Production scheduling: the classical solver proves the answer

The encoding, first

As on the logistics page, the quantum benchmark does not exist here, and the reason is the result. Putting job-shop scheduling on a quantum computer requires a time-indexed QUBO: a binary variable for every combination of job, machine and discrete time slot. The variable count is the product of all three, and it grows brutally.

A 15 by 15 shop needs 268,425 binary variables, so 268,425 logical qubits before error correction. The largest processor we can run is 108 physical qubits, the largest built anywhere is around 1,600, and the most logical qubits anyone has demonstrated is 96. The published 2029 roadmaps target hundreds of logical qubits. Every one of those numbers is three orders of magnitude short of this single instance.

What the classical solver does with the same instances

The word doing the work is "proven"

CP-SAT did not find a good schedule for the 15 by 15 shop. It found the best possible schedule and proved that nothing shorter exists, in 2.45 seconds.

That distinction matters more in a factory than in most places. A plant manager asking whether the line can run faster is asking a question with a definite answer, and a heuristic that returns a good schedule without a bound cannot give it. Every quantum approach to this problem is a heuristic. QAOA returns a sample, not a proof, so even at unlimited scale it would answer a weaker question than the classical solver already answers in seconds.

Where quantum could still matter here

Two honest caveats, because the picture above is not the whole industry.

Real shops are larger and messier. Hundreds of jobs, sequence-dependent setup times, maintenance windows, shift patterns and stochastic durations. CP-SAT does not always prove optimality there, and past a certain size it returns a good schedule with a gap rather than a guarantee. That is the regime where a better heuristic has value.

But the encoding gets worse, not better, in that regime. A larger, more constrained problem needs more time slots and more variables, so the qubit requirement rises faster than the classical difficulty does. Quantum approaches become relatively less applicable exactly as the problem becomes commercially interesting, which is the opposite of the usual pitch.

The question to ask a vendor

If a supplier proposes quantum scheduling, ask what makespan they achieve on a 15 by 15 shop and how long it takes. Then compare it against 126 in 2.45 seconds, proven optimal, on a laptop. The comparison is not unfair. It is the alternative you already have.

Ask the same question at whatever size your plant actually runs. If CP-SAT proves optimality there, no heuristic of any kind, quantum or classical, has anything to offer.