%0 Journal Article
%J Physical Review A
%D 2005
%T Unified derivations of measurement-based schemes for quantum computation
%A Andrew M. Childs
%A Debbie W. Leung
%A Michael A. Nielsen
%X 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.
%B Physical Review A
%V 71
%8 2005/3/17
%G eng
%U http://arxiv.org/abs/quant-ph/0404132v2
%N 3
%! Phys. Rev. A
%R 10.1103/PhysRevA.71.032318
%0 Journal Article
%J Physical Review A
%D 2003
%T Lower bounds on the complexity of simulating quantum gates
%A Andrew M. Childs
%A Henry L. Haselgrove
%A Michael A. Nielsen
%X We give a simple proof of a formula for the minimal time required to simulate a two-qubit unitary operation using a fixed two-qubit Hamiltonian together with fast local unitaries. We also note that a related lower bound holds for arbitrary n-qubit gates.
%B Physical Review A
%V 68
%8 2003/11/18
%G eng
%U http://arxiv.org/abs/quant-ph/0307190v1
%N 5
%! Phys. Rev. A
%R 10.1103/PhysRevA.68.052311
%0 Journal Article
%J Physical Review A
%D 2002
%T Universal simulation of Hamiltonian dynamics for qudits
%A Michael A. Nielsen
%A Michael J. Bremner
%A Jennifer L. Dodd
%A Andrew M. Childs
%A Christopher M. Dawson
%X What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? Dodd et al. (quant-ph/0106064) provided a partial solution to this problem in the form of an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling N-qubit Hamiltonian, and local unitaries. We extend this result to the case where the component systems have D dimensions. As a consequence we explain how universal quantum computation can be performed with any fixed two-body entangling N-qudit Hamiltonian, and local unitaries.
%B Physical Review A
%V 66
%8 2002/8/30
%G eng
%U http://arxiv.org/abs/quant-ph/0109064v2
%N 2
%! Phys. Rev. A
%R 10.1103/PhysRevA.66.022317