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Self-Organizing Quantum Neural Networks for Optimal Resource Allocation

Jincheng Zhang

Published Sep 2, 2026• 0 citations
Publisher

Abstract

This paper investigates the application of self-organizing quantum neural networks (SQNNs) to the problem of optimal resource allocation, a core challenge across diverse domains including finance, logistics, and telecommunications. Traditional classical neural networks frequently struggle to achieve optimal solutions when faced with complex constraints and dynamic environments. The central hypothesis of this work is that leveraging quantum computation through SQNNs, specifically utilizing qubit representations of resource states and exploiting entanglement, can significantly enhance the exploration of the solution space and lead to near-optimal resource allocation decisions. We propose a novel SQNN architecture designed to address this challenge. The architecture incorporates layers of quantum neurons that dynamically adjust their connectivity based on the input data, mimicking the self-organizing properties observed in biological neural networks. We present a theoretical framework outlining the key components of the SQNN and detail the mathematical formulation of the resource allocation problem being addressed. The core of the model is expressed as follows: Let *N* be the number of resources to be allocated. Let *K* be the number of potential allocation options for each resource. Let *xi* represent the allocation decision for resource *i*, where *xi* ∈ {1, 2, ..., *K*}. The objective is to minimize the cost function *C(x)*, which is defined as: *C(x) = ∑i=1N *Ci(xi)* where *Ci(xi)* represents the cost associated with resource *i* given the allocation *xi*. This cost function is subject to constraints *G(x) ≤ 0*, where *G* is a vector of constraints representing factors like capacity limits, demand requirements, and regulatory restrictions. The SQNN learns to approximate the optimal solution *x* that minimizes *C(x)* subject to the constraints *G(x) ≤ 0*. The network's self-organizing capability is achieved through a modified backpropagation algorithm adapted for quantum systems, incorporating quantum measurement and entangling operations to refine the network's internal state and improve its ability to represent and optimize the resource allocation problem. The efficacy of the SQNN is evaluated through simulations, demonstrating its potential to outperform classical neural networks in complex resource allocation scenarios.

DOI
10.5281/zenodo.22242986

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