Equivalence To Quantum Circuit Model
Any one-way computation can be made into a quantum circuit by using quantum gates to prepare the resource state. For cluster and graph resource states, this requires only one two-qubit gate per bond, so is efficient.
Conversely, any quantum circuit can be simulated by a one-way computer using a two-dimensional cluster state as the resource state, by laying out the circuit diagram on the cluster; Z measurements ( basis) remove physical qubits from the cluster, while measurements in the X-Y plane ( basis) teleport the logical qubits along the "wires" and perform the required quantum gates. This is also polynomially efficient, as the required size of cluster scales as the size of the circuit (qubits x timesteps), while the number of measurement timesteps scales as the number of circuit timesteps.
Read more about this topic: One-way Quantum Computer
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