Synchronization dynamics on the picosecond timescale in coupled Josephson junction neurons

📝 Abstract

Conventional digital computation is rapidly approaching physical limits for speed and energy dissipation. Here we fabricate and test a simple neuromorphic circuit that models neuronal somas, axons and synapses with superconducting Josephson junctions. The circuit models two mutually coupled excitatory neurons. In some regions of parameter space the neurons are desynchronized. In others, the Josephson neurons synchronize in one of two states, in-phase or anti-phase. An experimental alteration of the delay and strength of the connecting synapses can toggle the system back and forth in a phase-flip bifurcation. Firing synchronization states are calculated >70,000 times faster than conventional digital approaches. With their speed and low energy dissipation (10-17 Joules/spike), this set of proof-of- concept experiments establishes Josephson junction neurons as a viable approach for improvements in neuronal computation as well as applications in neuromorphic computing.

💡 Analysis

Conventional digital computation is rapidly approaching physical limits for speed and energy dissipation. Here we fabricate and test a simple neuromorphic circuit that models neuronal somas, axons and synapses with superconducting Josephson junctions. The circuit models two mutually coupled excitatory neurons. In some regions of parameter space the neurons are desynchronized. In others, the Josephson neurons synchronize in one of two states, in-phase or anti-phase. An experimental alteration of the delay and strength of the connecting synapses can toggle the system back and forth in a phase-flip bifurcation. Firing synchronization states are calculated >70,000 times faster than conventional digital approaches. With their speed and low energy dissipation (10-17 Joules/spike), this set of proof-of- concept experiments establishes Josephson junction neurons as a viable approach for improvements in neuronal computation as well as applications in neuromorphic computing.

📄 Content

Synchronization dynamics on the picosecond timescale in coupled Josephson junction neurons K. Segall1, M. LeGro1, S. Kaplan2, O. Svitelskiy1, S. Khadka1, P. Crotty1 and D. Schult3

1 Department of Physics and Astronomy, Colgate University, 13 Oak Drive, Hamilton, NY 13346 2 Consultant, 1800 Cherokee Drive, Estes Park CO, 80517 3 Department of Mathematics, Colgate University, 13 Oak Drive, Hamilton, NY 13346

Abstract: Conventional digital computation is rapidly approaching physical limits for speed and energy dissipation. Here we fabricate and test a simple neuromorphic circuit that models neuronal somas, axons and synapses with superconducting Josephson junctions. The circuit models two mutually coupled excitatory neurons. In some regions of parameter space the neurons are desynchronized. In others, the Josephson neurons synchronize in one of two states, in-phase or anti-phase. An experimental alteration of the delay and strength of the connecting synapses can toggle the system back and forth in a phase-flip bifurcation. Firing synchronization states are calculated >70,000 times faster than conventional digital approaches. With their speed and low energy dissipation (10-17 Joules/spike), this set of proof-of- concept experiments establishes Josephson junction neurons as a viable approach for improvements in neuronal computation as well as applications in neuromorphic computing.
Introduction The collective behavior of neural systems is a highly active area of study. It addresses basic questions from two major scientific challenges: understanding the human brain and building an efficient artificial learning processor. These questions require interdisciplinary examination, and even so are hard to make progress on. One approach takes a bottom-up approach, building and studying neural circuits at the cellular level. Another approach works top-down, looking to understand and emulate behaviors like synchronization,1 information processing and memory.
Model systems are a useful tool to go between top-down and bottom-up approaches. One can simulate neuron behaviors in a network of cellular-level objects. Digital simulations can model the time-dependent membrane potentials of large numbers of neurons, but are often limited by computational time. Analog models, such as electrical Very Large Scale Integration (VLSI) circuits, sacrifice a certain amount of detail in their simulation capability, but can simulate the interactions in parallel, much faster than digital simulations. In fact, analog models have the capability to go faster2,3 than the biology, potentially enabling studies of long-term behavior, learning and various neurological disorders.
In addition to providing a better understanding of neuroscience, analog model systems can be used to create artificial learning devices. Analog and digital neurons can be networked to form new kinds of “neuromorphic” processors that will help process complex and high-volume data.4,5 Tasks which deal with complex data, such as pattern recognition, are often inefficient when run on von Neumann-type machines. Neuromorphic circuits in silicon have been demonstrated modeling somas6 and synapses, have shown plasticity7 and learning, and have been integrated to the system level.4,8
The results can include much quicker runtimes, smaller size processors, and higher energy efficiency when dealing with such tasks.5
Power dissipation is a serious issue if computational neuron models and neuromorphic processors are to be scaled to large network sizes.9 Biological neurons dissipate about 10-11 Joules per spike. Neurons made from silicon circuits, however, are over 3 orders of magnitude higher than that at about 2x10-8 Joules/spike and digital neurons are even

Figure 1: Experimental details: (a) Block-diagram of the experiment. The first soma-axon-synapse (N1-A1-S1) combination is coupled to the second (N2-A2-S2); this mutually coupled loop (marked by the green dashed line) falls into a synchronized state. A copy of the pulses are coupled out onto JTLs (JTL1 and JTL2) and merged together in an OR gate. The in-phase state will fire at the same frequency as the neurons; the anti-phase state will fire at twice the frequency. (b) Circuit diagram of the two somas, N1 and N2. The X’s indicate Josephson junctions. Two currents, INB and Iin, bias the soma. (c) Circuit diagram of the synapse. A two-junction loop (DC SQUID) modifies the amplitude of the pulse coming in from the axon. Two currents (ISB and Imag) control the amount of modulation.
Following the SQUID, an LRC-filter smoothes the pulse; this converts it into a synaptic current. (d) Optical microscope picture of the circuit. The mutually-coupled loop is indicated by the green box, and the S2-N1 combination is indicated by the yellow box. The outputs voltages for the two JTLs and the OR gate are indicated; two other output voltages (not indicated) are ta

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