Cluster-State Quantum Computer 2D: Measurement-Based Computing

Gate-based quantum computers build a circuit qubit by qubit; the one-way quantum computer does the opposite — it prepares one large, highly entangled lattice up front (a cluster state) and then computes purely by measuring qubits, column by column, in an adaptively chosen basis. This 2D simulator renders a real cluster state as a pannable, zoomable lattice diagram: qubits start in |+⟩, wired together by CZ gates along every grid edge, and each "Measure Next Column" step samples a genuine probabilistic outcome from the θ-basis measurement, feeds that outcome forward as a Pauli-frame correction for the next column (toggle it off to see why that step matters), and destroys the measured qubits' entanglement links exactly as a real graph-state measurement does. A basis-angle dial and an entanglement-entropy chart track the computation live alongside the output bitstring as the resource lattice is consumed from left to right.