Understanding Traffic Jams Using Lindblad Superoperators

TL;DR

This paper introduces a quantum-inspired model using Lindblad superoperators to simulate and analyze traffic flow dynamics, capturing vehicle types and destinations within a quantum graph framework.

Contribution

It develops a novel quantum graph model with Lindblad dissipators to simulate traffic conditions, linking quantum dynamics to traffic flow analysis.

Findings

Model effectively encodes vehicle types and destinations.

Derives quantum Hamiltonian for bulk traffic dynamics.

Provides a framework for experimental realization of traffic simulations.

Abstract

We propose a model to simulate different traffic-flow conditions in terms of quantum graphs hosting an (N+1)-level dot at each site. Our model allows us to keep track of the type and of the destination of each vehicle. The traffic flow inside the system is encoded in a proper set of Lindbladian local dissipators that describe the time evolution of the system density matrix. Taking advantage of the invariance of the Lindblad master equation under inhomogeneous transformations we derive the quantum Hamiltonian for the bulk dynamics in a proper experimental setup.