Cluster States
A cluster state is a highly entangled multi-qubit resource; measurements on it drive measurement-based quantum computation.
Entanglement as a resource
A cluster state is a specific highly entangled state built on a lattice of qubits. Prepare every qubit in |+>, then apply a controlled-Z between each pair of neighbors. The result is a graph state whose entanglement structure mirrors the lattice.
Measurement-based (one-way) computation
In the one-way model, computation proceeds by measuring the cluster's qubits one at a time in adaptively chosen bases. Each measurement consumes entanglement and teleports the logical information forward, so the resource is used up as the computation runs -- hence 'one-way'. The choice of measurement angles, conditioned on earlier outcomes, implements the desired unitary.
Why it is useful
- Front-loads all entanglement into state preparation, then uses only single-qubit measurements.
- Natural fit for photonic hardware, where two-qubit gates are hard but measurements are easy.
- Equivalent in power to the circuit model -- a different route to universality.
Cluster and graph states also appear in error correction and in quantum networking, making them one of the most reused entanglement primitives.