Volkswagen: Quantum Traffic Optimization in Lisbon

The Problem

Traffic optimization is a combinatorial nightmare. Given hundreds of vehicles and thousands of possible routes, finding the globally optimal assignment grows exponentially with scale. Classical computers approximate it; quantum annealers are designed to search this kind of energy landscape natively.

Volkswagen wanted to test whether quantum hardware could provide practical routing advantages over classical GPS systems in a live urban environment.

What They Built

The team formulated the routing problem as a QUBO (Quadratic Unconstrained Binary Optimization), the native format for D-Wave hardware.

Each decision variable was binary: should taxi X take route Y at time T? The objective function minimized total travel time across all vehicles while respecting road capacity constraints. Adding a penalty term for constraint violations let them encode the full problem into the QUBO matrix.

# Simplified structure of the QUBO formulation
# Real problem had thousands of variables

import dimod

bqm = dimod.BinaryQuadraticModel('BINARY')

# For each vehicle-route pair: add variable
for vehicle in vehicles:
    for route in routes[vehicle]:
        bqm.add_variable(f'x_{vehicle}_{route}', cost(vehicle, route))

# Penalise assigning same vehicle to multiple routes
for vehicle in vehicles:
    route_vars = [f'x_{vehicle}_{r}' for r in routes[vehicle]]
    for i, r1 in enumerate(route_vars):
        for r2 in route_vars[i+1:]:
            bqm.add_interaction(r1, r2, penalty_weight)

# Submit to D-Wave
from dwave.system import EmbeddingComposite, DWaveSampler
sampler = EmbeddingComposite(DWaveSampler())
result = sampler.sample(bqm, num_reads=1000)

The Deployment

At the 2019 Web Summit in Lisbon, Volkswagen equipped 418 taxis with a routing app backed by the quantum system. As taxis completed trips and new passengers requested rides, the system re-optimized assignments in near real time.

D-Wave’s cloud API handled the problem submission. Results came back in under a minute for each optimization cycle.

Results

Volkswagen reported measurably shorter average journey times compared to the standard GPS baseline. The quantum system handled the full 418-vehicle problem without decomposing it - something that would require significant approximation on classical hardware at that scale.

The project was a proof of concept rather than a permanent deployment, but it demonstrated that quantum annealing could solve real logistics problems at city scale.

Technical Takeaways

• Problem type: Quantum annealing excels at combinatorial optimization where the objective can be mapped to an Ising Hamiltonian.
• Hybrid approach: The classical system handled data ingestion, UI, and post-processing. The quantum chip handled only the core optimization.
• Scalability: D-Wave’s Pegasus topology (later hardware) supports larger, denser problems. The same QUBO formulation scales directly.

Framework

Built with D-Wave’s Ocean SDK. The core library used was dimod for BQM construction and dwave-system for hardware access.

pip install dwave-ocean-sdk

Learn more: D-Wave Ocean Reference