Arbitrary multi-qubit generation

We propose and analyse a scheme for single-rail-encoded arbitrary multi-qubit quantum-state generation to provide a versatile tool for quantum optics and quantum information applications. Our scheme can be realised, for small numbers of qubits, with current technologies using single photon inputs, passive linear optics, and heralding measurements. The particular examples of two- and three-qubit cluster states are studied in detail. We show that such states can be prepared with a high probability of success. Our analysis quantifies the effects of experimentally relevant imperfections and inefficiencies. The general case of arbitrary N-qubit preparation is discussed and some interesting connections to the boson sampling problem are given.