Algorithm family
Graph optimization
Quantum Approximate Optimization Algorithm (QAOA)
Work with structured combinatorial problems, including Max-Cut.
Discuss a QAOA workload/ 01
Computational purpose
A family for parameterized optimization workflows over defined cost and mixing operations.The DecaQ result visualizer shows one Max-Cut workflow with a returned binary witness, objective scan and source context.
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Workload focus
Max-Cut · graph and combinatorial problems
Profile scope
A feasible cut, an objective expectation and a proven optimum are different claims. The output must be interpreted against the selected workload. The platform is described as supporting service profiles up to 400 logical qubits; this is not a blanket guarantee for arbitrary circuits or every operator.
Explainer · toy example
How QAOA looks for a large cut
Max-Cut splits a graph's nodes into two groups so that as many edges as possible run between them. This toy graph has 8 nodes and 12 edges, and every brightness below comes from an exact simulation of it.
An 8-node, 12-edge toy graph in six stages. All nodes start half in each group. The cost step adds phases, the mixer turns them into brightness on the edges most likely to be cut, and both run twice. Measuring gives one split; the bit string shown cuts 9 of 12 edges, the best of 5 runs. A classical optimiser then tunes the angles so the average cut rises over 28 attempts; one run is not a proof.
Illustration · 8 nodes, 12 edges
- Half-and-half node: in neither group yet
- Brighter edge: more likely to be cut
Illustration · 8 nodes, 12 edges
- Half-and-half node: in neither group yet
- Brighter edge: more likely to be cut
01 / 06 · Start
An even mix
Every bit string starts with the same weight, so no node belongs to either group yet: each one is half and half.
02 / 06 · Layer 1
Cost (γ₁)
The cost step tags each bit string with a phase set by how many edges it cuts, which changes the colour but not yet the brightness.
03 / 06 · Layer 1
Mixer (β₁)
The mixer moves weight between bit strings that differ in one node and turns those phases into brightness: the edges more likely to be cut glow brighter.
04 / 06 · Layer 2
Cost and mixer again (γ₂, β₂)
Both steps run once more (p = 2), and every node is still exactly half and half, because flipping every node gives the same cut.
05 / 06 · Measure
One bit string
Measuring returns a single bit string, so each node snaps into one group and the edges between the two groups light up.
Bit string, nodes 0–7
10101101
cut: 9 of 12
One returned bit string, the best of 5 runs on this toy graph (illustration).
A feasible cut, an objective expectation and a proven optimum are different claims.
06 / 06 · Classical loop
Tune the angles
Between attempts a classical optimiser, not the quantum circuit, adjusts the angles (γ, β), and the average cut over many runs drifts up.
Loop- classical optimiser
- (γ, β)
- circuit + measure
- average cut
Average cut per attempt
Attempts
Each dot averages 64 runs.
The average improves; one run is not a proof.