QAOA

QAOA is a circuit for optimisation problems written as a cost over bitstrings — a graph to cut, a QUBO to minimise. It alternates two layers p times: a cost layer that phases each bitstring by its cost, and a mixer that moves amplitude between bitstrings. The angles of the layers are tuned; ROX OS tunes them offline on a statevector where the size allows.

The measure is a ratio: the share of edges cut, or the weighted share of terms satisfied. A random bitstring gives 0.500. Deeper p can give a better ideal ratio — and a larger load. Somewhere the load crosses the machine's capacity: that is the edge on the curve.

On the record: MaxCut on a 16-qubit chain, depth ladders up to p = 230 on IBM and up to p = 48 on IQM Garnet, both arms, sealed. See Proof for the records, wins and losses.