Stochastic Quantum Spiking Neural Networks with Quantum Memory and Local Learning

TL;DR

A novel stochastic quantum spiking neuron model, dubbed SQS neural networks (SQSNN), is proposed that can be trained via a hardware-friendly local learning rule, eliminating the need for global classical backpropagation.

Abstract

Neuromorphic and quantum computing have recently emerged as promising paradigms for advancing artificial intelligence, each offering complementary strengths. Neuromorphic systems built on spiking neurons excel at processing time series data efficiently through sparse, event-driven computation, consuming energy only upon input events. Quantum computing, on the other hand, operates on state spaces that grow exponentially in dimension with the number of qubits -- as a consequence of tensor-product composition -- with quantum states admitting superposition across basis states and entanglement between subsystems. Hybrid approaches combining these paradigms have begun to show potential, but existing quantum spiking models have important limitations. Notably, they implement classical memory mechanisms on single qubits, requiring repeated measurements to estimate firing probabilities, while relying on conventional backpropagation for training. In this paper, we propose a novel stochastic quantum spiking (SQS) neuron model that addresses these challenges. The SQS neuron uses multi-qubit quantum circuits to realize a spiking unit with internal quantum memory, enabling event-driven probabilistic spike generation in a single shot during inference. Furthermore, we study networks of SQS neurons, dubbed SQS neural networks (SQSNN), and demonstrate that they can be trained via a hardware-friendly local learning rule, eliminating the need for global classical backpropagation. The proposed SQSNN model is shown via experiments with both conventional and neuromorphic datasets to improve over previous quantum spiking neural networks, as well as over classical counterparts, when fixing the overall number of trainable parameters.

Figures (11)

• Figure 1: Schematic of an SQS neuron with $N=3$ input-output qubits (green) and $N_{\rm mem}=3$ memory qubits (orange), receiving input from $P$ presynaptic neurons. At each time $t$, incoming presynaptic spikes are weighted into input currents $\hbox{\boldmath{$z$}}_t = [z_t^1,\ldots,z_t^N]$. The currents determine rotation angles $\hbox{\boldmath{$\phi$}}_t$ applied to the input qubits (blue gates). A parameterized quantum circuit (PQC, gray box) with trainable parameters $\hbox{\boldmath{$\theta$}}$ entangles input and memory qubits, updating the neuron’s state. The $N$ input qubits are then measured (meter symbols) to produce output spikes $\hbox{\boldmath{$s$}}_t$ (red arrows), after which those qubits are reset to the ground state $|0\rangle$. The memory qubits are not measured, preserving quantum information (orange shading) that influences subsequent time steps. This internal quantum memory allows the SQS neuron to exhibit complex temporal dynamics, while not requiring multi-shot measurements.
• Figure 2: Schematic of the QLIF neuron with $P$ presynaptic inputs brand2024quantum. A single qubit (green) serves as the neuron’s internal state, evolving in discrete time steps via a measure-and-prepare scheme. At each time $t$, input spikes from $P$ presynaptic neurons are weighted (blue arrows) and encoded as a rotation $\phi_t$ on the qubit. The qubit is measured multiple times to estimate a spike probability (red arrow), which is compared against a threshold to decide if the neuron fires. This design requires repeated quantum measurements and uses a classical memory (accumulated threshold voltage), mimicking a leaky integrate-and-fire process.
• Figure 3: Illustration of the connection between a set of $P$ presynaptic neurons and the SQS neuron of interest. The $n$-th input current $z_{t}^n$ of the SQS neuron is computed as the weighted sum of the corresponding spiking signal $\{x_{t,p}^n\}_{p=1}^P$ from the $P$ presynaptic neurons as in equation \ref{['current']}.
• Figure 4: Illustration of an SQS-based neural network (SQSNN) with six neurons ($\mathcal{S}=\{1,\dots,6\}$). Edges $(i \to j)$ indicate neuron $i$ feeds into neuron $j$. Neurons $\{1,2,3,4,5\}$ are hidden, and neuron $6$ is the only output neuron ($\mathcal{O}=\{6\}$). Output neurons have no outgoing edges. Each node is an SQS neuron as in Fig. \ref{['gmodel']}, with a self-loop denoting dependence on its own past spikes. The network’s joint spike probability factorizes along these connections: e.g., neuron $6$’s spiking at time $t$ depends only on the past spikes of neurons 4, 5 (its parents, denoted as $\mathcal{P}_6$) and on its own past spikes.
• Figure 5: Illustration of the proposed local zero-th order learning rule. At each iteration, the proposed local zeroth-order learning rule implements: ① $M$ global forward passes, where $M$ is a constant $M$ independent of the number of parameters, ② the evaluation of $M$ global feedback signals at the output SQS neurons, and ③ local perturbation-based, zeroth-order updates within each neuron.