QAOA Max-Cut Landscape Explorer

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 plots the objective:

E(γ,β) = ⟨ψ(γ,β)| C |ψ(γ,β)⟩

as a literal 3D terrain over the two variational angles. That is exactly the 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 terrain by hand; the height under the ball is the live expectation value.
Run gradient ascent — a finite-difference climber takes small steps uphill (∂E/∂γ, ∂E/∂β) from the current point, the same first-order method a classical optimizer (e.g. COBYLA/Adam) uses in practice.
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 spike 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)

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