A cluster state (or graph state) is a highly entangled multi-qubit resource. It's prepared by placing qubits in |+⟩ = (|0⟩+|1⟩)/√2 and applying controlled-Z gates along every edge of a 2D lattice.
The key insight: any quantum circuit can be "consumed" by measuring qubits one-by-one in chosen bases. The measurement result propagates logical operations through the remaining entangled qubits via the teleportation protocol. Measuring in the X-Y plane (angle θ) applies a rotation gate; feed-forward corrections handle randomness.
Nodes glow when entangled; measured qubits (marked ×) collapse their neighbors' state, propagating the computation flow left→right. Edge color encodes the current Bell-pair entanglement strength between connected qubits.