rhumb.
Everything upstream of the solver is deterministic engineering: a live twin, a REST contract, a cost matrix, a QUBO. Everything downstream is swappable, and the stops can be parcels, engineer visits, care calls or collection points. That is what makes the platform quantum-ready without betting the product on quantum hardware.
Held-Karp exact solutions at small scale; nearest-neighbour + 2-opt beyond. Always-on honesty baseline: every other backend must beat it or say so.
Path-integral Monte Carlo via neal / OpenJij, the method used for parameter tuning in the QATO research programme.
Toshiba's SB algorithm on PyTorch, running hundreds of parallel solution agents per GPU. Runs on a laptop (Apple silicon) or scales unchanged to CUDA clusters such as Hartree's Mary Coombs system.
The same QUBO submits directly to D-Wave Advantage2 via Ocean/Leap. When quantum hardware wins on a problem class, swapping it in is configuration, not engineering. The formulation carries to gate-model machines too: we studied QAOA on fault-tolerant hardware with PsiQuantum in QuEST.
Every stochastic backend's best tour is refined classically (2-opt) before acceptance, the hybrid pattern that consistently beats either half alone.
A benchmark harness prices every backend on identical instances (cost, optimality gap, wall time, feasibility rate), from 10-stop rounds to 3,600-variable QUBOs beyond early quantum chip capacity.
Stop ordering becomes a grid of binary switches: xi,p = "stop i sits at position p". Drive times act as couplings, and constraint penalties ensure that every illegal schedule costs more than any legal one:
Identical formulation across the browser demo, the Python service and the quantum backends. See it working, and the maths behind each strategy, in the playable delivery twin.
The road data is national infrastructure we already operate: the complete street networks of the UK, Ireland and the Netherlands (70 GB), pre-processed into an indexed store on plain object storage and shared with our driving-simulation programme, which also runs a self-hosted OSRM routing authority over the same data. The twin on this site surveys any UK postcode, or any city from Belfast to Rotterdam, live in about two seconds, then prices a full day for any visiting fleet: £ per day, £ per stop, CO2, annualised.
Rounds of 10–20 stops solve in milliseconds in a browser tab. Fleet-wide joint optimisation, signal-phase co-optimisation and disruption replanning grow into tens of thousands of binary variables, the regime where GPU annealing-class solvers and, eventually, quantum annealers earn their keep, and the scale D-Wave's current systems and announced roadmap are aimed at. Industry pilots by Volkswagen, Toyota and DENSO already report 6–26% gains in routing and traffic flow. Because the cost model never changes, today's benchmarks remain tomorrow's acceptance tests. A 10% saving is roughly ten thousand driver-hours a year for a hundred-van depot.