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Journal of Applied Physics

Spiking neuron circuits using superconducting quantum phase-slip junctions

Ran Cheng, Uday S. Goteti, Michael C. Hamilton

Published Oct 9, 2018• 52 citations
Publisher

Abstract

Superconducting circuits that operate by propagation of small voltage or current pulses, corresponding to propagation of single flux or charge quantum, are naturally suited for implementing spiking neuron circuits. Quantum phase-slip junctions (QPSJs) are 1-D superconducting nanowires that have been identified as exact duals to Josephson junctions, based on charge-flux duality in Maxwell’s equations. In this paper, a superconducting quantized-charge circuit element, formed using quantum phase-slip junctions, is investigated for use in high-speed, low-energy superconducting spiking neuron circuits. By means of a SPICE model developed for QPSJs, operation of this superconducting circuit to produce and transport quantized charge pulses, in the form of current pulses, is demonstrated. The resulting quantized-charge-based operation emulates spiking neuron circuits for brain-inspired neuromorphic applications. Additionally, to further demonstrate the operation of QPSJ-based neuron circuits, a QPSJ-based integrate and fire neuron circuit is introduced, along with simulation results using WRSPICE. Estimates for operating speed and power dissipation are provided and compared to Josephson junction and CMOS-based spiking neuron circuits. Current challenges are also briefly mentioned.

DOI
10.1063/1.5042421

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Superconducting circuits that operate by propagation of small voltage or current pulses, corresponding to propagation of single flux or charge quantum, are naturally suited for implementing spiking neuron circuits. Quantum phase-slip junctions (QPSJs) are 1-D superconducting nanowires that have been identified as exact duals to Josephson junctions, based on charge-flux duality in Maxwell’s equations. In this paper, a superconducting quantized-charge circuit element, formed using quantum phase-slip junctions, is investigated for use in high-speed, low-energy superconducting spiking neuron circuits. By means of a SPICE model developed for QPSJs, operation of this superconducting circuit to produce and transport quantized charge pulses, in the form of current pulses, is demonstrated. The resulting quantized-charge-based operation emulates spiking neuron circuits for brain-inspired neuromorphic applications. Additionally, to further demonstrate the operation of QPSJ-based neuron circuits, a QPSJ-based integrate and fire neuron circuit is introduced, along with simulation results using WRSPICE. Estimates for operating speed and power dissipation are provided and compared to Josephson junction and CMOS-based spiking neuron circuits. Current challenges are also briefly mentioned.
Superconducting digital computing systems, primarily involving Josephson junctions are actively being pursued as high performance and low energy dissipating alternatives to CMOS-based technologies for petascale and exascale computers, although several challenges still exist in overcoming barriers to practically implement these technologies. In this paper, we present an alternative superconducting logic structure: quantized charge-based logic circuits using quantum phase-slip junctions, which have been identified as dual devices to Josephson junctions. Basic principles of logic implementation using quantum phase-slips are presented in simulations with the help of a SPICE model that has been developed for the quantum phase-slip structures. Circuit elements that form the building blocks for complex logic circuit design are introduced. Two different logic gate designs: or gate and xor gate are presented to demonstrate the usage of the building blocks introduced.
Quantum phase‐slips, which are the exact duals of Josephson junctions (JJs), are promising for several applications in classical and quantum superconducting electronic circuits. The experimental testing of the phase‐slip phenomena and identifying these applications has been challenging. In this reported work, the use of a dual to a JJ model to implement a SPICE model of a quantum phase‐slip junction (QPSJ) in JSPICE3, in order to explore possible circuit applications, is demonstrated. A transient analysis model of the device is presented and an example of an I–V curve simulation of the device, along with a simulation of a possible circuit application of the device, are also shown.
In this paper, we explore a new set of circuits that incorporate both single-flux-quantum and quantized charge-based complementary quantum logic circuits. Circuits that convert single-flux quantum voltage pulses to quantized charge pulses and vice versa, leading to circuits that simplify logic and integration operations of individual flux and charge-based logic circuits, are introduced. These include fan-out circuits that enable single flux input to several charge outputs as well as control gate circuit with charge input controlling flux output. The operation of these circuits is demonstrated in simulations using WRSPICE. An XOR gate implementation is presented as an example to illustrate the operation of these circuits. The developed complementary quantum logic circuits show promise for higher power efficiency and simpler design in the form of fewer junctions for a given logic implementation, leading to the possibility of higher integration density.
In this article, the quantum phase slip junction (QPSJ) based full adder, multiplexer, and demultiplexer memoryless circuits for superconducting digital applications are designed for the first time. Generally, the memoryless circuits are implemented by interconnection of the basic gates (i.e., AND, OR, NOT). So in this article, the structures of the QPSJ-based AND and OR gates are also modified in order to reduce the complexity of their connections to the other gates by removing or changing the location of the clock pulse from their output branches. When a gate is connected to the next one, the elements of the second gate are loaded to the circuit of the first gate. The output current of the first gate will be affected due to this loading and no Cooper pair may be produced at its output and the next connected gate will not be switched. Therefore, the main tip in designing of these circuits is that each constituent gate must provide the necessary output current to drive the next connected gates, since each gate is driven by one Cooper pair. In this article, providing sufficient output current for each gate has been observed by 1) selecting proper critical voltages of the QPSJs and 2) by adding extra elements to or removing some elements from the connected gates in the proposed memoryless circuits.
Abstract Quantum circuit theory is a powerful tool to describe superconducting circuits. In its language, quantum phase slips (QPSs) are considered to be the exact dual to the Josephson effect. This duality renders the integration of QPS junctions into a unified theoretical framework challenging. As we argue, different existing formalisms may be inconsistent, and the correct inclusion of time-dependent flux driving requires introducing a large number of auxiliary, nonphysical degrees of freedom. We resolve these issues by describing QPS junctions as inductive rather than capacitive elements, and reducing the Hilbert space to account for a compact superconducting phase. Our treatment provides an approach to circuit quantization exclusively in terms of node-flux-node variables, and eliminates spurious degrees of freedom. Finally, the inductive treatment reveals the possibility of a voltage-dependent renormalization of the QPS amplitude, by accounting for spatial variations of the electric field built up across the junction.
Superconducting Josephson junctions and quantum phase slip (QPS) junctions create various hybrid circuits combined with nonsuperconducting elements. Those circuits require a common analysis method to bridge the gap between superconducting and nonsuperconducting electronics. This article presents an electromagnetic-flux-distribution model to unify the analyses of superconducting and non-superconducting circuits. This model uses electric and magnetic fluxes as the variables to unify the definitions of circuit elements and circuit laws; it derives general circuit equations of the circuits viewed from both electric and magnetic fields, to depict their dynamics and duality principles. This method is demonstrated in the analyses of a Josephson junction circuit and its dual QPS junction circuit. It shows that Josephson junction circuits are the magnetic-flux distribution network tuned by the Josephson current, while QPS junction circuits are the electric-flux distribution network modulated by the QPS voltage.