Cluster-State Quantum Computer: 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 simulator renders a real 2D cluster state in 3D: 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, and destroys the measured qubits' entanglement links exactly as a real graph-state measurement does. Live readouts track computation progress, the entanglement entropy crossing the active cut, and the output bitstring as the resource lattice is consumed from left to right.