Vehicle routing under capacity. Knapsack loading. Shift rostering with fairness rules. Each is a combinatorial cliff where one more constraint doubles the pain. We formulate them as energy landscapes and let a quantum sampler roll downhill — measurably better than chance.
The moment trucks have limits and depots have windows, routing leaves easy territory. Our QAOA demonstration finds the true optimum with 32.5% of samples — random guessing manages 3.1%.
Weight, volume, priority, incompatibility — loading is the oldest NP-hard problem wearing a safety vest. As a QUBO it runs today at demonstration scale.
A schedule is only optimal if the crew shows up. Fairness constraints fold into the same energy landscape, so the sampler prefers rosters people can live with.
We take one lane, one depot, one roster — your data, anonymised — and write the QUBO: variables, penalties, and what a violation actually costs you.
Training runs where every objective evaluation is a real circuit execution. You watch the sample distribution shift toward feasible optima, quantified against guessing.
Where your instance sizes sit against today's hardware, when the crossover could arrive, and what your OR team should do meanwhile — pursue, park, or drop.
These programs are published in our algorithm library. The numbers below come from recorded executions we can reproduce on demand.
Capacity-constrained routing trained with QAOA.
Measured: True optimum captured 32.5% of shots vs 3.1% guessing — a 10.4× concentration.
Constrained loading as a QUBO with slack variables.
Measured: Feasible optimum dominates the sample distribution after training.
Workforce rostering with coverage and fairness penalties.
Measured: Best sampled roster satisfied every hard constraint.
Results are from the library items' own recorded runs on our simulator — the same one your browser uses.
At real fleet scale, mature OR solvers — CPLEX, OR-Tools, your dispatcher's intuition — still win. Our routing program's own output says exactly that. What you buy today is formulation capital.
A lane, a load plan, a roster — describe the constraint that bites and an engineer replies.