Navigating Quantum Missteps in Agent-Based Modeling: A Schelling Model Case Study

TL;DR

This paper reveals fundamental incompatibilities between traditional agent-based modeling and quantum optimization, demonstrating how rethinking problem formulation can lead to more efficient classical solutions and clarify quantum advantage conditions.

Contribution

It introduces a structural reformulation of agent-based models that avoids quantum pitfalls, enabling better classical solutions and setting clearer benchmarks for quantum advantage.

Findings

Traditional ABM observations undermine quantum superposition.

Reconceptualizing the problem improves classical solution speed.

A new lower bound for quantum advantage is established.

Abstract

Quantum computing promises transformative advances, but remains constrained by recurring misconceptions and methodological pitfalls. This paper demonstrates a fundamental incompatibility between traditional agent-based modeling (ABM) implementations and quantum optimization frameworks like Quadratic Unconstrained Binary Optimization (QUBO). Using Schelling's segregation model as a case study, we show that the standard practice of directly translating ABM state observations into QUBO formulations not only fails to deliver quantum advantage, but actively undermines computational efficiency. The fundamental issue is architectural. Traditional ABM implementations entail observing the state of the system at each iteration, systematically destroying the quantum superposition required for computational advantage. Through analysis of Schelling's segregation dynamics on lollipop networks, we demonstrate how abandoning the QUBO reduction paradigm and instead reconceptualizing the research question, from "simulate agent dynamics iteratively until convergence" to "compute minimum of agent moves required for global satisfaction", enables a faster classical solution. This structural reconceptualization yields an algorithm that exploits network symmetries obscured in traditional ABM simulations and QUBO formulations. It establishes a new lower bound which quantum approaches must outperform to achieve advantage. Our work emphasizes that progress in quantum agent-based modeling does not require forcing classical ABM implementations into quantum frameworks. Instead, it should focus on clarifying when quantum advantage is structurally possible, developing best-in-class classical baselines through problem analysis, and fundamentally reformulating research questions rather than preserving classical iterative state change observation paradigms.