Superconducting Optoelectronic Circuits for Neuromorphic Computing

Neural networks have proven effective for solving many difficult computational problems, yet implementing complex neural networks in software is computationally expensive. To explore the limits of information processing, it is necessary to implement new hardware platforms with large numbers of neurons, each with a large number of connections to other neurons. Here we propose a hybrid semiconductor-superconductor hardware platform for the implementation of neural networks and large-scale neuromorphic computing. The platform combines semiconducting few-photon light-emitting diodes with superconducting-nanowire single-photon detectors to behave as spiking neurons. These processing units are connected via a network of optical waveguides, and variable weights of connection can be implemented using several approaches. The use of light as a signaling mechanism overcomes fanout and parasitic constraints on electrical signals while simultaneously introducing physical degrees of freedom which can be employed for computation. The use of supercurrents achieves the low power density ($1\mathrm{mW}/{\mathrm{cm}}^2$ at 20-MHz firing rate) necessary to scale to systems with enormous entropy. Estimates comparing the proposed hardware platform to a human brain show that with the same number of neurons ($10^{11}$) and 700 independent connections per neuron, the hardware presented here may achieve an order of magnitude improvement in synaptic events per second per watt.

Figure 1

Schematic representation of the proposed device concept. SC, superconducting; SNSPD, superconducting-nanowire single-photon detector; Rx, receive; Tx, transmit; WG waveguide.

Figure 2

(a) PND neuron circuit. (b) A PND with all wires superconducting. (c) A PND where one of the wires is driven normal by absorption of a single photon, redirecting the current through the other four. (d) A PND with two normal wires due to absorption of two photons. (e) A PND with all wires driven normal by exceeding the critical current. A LED in parallel with this PND now receives current, causing a firing event.

Figure 3

Monte Carlo simulation of spike probability. (a) PND with ten SNSPDs. (b) The same simulation as (a) but with four traces isolated for clarity. (c) The number of absorbed photons which gives a 50% absorption probability plotted as a function of bias current. Traces for PNDs with 10, 20, and 40 nanowires are shown.

Figure 4

The spiderweb neuron. The scale bar is shown for reference, but significantly more compact implementations of this device can be achieved.

Figure 5

(a) SND circuit. (b) Component diagram indicating either SND or PND array. This circuit symbol is used throughout this article.

Figure 6

Electrical characteristics for SND with $l_{\mathrm{wire}}=100\mu \mathrm{m}$. (a) Resistance versus number of photons for the SND. Inset shows the exponential current-voltage curve for the LED. Photons out versus photons in for SNDs with (b) $i_c=4\mu \mathrm{A}$, $\eta =1\%$ and (c) $i_c=8\mu \mathrm{A}$, $\eta =0.1\%$. Here, $\eta$ is the efficiency of the LED.

Figure 7

Various neuromorphic circuit configurations. (a) PND with nTron amplifier. (b) Integrate-and-stop firing. (c) Neuron with the possibility for both excitatory and inhibitory excitation. In this figure, green corresponds to photons inhibiting firing and red to photons exciting firing. These photons can have different colors. (d) Firing of the upper neuron inhibits firing of the lower neuron. (e) Circuit for achieving self- and upstream feedback.

Figure 8

(a) Energy required to generate a single photon versus number of photons emitted for four different LED efficiencies. (b) Contributions to total energy consumption for a 10% efficient LED.

Figure 9

Schematic of a monolithically integrated electrically injected emissive-center LED in Si for the proposed neuromorphic computing application.

Figure 10

The spiderweb neuron. (a) Overview of the device. (b) Dendritic arbor design which combines light from multiple neurons.

Figure 11

(a) Schematic overview of the stingray neuron. (b) FDTD simulation of the dendritic arbor for the stingray neuron with SNSPDs present to absorb the light and (c) without SNSPDs present.

Figure 12

Photonic synapses with electromechanically tunable coupling. (a) Interplane waveguide coupler. (b) Lateral waveguide coupler. The inset shows an abstract representation of the synaptic circuit element used in subsequent network diagrams.

Figure 13

Abstract symbol definition for general neuron with inhibition and gain.

Figure 14

(a) Schematic of the MLP implemented with the SOEN platform. (b) Cross section in the $x\text{−}z$ plane. (c) Three-dimensional schematic of stacked die. (a) illustrates layers of neurons in the network, (b) illustrates planes of routing waveguides, and (c) illustrates sheets of stacked die.

Figure 15

(a) Length and width of layer versus number of neurons in a layer assuming each neuron in a given layer is connected to each neuron in the next layer. (b) Number of neurons per centimeter squared versus the number of connections per neuron.

Figure 16

Schematic of a SOEN model of the mammalian visual cortex.

Figure 17

Absorption of light propagating in a waveguide with SNSPD on top in (a) parallel and (b) perpendicular configurations, for different spacer heights between the SNSPD and waveguide. (c) Absorption in waveguides of different thicknesses for different spacer heights.

Figure 18

Mean number (a) and standard deviation (b) of absorbed photons versus number of incident photons for neuron designs where light is directed past each nanowire once (single pass). Mean number (c) and standard deviation (d) of absorbed photons versus number of incident photons for neuron designs where light is directed past each nanowire ten times.

Figure 19

Flux-dissipating version of the spiderweb neuron.

Figure 20

(a) Flux-trapping PND circuit. (b) An alternative PND design which avoids flux trapping.

Figure 21

Effective indices of refraction for various guided modes in a waveguiding layer with index of refraction $n=3.52$ and cladding $n=1.46$. (a) Slab mode calculations of both TE and TM modes for different film thicknesses showing different vertical mode orders. (b) TE and TM modes for different waveguide widths in a film of height 200 nm. The cladding index is shown as the dashed line in both (a) and (b).

Figure 22

Supermode propagation constants for 200-nm-thick, 350-nm-wide waveguides with 3.52 core index and 1.46 cladding index at $\lambda =1220\mathrm{nm}$. The inset shows the fractional splitting, and the mode profiles show the symmetric mode for gaps of 100 and 600 nm.