A Quantum Leaky Integrate-and-Fire Spiking Neuron and Network

TL;DR

This work addresses scalability and energy efficiency in quantum machine learning by proposing a Quantum Leaky Integrate-and-Fire (QLIF) neuron implemented as a two-gate, single-qubit circuit using $R_X$ rotations and $T_1$-driven leakage. These neurons serve as building blocks for Quantum Spiking Neural Networks (QSNN) and Quantum Spiking Convolutional Neural Networks (QSCNN), trained with backpropagation through time (BPTT) and SpikeProp using surrogate gradients and the arctan formulation. The authors demonstrate competitive accuracy on MNIST, Fashion-MNIST, and Kuzushiji-MNIST, while achieving substantial speedups in simulation and showing robustness to noise, highlighting the practicality of quantum neuromorphic computing on NISQ devices. Overall, the paper presents a compact, hardware-friendly quantum neuromorphic approach that leverages minimal circuit depth and natural quantum noise to perform temporal processing efficiently.

Abstract

Quantum machine learning is in a period of rapid development and discovery, however it still lacks the resources and diversity of computational models of its classical complement. With the growing difficulties of classical models requiring extreme hardware and power solutions, and quantum models being limited by noisy intermediate-scale quantum (NISQ) hardware, there is an emerging opportunity to solve both problems together. Here we introduce a new software model for quantum neuromorphic computing -- a quantum leaky integrate-and-fire (QLIF) neuron, implemented as a compact high-fidelity quantum circuit, requiring only 2 rotation gates and no CNOT gates. We use these neurons as building blocks in the construction of a quantum spiking neural network (QSNN), and a quantum spiking convolutional neural network (QSCNN), as the first of their kind. We apply these models to the MNIST, Fashion-MNIST, and KMNIST datasets for a full comparison with other classical and quantum models. We find that the proposed models perform competitively, with comparative accuracy, with efficient scaling and fast computation in classical simulation as well as on quantum devices.

Figures (6)

• Figure 1: A low-pass filter resistor-capacitor (RC) circuit of the LIF neuron. The circuit describes how membrane potential dynamics of a neuron are simulated by a time-varying input current $I_\mathrm{in}$. The membrane potential, $U(t)$, is decomposed into a resistor and capacitor which form a linear differential equation describing a spiking neuron.
• Figure 2: A Quantum Leaky Integrate-and-Fire (QLIF) neuron processing input spike stimuli. Spikes to the excited state population are modelled through rotation gates ($R_X$). The lack of a spike is processed as a delay gate ($\Delta$), during which the qubit does nothing for a time $t$, and the excited state population decays exponentially. In the construction of a QLIF neural network, multiple inputs are aggregated through the dendrites to produce a set of outputs after being processed by the neuron.
• Figure 3: Compact circuit structure of a QLIF neuron processing binary spike input stimulus. Input spikes are processed as rotation gates ($R_X$) to increase the excited state population. Absent input spikes are processed as delay gates ($\Delta$), during which the qubit does nothing for a short period of time and is decayed by noise from the environment. Due to the simple circuit structure, the previous state can be compacted to a single rotation gate which can re-instate the excited state population of the previous measurement. This serves as the memory of the neuron, before the next input is processed.
• Figure 4: Classical LIF vs QLIF neuron behaviour processing a train of input spikes, producing a series of output spikes based on a threshold shown by the grey dashed line. Input spikes are randomly generated here, and processed over 60 time-steps by the LIF and QLIF neurons to demonstrate the behavioural similarity between the neurons. Classical LIF membrane potential is shown in blue, while the QLIF excited state population is shown in magenta.
• Figure 5: A Quantum Spiking Neural Network structure, processing an image converted to brightness values and then to spike trains to pass through the network. The network trains two planes of weighted synapses ($\theta$ and $\tau$) in parallel for each neuron. The parameter $\theta$ controls the spike intensity through the angle of the $R_X$ rotation gate. The parameter $\tau$ controls the decay rate through the delay gate $\Delta$, during which the qubit is left to idle and undergo relaxation to a ground state (Bottom right). Only one of these operations occurs based on the binary input, after a memory rotation gate which reinstates the excited state of the previous time step measurement (Top left). Each neuron processes a series of input spikes/no-spikes (Bottom left). Throughout the diagram $\theta$ is blue and $\tau$ is magenta.