Abstract
We provide a set of prescriptions for implementing a circuit model algorithm as measurement
based quantum computing via a large discrete cluster state constructed sequentially, from qubits
implemented as single photons. We describe a large optical discrete graph state capable of searching
logical 4 and 8 element lists as an example. To do so we have developed several prescriptions based
on analytic evaluation of the evolution of discrete cluster states and graph state equations. We
describe the cluster state as a sequence of repeated entanglement and measurement steps using a
small number of single photons for each step. These prescriptions can be generalized to implement
any logical circuit model operation with appropriate single photon measurements and feed forward
error corrections. Such a cluster state is not guaranteed to be optimal (i.e. minimum number of
photons, measurements, run time).