Meridian - Quantum-Verified Route Optimization OS

Project Meridian

Inspiration

We got the problem statement and the first thing we did was grab a piece of paper and draw. A circle at the top for the quantum engine. A diamond in the middle for something that watches everything. An oval at the bottom for the problem. Three arrows going in every direction between them. We stared at that sketch for a while and realized we weren't looking at a routing solver. We were looking at a living system. One where the quantum computer, the verification layer, and the problem itself are constantly talking to each other, feeding each other, correcting each other. That sketch is Meridian. We just had to build it.

What it does

Meridian takes a vehicle routing problem and solves it using quantum optimization running on qBraid. But the interesting part is not the solving. The interesting part is what happens after. Most quantum systems hand you an answer and walk away. Meridian has a layer called Glass Box that reads the entire probability distribution the quantum circuit produced, figures out how confident it is, and then explains the decision in plain language. Which route won. What the next best option was. How far apart they were. How many iterations it took to get there. On top of that the system watches itself. If circuits get too deep it backs off. If something is taking too long it switches modes. If a vehicle's route comes back low confidence it reruns with adjusted parameters. The whole thing is designed so there is always an answer, no matter what goes wrong.

How we built it

Three layers. The first layer is classical. We sort customers by their angle from the depot, assign them to vehicles in order, and run a quick greedy pass to get a rough route. That rough route becomes the starting point for the quantum circuit. The quantum computer never has to start from scratch. The second layer is quantum. Each vehicle cluster becomes its own QUBO problem. We encode position variables, write the distance objective, add two constraint penalties, and let QAOA find the minimum on qBraid's statevector simulator. The penalty weight is not hardcoded. It watches how many constraints are being violated each round and adjusts itself. The optimizer also has an early stopping mechanism so it does not waste time on flat landscapes. The third layer is Glass Box. Every event in the system publishes to a central bus. Glass Box reads all of it, logs all of it, and at the end produces a full audit trail for every decision that was made. Confidence scores. Route explanations. Penalty history. Approximation ratio versus the classical optimal. The whole picture.

Challenges we ran into

Instance 4 has 12 customers and 4 vehicles. If you encode that naively as a single QUBO you need over 100 qubits. That kills most approaches at this competition. We decomposed it. Classical clustering first, then independent quantum circuits per vehicle. That kept every sub-problem at 16 qubits maximum. The problem got harder as we scaled up and our qubit count stayed flat. The other real challenge was the penalty weight. In a QUBO the penalty A has to be large enough to enforce constraints but not so large that the whole landscape flattens and the optimizer cannot find anything. We spent a lot of time on the adaptive loop that reads violation rates and tunes A across iterations. That is where most of the solution quality lives.

Accomplishments that we're proud of

All 4 instances solved. All constraints satisfied. All routes explained. The Glass Box confidence scores are real. They are computed from actual measurement distributions, not hardcoded. When a vehicle says it chose a route with 68% confidence that number means something. The system has never crashed during testing. Every failure mode we could think of has a handler. Five tier fallback cascade. Timeout limits at every layer. Convergence detection on the optimizer. The thing just keeps running.

What we learned

Quantum advantage is not about power. It is about knowing what to give the quantum computer. The decomposition insight is more valuable than any circuit optimization we did. Explainability in quantum systems is not a nice to have. If you cannot tell someone why the circuit chose what it chose, the answer is not trustworthy enough for real use. Glass Box is not a feature we bolted on. It changed how we thought about the whole system.

What's next for Meridian

Run it on real quantum hardware through qBraid. The fidelity monitor is already built for that. Extend Glass Box into a formal framework for quantum decision verification. There is a paper here that connects directly to existing work on AI interpretability. Multi-objective routing. Right now we minimize distance. The real world also cares about time, fuel, and emissions. The architecture already has the hook for weighted QUBO encoding. And honestly, the same system works for problems that have nothing to do with routing. Drug molecule placement. Financial portfolio construction. Satellite scheduling. The problem statement changes. The three layer architecture does not.