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

TL;DR

This paper develops a quantum model of a memristive Leaky Integrate-and-Fire neuron, combining neuromorphic principles with quantum physics, and demonstrates its advantages over classical and phenomenological models in sound localization tasks.

Contribution

It introduces a canonical quantization framework for memristive LIF neurons, bridging neuromorphic engineering and quantum systems, and shows improved performance in quantum neuromorphic applications.

Findings

Quantum memristive LIF exhibits memory effects and spiking behavior.

Outperforms classical and phenomenological quantum LIF models in sound localization.

Provides a foundational model for quantum neuromorphic computing.

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.