QAOA Max-Cut Contour Map | mysimulator.uk

Graph

QAOA Angles (p = 1)

Cost angle γ 0.00

Mixer angle β 0.00

Live Readouts

Expected cut ⟨C⟩

0.00

Approx. ratio

Classical max-cut

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Ascent step

How it works

QAOA solves Max-Cut by preparing |ψ(γ,β)⟩ = e^(-iβB) e^(-iγC) |+⟩^⊗n, where C = Σ_(i,j)∈E (1−Z_iZ_j)/2 is the cost Hamiltonian (its eigenvalue on a bitstring is the number of edges it cuts) and B = Σ_i X_i is the mixer. This page simulates the full 2ⁿ-amplitude statevector for a small graph and draws the objective:

E(γ,β) = ⟨ψ(γ,β)| C |ψ(γ,β)⟩

as a 2D topographic contour map over the two variational angles — colour bands are elevation ranges and the thin lines are isolines of equal expected cut, exactly like a hiking map. That is the same surface a real quantum-classical hybrid loop searches: a quantum processor evaluates E at one (γ,β) point, a classical optimizer proposes the next point, and the cycle repeats until convergence.

γ / β sliders — move the marker across the map by hand; the colour and stat panel under the marker are the live expectation value.
Run gradient ascent — a finite-difference climber takes small steps uphill (∂E/∂γ, ∂E/∂β), the same first-order method a classical optimizer (e.g. COBYLA/Adam) uses in practice. Its path is traced live on the map as a bright polyline, so you can watch it climb ridgelines and stall on saddle points from directly overhead.
Randomize start — jumps to a random (γ,β), useful for seeing that the landscape has several local optima — a real obstacle for QAOA training at larger circuit depth.
The gold diamond marks the best point found by a dense grid scan of this landscape — the closest this page comes to the true global optimum.

Approximation ratio = ⟨C⟩ / C_max, where C_max is the classical (brute-force) maximum cut of the graph — the standard way QAOA's output quality is reported in the literature.

Current (γ,β) marker Best point found (grid scan) Gradient-ascent trail