Superconducting disordered neural networks for neuromorphic processing with fluxons

Abstract

In superconductors, magnetic fields are quantized into discrete fluxons (flux quanta Φ₀), made of microscopic circulating supercurrents. We introduce a multiterminal synapse network comprising a disordered array of superconducting loops with Josephson junctions. The loops can trap fluxons defining memory, while the junctions allow their movement between loops. Dynamics of fluxons through such a disordered system through a complex reconfigurable energy landscape represents brain-like spiking information flow. In this work, we experimentally demonstrate a three-loop network using YBa₂Cu₃O_{7 - δ}-based superconducting loops and Josephson junctions, which exhibit stable memory configurations of trapped flux in loops that determine the rate of flow of fluxons through synaptic connections. The memory states are, in turn, affected by the applied input signals but can also be externally configured electrically through control current/feedback terminals. These results establish a previously unexplored, biologically similar architectural approach to neuromorphic computing that is scalable while dissipating energy of atto Joules/spike.

Fig. 1.. Schematic of four by four superconducting disordered loop neural networks with helium ion beamdefined Josephson junctions.

(A) Synapse network with four input, four output, and four control current/feedback channels to represent all the individual synaptic connections of the recurrent neural network shown in (B). The network comprises 10 superconducting loops connected through various Josephson junctions of different sizes. Incoming and outgoing spike trains are schematically represented for terminals I₁ and O₁. The input spike trains from all the terminals are converted into current pulses that take various time-dependent paths through Josephson junctions shown as i₁, i₂, etc. Some current pulses switch Josephson junctions above their critical currents and are stored as circulating currents in adjacent loops (i.e., flux perpendicular to the plane), representing the memory state of the synapse. The switching event and the generation/transfer of flux quanta are schematically shown using the dotted circle, and the flux stored in various loops is represented as n₁Φ₀, n₂Φ₀, etc. (B) Schematic of an equivalent recurrent neural network with four input (labeled I₁, I₂, I₃, and I₄), four output channels (labeled O₁, O₂, O₃, and O₄), and four external control current/feedback channels for external memory configuration. (C) Flux quanta propagation through the synapse network shown in (A). Flux can get trapped in loops and can propagate along different paths through the junctions to various output terminals. Variations in memory states result in differences in populations of flux quanta at each of the outputs.

Fig. 2.. Experimental three-loop one by one superconducting disordered neural network.

(A) Optical microscope image of a YBCO-based three-loop network with focused helium ion Josephson junctions used in the experiment to study the synaptic properties between one input-output terminal pair shown as I₁ and O₁. A control current parameter with current flowing between B₁ and the ground can be used to change the memory configurations. Experiments involve excitation of the device with currents I₁ and B₁. The input and the control current are also varied in time relative to each other. (B) Schematic of a three-loop network showing currents and flux configurations in memory state S₁. Outgoing flux corresponds to anticlockwise-circulating currents in loop 2. (C) Three-loop network schematic showing memory state S₂ with an outgoing flow rate of zero. Currents and flux configuration correspond to the superconducting state of junction at O₁, with the current difference i₂ − i₃ below its critical current. (D) Three-loop network schematic showing memory state S₄ with increased outgoing flux flow. One of the junctions in loop 3 is in the superconducting state (i.e., i₅ − i₆ below its critical current), resulting in additional current diverted to the output. (E) Three-loop network schematic showing memory state S₅ with outgoing flux corresponding to clockwise-circulating current in loop 2.

Fig. 3.. Electrical characteristicsstatic operation.

Current-voltage characteristics of the three-loop network shown in Fig. 2 corresponding to the experimental results of static operation. (A) Current at input I₁ continuously varied between −1 and 1 mA is plotted against the measured input voltage V_I1, while a constant control current is applied at B₁. Ten different measurements corresponding to currents at B₁ with values from 0 to 90 μA with an increment of 10 μA are plotted. (B) Current at input I₁ continuously varied between −1 and 1 mA is plotted against the measured output voltage V_O1 at different constant control currents B₁ ranging from 0 to 90 μA with an increment of 10 μA. (C) Current at B₁ continuously varied between −90 and 90 μA is plotted against the measured input voltage V_I1 while a constant input current is applied at I₁ (constant values ranging between 0 and 200 μA with an increment of 20 μA). (D) Current at B₁ continuously varied between −90 and 90 μA is plotted against the measured input voltage V_O1 while a constant input current is applied at I₁ (constant values ranging between 0 and 200 μA with an increment of 20 μA).

Fig. 4.. Evolution of memory states observed as different rates of flow of flux.

Experimental observation of stable memory states in superconducting synapse networks in the form of rate of flow of flux between input-output terminals defined in a state space of voltages (or frequencies of spiking signals into the network) and control currents. (A) Rate of flow of flux quanta ($\frac{d{V}_{O1}}{d{V}_{I1}}$) through the three-loop disordered array synapse network (Fig. 2A) measured at 28 K while varying the input voltage V_I1 (or corresponding current I₁) at different constant current biases B₁. The curves are offset in the y axis, with an offset value proportional to control current B₁ (i.e., an offset of 0.2 per 1 μA of B₁). Stable memory states are observed as constant rates of flow of flux labeled from S₁ to S₅. Three stable states exist at B₁ of 0 μA, with two new states emerging as B₁ are increased. (B) Rate of flow of flux quanta ($\frac{d{V}_{O1}}{d{V}_{I1}}$) through the three-loop synapse network (Fig. 2A) measured while continuously varying the input voltage V_O1 (or corresponding current B₁) at different constant current inputs I₁. Three different stable memory states are revealed initially, with two additional emergent states as I₁ is increased. The curves are offset in the y axis, with an offset value proportional to control current B₁ (i.e., an offset 1 per 2 μA of I₁). The voltages at which these states occur, and the width of the states can be configured using I₁.

Fig. 5.. Dynamic transitions between memory states dependent on relative phase difference of input signals.

Dynamic memory states and the corresponding state transitions experimentally observed in the state space of V_I1 and V_O1 as the phase difference δ is varied from 0 to 2π between sinusoidal current inputs I₁ and B₁, both 1 Hz of frequency and 1 mA and 100 μA of amplitudes, respectively. The movement of states and the state transitions around the space as δ is varied are labeled T₁, T₂, and T₃.

Fig. 6.. Electrical scan of state space of operation of the three-loop one by one superconducting neural network.

Dynamic memory states and the corresponding state transitions experimentally observed in the state space of V_I1 and V_O1, as the frequency of sinusoidal control current B₁ is varied from 1 to 100 Hz with the input current at 1 Hz. The amplitudes of I₁ and B₁ are 1 mA and 100 μA, respectively. (A) $\frac{f_{I1}}{f_{B1}}=1$. (B) $\frac{f_{I1}}{f_{B1}}=1/2$. (C) $\frac{f_{I1}}{f_{B1}}=1/3$. (D) $\frac{f_{I1}}{f_{B1}}=1/4$. (E) $\frac{f_{I1}}{f_{B1}}=1/5$. (F) $\frac{f_{I1}}{f_{B1}}=1/10$. (G) $\frac{f_{I1}}{f_{B1}}=1/20$. (H) $\frac{f_{I1}}{f_{B1}}=1/50$. (I) $\frac{f_{I1}}{f_{B1}}=1/100$. Different memory states, labeled from S₁ to S₁₃, and transitions between them can be observed that overlap with the states observed in Fig. 4 (A and B).