The last two decades have witnessed the rapid growth of quantum information processing as an active field of multidisciplinary science and technology. Tremendous theoretical and experimental progress has been made in quantum communication and quantum computation, and it seems clear that some of this progress will soon result in practical applications outside the laboratory.

Quantum computation aims to build a quantum computer and to explore the origins and limits of quantum computing power. The original circuit model of a quantum computer, due to Deutsch, has a strong formal similarity with the circuit model of a classical computer. Both models depict a computation as processing via the wiring of a number of fiducial gates, each of which dynamically couples a small number of input (qu)bits in a controlled manner. In other words, unitary evolution is the basic mechanism of information processing in the circuit model of quantum computers.

Starting with a given fixed state of many qubits, measurement based quantum computation (MBQC) processes information by applying a sequence of measurements to designated qubits in designated bases. This is remarkable, given the probabilistic nature of quantum measurement and the murky physical status of the dynamics of 'wavefunction collapse'. The final result of the computation is determined from the classical data of all the measurement outcomes. There exist two principle models: the teleportation based model and the 'one-way quantum computer' of 'cluster state computation'. The formalism of cluster states has proven to be a powerful way of describing the essential entanglement resources needed to perform quantum information processing. Unlike the circuit model, the MBQC models have no natural classical counterpart.

There are a number of physical architectures for which measurements on the relevant systems are more easily performed than controlled unitary evolution. Moreover, it appears the MBQC models can offer novel computational benefits, especially regarding issues of fault-tolerance and parallelizability of algorithms. As a result, the theory of MBQC is now shaping the latest experimental proposals across the full spectrum of quantum information processing technologies. Naturally, understanding the scope of measurement based quantum computation is also yielding many insights into what is necessary (as opposed to merely sufficient) for us to harness the power of quantum computers.

Quantum communication aims to offer efficient and secure ways of information exchange, directly based on quantum mechanics. Photons serve as natural information carriers, owing to their robustness against decoherence. A major problem for photonic communication systems is due to photon loss. It turns out that this difficulty can be overcome by the quantum repeater, a measurement-based technique. The basic idea is to divide the transmission channel into many segments and perform some quantum measurement on each segment. Additional measurement-based protocols and technologies have also been demonstrated to improve the quality of quantum communication, such as entanglement swapping and purification.

The articles in this invited Focus Issue cover topics both in measurement-based quantum communication and computation, but the emphasis is given to quantum computation. A significant number of articles deal with the preparation of cluster states, the experimental realization of a one-way quantum computer, and the associated efficiency and benefits. We hope that you will find that some of these new results are of interest to you, and further hope that the issue will increase your interest in this interdisciplinary research field if you are a non-expert.

Focus on Measurement-Based Quantum Information Processing Contents

A proof-of-principle experiment of eliminating photon-loss errors in cluster states
Wei-Bo Gao, Xiao-Qi Zhou, Jin Zhang, Tao Yang and Jian-Wei Pan

Continuous variable multipartite entanglement and optical implementations of quantum communication networks
Yimin Lian, Changde Xie and Kunchi Peng

Generalized flow and determinism in measurement-based quantum computation
Daniel E Browne, Elham Kashefi, Mehdi Mhalla and Simon Perdrix

The entanglement of the four-photon cluster state
C Schmid, N Kiesel, W Wieczorek and H Weinfurter

Optical zeno gate: bounds for fault tolerant operation
Patrick M Leung and Timothy C Ralph

Towards experimental entanglement connection with atomic ensembles in the single excitation regime
Julien Laurat, Chin-wen Chou, Hui Deng, Kyung Soo Choi, Daniel Felinto, Hugues de Riedmatten and H J Kimble

Towards minimal resources of measurement-based quantum computation
Simon Perdrix

Experimental realization of a quantum game on a one-way quantum computer
Robert Prevedel, André Stefanov, Philip Walther and Anton Zeilinger

Fundamentals of universality in one-way quantum computation
M Van den Nest, W Dür, A Miyake and H J Briegel

Loss tolerant linear optical quantum memory by measurement-based quantum computing
Michael Varnava, Daniel E Browne and Terry Rudolph

Graph state generation with noisy mirror-inverting spin chains
Stephen R Clark, Alexander Klein, Martin Bruderer and Dieter Jaksch

One-way quantum computing in adecoherence-free subspace
M S Tame, M Paternostro and M S Kim

Cluster state preparation using gates operating at arbitrary success probabilities
K Kieling, D Gross and J Eisert

Topological fault-tolerance in cluster state quantum computation
R Raussendorf, J Harrington and K Goyal

Strategies for the preparation of large cluster states using non-deterministic gates
Peter P Rohde and Sean D Barrett

A repeat-until-success quantum computing scheme
A Beige, Y L Lim and L C Kwek

Efficient growth of complex graph states via imperfect path erasure
Earl T Campbell, Joseph Fitzsimons, Simon C Benjamin and Pieter Kok

Investigation of a single-photon source based on quantum interference
T B Pittman, J D Franson and B C Jacobs

Entanglement and local information access for graph states
Damian Markham, Akimasa Miyake and Shashank Virmani

The efficiencies of generating cluster states with weak nonlinearities
Sebastien G R Louis, Kae Nemoto, W J Munro and T P Spiller

A direct approach to fault-tolerance in measurement-based quantum computation via teleportation
Marcus Silva, Vincent Danos, Elham Kashefi and Harold Ollivier

Experimental ancilla-assisted qubit transmission against correlated noise
T Yamamoto, R Nagase, J Shimamura, S K Özdemir, M Koashi and N Imoto

Terry Rudolph, Imperial College, London, UK
Jian-Wei Pan, University of Science and Technology of China, Hefei, People's Republic of China and Universität Heidelberg, Germany