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My research interest is in quantum computation, in particular computational models, quantum faulttolerance and foundational aspects. For my general approach to quantum computation, read here.
I have invented the oneway quantum computer (QCc) together with Hans Briegel (UK patent GB 2382892, US patent 7,277,872). The QCc is a scheme of universal quantum computation by local measurements on a multiparticle entangled quantum state, the socalled cluster state. Quantum information is written into the cluster state, processed and read out by onequbit measurements only. As the computation proceeds, the entanglement in the resource cluster state is progressively destroyed. Measurements replace unitary evolution as the elementary process driving a quantum computation.
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The oneway quantum computer (QCc): A universal resource for the QCc is the cluster state, a highly entangled multqubit quantum state that can be easily generated unitarily by the Ising interaction on a square lattice. In the figure to the left, the qubits forming the cluster state are represented by dots and arrows. The symbol used indicates the basis of local measurement. Dots represent cluster qubits measured in the eigenbasis of the Pauli operator Z, arrows denote measurement in a basis in the equator of the Bloch sphere. The pattern of measurement bases can be regarded as representing a quantum circuit, i.e., the "vertical" direction on the cluster specifies the location of a logical qubit in a quantum register, and the "horizontal" direction on the cluster represents circuit time. However, this simple picture should be taken with a grain of salt: The optimal temporal order of measurements has very little to do with the temporal sequence of gates in the corresponding circuit. 
I also work in the field of faulttolerant quantum computation. Errorcorrection is what a largescale quantum computer spends most of its computation time with, and it is important to devise errorcorrection methods which allow for a high error threshold at a moderate operational overhead. My research interest is in faulttolerance for quantum systems with a geometrical constraint, e.g. lowdimensional lattice systems, and in topological methods.
With my collaborators Jim Harrington (Los Alamos National Laboratory) and Kovid Goyal (Caltech), I have presented a faulttolerant oneway quantum computer [arXiv:quantph/0510135], and have described a method for faulttolerant quantum computation in a twodimensional lattice of qubits requiring local and translationinvariant nearestneighbor interaction only [arXiv:quantph/0610082], [arXiv:quantph/0703143]. For our method, we have obtained by far the highest known threshold for a twodimensional architecture with nearestneighbor interaction, namely 0.75 percent. A high value of the error threshold is important for realization of faulttolerant quantum computation because it relaxes the accuracy requirements of the experiment. The imposed constraint of nearestneighbor interaction in a twodimensional qubit array is suggested by experimental reality: Many physical systems envisioned for the realization of a quantum computer are confined to two dimensions and prefer shortrange interaction, for example optical lattices, arrays of superconducting qubits and quantum dots.

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Faulttolerant topological CNOTgate: Holes puncture a the surface of a Kitaev's surface code, creating pieces of boundary. Each pair of holes gives rise to an encoded qubit. There are two types of holes and hence qubits, primal and dual. The CNOTgate is implemented by moving two holes around another, one being primal and the other dual. Also shown is the string corresponding to an encoded Pauli operator X on the control qubit and its evolution from the initial to the final codes surface. As expected for conjugation under the CNOT, X_c evolves into X_c X_t. The CNOT in the opposite direction  the primal qubit being the target and the dual qubit being the control  is also possible. It requires pairwise insertion and removal of holes from the code surface, i.e., the topology of the code surface for that gate changes with time. 
TzuChieh Wei, Ian Affleck, Robert Raussendorf, The 2D AKLT state is a universal quantum computational resource, Phys. Rev. Lett. 106, 070501 (2011).
R. Raussendorf and J. Harrington, Faulttolerant quantum computation with high threshold in two dimensions, arXiv:quantph/0610082, Phys. Rev. Lett. 98, 150504 (2007).
R. Raussendorf and H.J. Briegel, Computational model underlying the oneway quantum computer, arXiv:quantph/0108067, Quant. Inf. Comp. 6, 443 (2002).
R. Raussendorf and H.J. Briegel, A oneway quantum computer, Phys. Rev. Lett. 86, 5188 (2001).
A complete list of my publications can be found here.
Contextuality and Wigner function negativity in qubit quantum computation. [Published May 17, 2017] We describe schemes of quantum computation with magic states on qubits for which contextuality and negativity of the Wigner function are necessary resources possessed by the magic states. These schemes satisfy a constraint. Namely, the nonnegativity of Wigner functions must be preserved under all available measurement operations. Furthermore, we identify stringent consistency conditions on such computational schemes, revealing the general structure by which negativity of Wigner functions, hardness of classical simulation of the computation, and contextuality are connected.
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State space for the onequbit states. This plot illustrates the difference between positive Wigner functions and noncontextual hidden variable models. The physical states lie within or on the Bloch sphere (BS). The two tetrahedra contain the states positively represented by the Wigner functions W and W, respectively. The state space describable by a noncontextual HVM is a cube with corners (+/ 1, +/ 1, +/ 1). It contains the Bloch ball. 
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I obtained my PhD from the Ludwig Maximilians University in Munich, Germany in 2003. My PhD thesis [Int. J. of Quantum Information 7, 1053  1203 (2009).] is on measurementbased quantum computation. I was postdoc at Caltech (200306) and at the Perimeter Institute for Theoretical Physics (200607), and Sloan Research Fellow 2009  2011. I am Associate Professor at the Department of Physics and Astronomy of the University of British Columbia, and scholar of the Cifar Quantum Information program.