. Rev. Appl."},{"key":"ncead207abib25","doi-asserted-by":"publisher","first-page":"2571","DOI":"10.1038\/s41467-022-30305-8","article-title":"Neural sampling machine with stochastic synapse allows brain-like learning and inference","volume":"13","author":"Dutta","year":"2022","journal-title":"Nat. Commun."},{"key":"ncead207abib26","doi-asserted-by":"crossref","DOI":"10.1109\/SSCI.2017.8285425","article-title":"Stochastic synapse reinforcement learning (SSRL)","author":"Shah","year":"2017"},{"year":"2022","author":"Krylov","key":"ncead207abib27"},{"key":"ncead207abib28","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1109\/77.80745","article-title":"RSFQ logic\/memory family: a new Josephson-junction technology for sub-terahertz-clock-frequency digital systems","volume":"1","author":"Likharev","year":"1991","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ncead207abib29","doi-asserted-by":"publisher","first-page":"760","DOI":"10.1109\/TASC.2010.2096792","article-title":"Energy-efficient single flux quantum technology","volume":"21","author":"Mukhanov","year":"2011","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ncead207abib30","doi-asserted-by":"publisher","DOI":"10.1109\/TASC.2013.2244634","article-title":"Energy-efficient superconducting computing - power budgets and requirements","volume":"23","author":"Holmes","year":"2013","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ncead207abib31","doi-asserted-by":"publisher","DOI":"10.1088\/0953-2048\/26\/12\/125009","article-title":"Artificial neural network based on squids: demonstration of network training and operation","volume":"26","author":"Chiarello","year":"2013","journal-title":"Supercond. Sci. Technol."},{"key":"ncead207abib32","doi-asserted-by":"publisher","DOI":"10.1063\/5.0150687","article-title":"A superconducting synapse exhibiting spike-timing dependent plasticity","volume":"122","author":"Segall","year":"2023","journal-title":"Appl. Phys. Lett."},{"key":"ncead207abib33","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TASC.2021.3138369","article-title":"A new family of biosfq logic and memory cells","volume":"32","author":"Semenov","year":"2022","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ncead207abib34","doi-asserted-by":"publisher","first-page":"2452","DOI":"10.1109\/20.133715","article-title":"Sensitivity of the balanced Josephson-junction comparator","volume":"27","author":"Filippov","year":"1991","journal-title":"IEEE Trans. Magn."},{"key":"ncead207abib35","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TASC.2019.2904919","article-title":"Advanced fabrication processes for superconductor electronics: current status and new developments","volume":"29","author":"Tolpygo","year":"2019","journal-title":"IEEE Trans. Appl. Supercond."},{"article-title":"WRspice reference manual. Whiteley research inc","year":"2022","author":"Whiteley","key":"ncead207abib36"},{"key":"ncead207abib37","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TASC.2021.3063329","article-title":"Gray zone and threshold current measurements of the Josephson balanced comparator","volume":"31","author":"Filippov","year":"2021","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ncead207abib38","doi-asserted-by":"publisher","first-page":"747","DOI":"10.1109\/TASC.2003.814027","article-title":"Digital SQUIDs: new definitions and results","volume":"13","author":"Semenov","year":"2003","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ncead207abib39","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TASC.2017.2759239","article-title":"Design for testability of SFQ circuits","volume":"27","author":"Krylov","year":"2017","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ncead207abib40","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TASC.2019.2896137","article-title":"Clockless dynamic SFQ and gate with high input skew tolerance","volume":"29","author":"Rylov","year":"2019","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ncead207abib41","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TASC.2020.2978428","article-title":"Asynchronous dynamic single flux quantum majority gates","volume":"30","author":"Krylov","year":"2020","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ncead207abib42","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TASC.2021.3070802","article-title":"Splitter trees in single flux quantum circuits","volume":"31","author":"Jabbari","year":"2021","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ncead207abib43","first-page":"pp 384","article-title":"Design of multiple fanout clock distribution network for rapid single flux quantum technology","author":"Katam","year":"2017"},{"key":"ncead207abib44","doi-asserted-by":"publisher","first-page":"2438","DOI":"10.1109\/TVLSI.2020.3023054","article-title":"Design methodology for distributed large scale ERSFQ bias networks","volume":"28","author":"Krylov","year":"2020","journal-title":"IEEE Trans. Very Large Scale Integr. (VLSI) Syst."}],"container-title":["Neuromorphic Computing and Engineering"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2634-4386\/ad207a","content-type":"text\/html","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2634-4386\/ad207a\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2634-4386\/ad207a","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2634-4386\/ad207a\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2634-4386\/ad207a\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2634-4386\/ad207a\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2634-4386\/ad207a\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2634-4386\/ad207a\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,23]],"date-time":"2024-02-23T08:59:02Z","timestamp":1708678742000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2634-4386\/ad207a"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,23]]},"references-count":44,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,2,23]]},"published-print":{"date-parts":[[2024,3,1]]}},"URL":"https:\/\/doi.org\/10.1088\/2634-4386\/ad207a","relation":{},"ISSN":["2634-4386"],"issn-type":[{"type":"electronic","value":"2634-4386"}],"subject":[],"published":{"date-parts":[[2024,2,23]]},"assertion":[{"value":"Harnessing stochasticity for superconductive multi-layer spike-rate-coded neuromorphic networks","name":"article_title","label":"Article Title"},{"value":"Neuromorphic Computing and Engineering","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2024 The Author(s). Published by IOP Publishing Ltd","name":"copyright_information","label":"Copyright Information"},{"value":"2023-08-04","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2024-01-19","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2024-02-23","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}