Unified derivations of measurement-based schemes for quantum computation

We present unified, systematic derivations of schemes in the two known measurement-based models of quantum computation. The first model (introduced by Raussendorf and Briegel Phys. Rev. Lett. 86 5188 (2001)]) uses a fixed entangled state, adaptive measurements on single qubits, and feedforward of the measurement results. The second model (proposed by Nielsen Phys. Lett. A 308 96 (2003)] and further simplified by Leung Int. J. Quant. Inf. 2 33 (2004)]) uses adaptive two-qubit measurements that can be applied to arbitrary pairs of qubits, and feedforward of the measurement results. The underlying principle of our derivations is a variant of teleportation introduced by Zhou, Leung and Chuang Phys. Rev. A 62 052316 (2000)]. Our derivations unify these two measurement-based models of quantum computation and provide significantly simpler schemes.