QAOA Cost Landscape 3D Simulator

QAOA Landscape

MaxCut graph Triangle

Learning rate 0.25

Grid resolution 28

p=1 QAOA circuit

|ψ(γ,β)⟩ = U_B(β) U_C(γ) H^⊗ⁿ|0⟩ⁿ, cost C = Σ_edges (1−ZᵢZⱼ)/2 (MaxCut). The surface height at each (γ,β) is the exact expectation ⟨ψ|C|ψ⟩. The ball estimates the local gradient by finite difference and steps downhill — a classical optimizer driving a real hybrid quantum-classical loop.

Cost ⟨C⟩

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Best cut found

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γ, β

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Steps

Why a landscape, not a circuit diagram

A single QAOA layer has exactly two free angles (γ, β), so its entire cost function is a 2D surface over a 3D plot — something a per-qubit circuit diagram cannot show directly.
The ridge and basin structure here is real: it comes from evaluating the exact statevector at every grid point, not a stylized bowl.
The rolling ball is literally gradient descent — the same update rule (COBYLA/SPSA/Adam in practice) that drives real VQE/QAOA hardware runs between shots on the QPU.

low cost high cost optimizer walker

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