Collective motion from quantum-inspired dynamics in visual perception

TL;DR

The paper addresses how vision-based perceptual decisions can drive collective motion by introducing a quantum-inspired framework in which each agent carries a perceptual Hilbert space and a Hermitian perception operator $O_i^k$. The expectation value $\langle O_i^k\rangle$ acts as the driving force on momentum updates, enabling superposition and entanglement of neighbor decisions and yielding Vicsek-like flocking as a special case for certain perceptual states. It introduces two cohesion metrics, perceptual strength $\mathcal{P}$ and perceptual energy $\mathcal{E}$, and demonstrates through numerics that different perceptual states (uniform/random superpositions vs. Bell/GHZ/W-type entanglements) exhibit distinct robustness to noise and different capacities to sustain order. The framework links cognitive-like perceptual dynamics to classical collective behavior, offering a principled approach to perception-driven multi-agent coordination with potential applications in swarm robotics and biological flocking studies. $\langle \phi_v \rangle$ and the perceptual metrics $\mathcal{P}$ and $\mathcal{E}$ illustrate how cognitive decision processes shape macroscopic order, and the method provides a bridge between quantum-inspired perception and emergent classical patterns.

Abstract

We propose a model of collective behavior in self-propelled active agents that incorporates a perceptual decision-making process. In this framework, the decision-making dynamics is modeled using quantum formalism. The perceptual decision state of each agent is an entangled or superposed state of the decision states for the neighboring agents within the vision cone. We suggest that in this framework, the force driving the movement of active agents is governed by the quantum average of its perception operator, providing a bridge between perceptual decision-making processes and classical dynamics. Additionally, we introduce two perceptual measures of cohesion in the flock, namely, perception strength and perceptual energy, to characterize collective behavior in terms of decision-making dynamics. Our model demonstrates that, with an appropriate choice of perceptual decision state, the well-known Vicsek model of flocking behavior can be derived as a specific case of this quantum-inspired approach. This approach provides fresh insights into collective behavior and multi-agent coordination, revealing how classical patterns of collective behavior emerge naturally from perception.

Figures (8)

• Figure 1: An agent $\text{A}_i$ perceives few neighbors $\text{A}_j$ in its vision cone defined by angular width $\alpha$ along the direction of motion and constrained to a radial range between $r_{\min}$ and $r_{\max}$. The perceptual decision state of $\text{A}_i$ in relation to neighbor $\text{A}_j$ is denoted as a superposed state $\ket{\text{P}_i^j}$.
• Figure 2: Representation of perception operator for the two neighbors case as a weighted graph (up to an overall factor of $\frac{1}{n}$).
• Figure 3: Flocking patterns for (a) $\Phi^+$and (b) $\text{GHZ}_3$ states at noise strength $\eta=0.2$ and $t=100$.
• Figure 4: Order parameter vs. time steps at $\eta = 0.2$: (a) Uniform and random superposition states; (b) Maximally entangled states for $n=2$ and $n=3$.
• Figure 5: Order parameter vs. noise strength $\eta$: (a) Uniform and random superposition states; (b) Maximally entangled states for $n=2$ and $n=3$.