Canonical Quantization of a Memristive Leaky Integrate-and-Fire Neuron Circuit

TL;DR

The paper addresses the challenge of unifying quantum dynamics with memory-enabled neuromorphic computing by developing a fully quantized memristive LIF neuron. It achieves this via a canonical quantization that replaces a dissipative memristor with a transmission-line bath, yielding a microscopic Hamiltonian and a GKSL-based open-system description that reproduces classical memristive LIF behavior in the adiabatic, weak-coupling limit. The work introduces a quantum memristor and a quantum LIF neuron, demonstrates memristive I–V hysteresis and spiking behavior, and shows improved sound localization performance over classical and phenomenological quantum models in a Jeffress-style benchmark. This framework provides a principled foundation for quantum neuromorphic computing and suggests a path toward quantum spiking networks and quantum machine learning with memory-enabled neural elements.

Abstract

We present a theoretical framework for a quantized memristive Leaky Integrate-and-Fire (LIF) neuron, uniting principles from neuromorphic engineering and open quantum systems. Starting from a classical memristive LIF circuit, we apply canonical quantization techniques to derive a quantum model grounded in circuit quantum electrodynamics. Numerical simulations demonstrate key dynamical features of the quantized memristor and LIF neuron in the weak-coupling and adiabatic regime, including memory effects and spiking behavior. Applications of this model to a sound localization benchmark show that it outperforms a phenomenological quantum LIF model as well as a classical LIF. This work establishes a foundational model for quantum neuromorphic computing, offering a pathway towards biologically inspired quantum spiking neural networks and new paradigms in quantum machine learning.

Figures (7)

• Figure 1: A pinched hysteresis loop in the $I$-$V$ plane of a memristor driven by a periodic input current $I(t) = I_0 \sin(\omega t)$. The parameters are $D=1\times10^{-9}$, $w=0.5\times10^{-9}$, $R_\mathrm{on}=1\times10^3$, $R_\mathrm{off}=1\times10^5$, $V_0=4.0$, $\omega=2\pi\times10^3$, over $2\,000$ time-steps.
• Figure 2: Leaky Integrate-and-Fire (LIF) neurons modeled as low-pass filter RC circuits. a) LIF circuit constructed with a resistor. b) LIF circuit constructed with a memristor in place of a resistor. The memristor is dependent on the history of the charge $q(t)$ that has passed through the circuit before.
• Figure 3: Memristive LIF circuit: the membrane node is driven by an AC current source $I_{\mathrm{in}}(t) = I_0 \sin(\omega t)$, and weakly coupled via a capacitor $C_C$ to a semi-infinite transmission line. Each node $\phi_i$ in the TL has capacitance $C_0$ and inductance $L_0$, while $C_m$ is the membrane capacitance.
• Figure 4: A pinched hysteresis loop in the $I$-$V$ plane of a quantum memristor driven by a periodic input current $I(t) = I_0 \sin(\omega t)$. The parameters are $C_m = 1.0$, $R_\mathrm{on}=1\times10^3$, $R_\mathrm{off}=1\times10^5$, $q_\mathrm{max}=1.0$, $I_0=1.0$, $\omega=\pi$, over $2\,000$ time-steps.
• Figure 5: A quantum memristive leaky integrate-and-fire neuron being stimulated by a sinusoidal input current, producing output spikes based on incorporated thresholding and refractory mechanisms. The top pane is the input driving current stimulating the neuron circuit with an input current $I(t) = I_0 \sin(\omega t)$. The center pane is the voltage expectation value evolution under the driving current, with spikes indicated where the membrane threshold is crossed and the state is reset. The bottom pane is of the output spikes from the driven LIF neuron.