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My research interest is in quantum computation, in particular computational models. One object of study in this field is the one-way quantum computer, a scheme of quantum computation consisting of local measurements on an entangled universal resource state. The questions I ask are ``What are the elementary building blocks of the one-way quantum computer? What is their composition principle?'' I hope that the answer to these questions will give clues for how to construct novel quantum algorithms. Another model of quantum computation that I study are quantum cellular automata (QCA). I am, for example, interested in the question of whether and what type of quantum algorithms can be encoded the shape of the boundary of a finitely extended quantum cellular automaton.
I have invented the one-way 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 multi-particle entangled quantum state, the so-called cluster state. Quantum information is written into the cluster state, processed and read out by one-qubit 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.
The one-way quantum computer (QCc): A universal resource for the QCc is the cluster state, a highly entangled mult-qubit 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 fault-tolerant quantum computation. Error-correction is what a large-scale quantum computer spends most of its computation time with, and it is important to devise error-correction methods which allow for a high error threshold at a moderate operational overhead. My research interest is in fault-tolerance for quantum systems with a geometrical constraint, e.g. low-dimensional lattice systems, and in topological methods.
With my collaborators Jim Harrington (Los Alamos National Laboratory) and Kovid Goyal (Caltech), I have presented a fault-tolerant one-way quantum computer [arXiv:quant-ph/0510135], and have described a method for fault-tolerant quantum computation in a two-dimensional lattice of qubits requiring local and translation-invariant nearest-neighbor interaction only [arXiv:quant-ph/0610082], [arXiv:quant-ph/0703143]. For our method, we have obtained by far the highest known threshold for a two-dimensional architecture with nearest-neighbor interaction, namely 0.75 percent. A high value of the error threshold is important for realization of fault-tolerant quantum computation because it relaxes the accuracy requirements of the experiment. The imposed constraint of nearest-neighbor interaction in a two-dimensional 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 short-range interaction, for example optical lattices, arrays of superconducting qubits and quantum dots.
Fault-tolerant topological CNOT-gate: 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 CNOT-gate 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.
Tzu-Chieh Wei, Ian Affleck, Robert Raussendorf, The 2D AKLT state is a universal quantum computational resource, Phys. Rev. Lett. 106, 070501 (2011).
R. Raussendorf and H.-J. Briegel, Computational model underlying the one-way quantum computer, arXiv:quant-ph/0108067, Quant. Inf. Comp. 6, 443 (2002).
R. Raussendorf and H.-J. Briegel, A one-way quantum computer, Phys. Rev. Lett. 86, 5188 (2001).
H.-J. Briegel and R. Raussendorf, Persistent Entanglement in Arrays of Interacting Particles , arXiv:quant-ph/0004051, Phys. Rev. Lett. 86, 910 (2001).
A complete list of my publications can be found here.
Experimental demonstration of topological error correction. [Posted June 7, 2012] Here we report the experimental demonstration of topological error correction with an eight-photon cluster state. We show that a correlation can be protected against a single error on any quantum bit. Also, when all quantum bits are simultaneously subjected to errors with equal probability, the effective error rate can be significantly reduced. Our work demonstrates the viability of topological error correction for fault-tolerant quantum information processing.
The present experiment uses an 8-qubit cluster state which shares topological features with its larger (potentially much larger) cousin, the three-dimensional cluster state. A 3D cluster state is for measurement-based quantum computation (MBQC) what the Kitaev surface code is for the circuit model: a fault-tolerant fabric in which protected quantum gates can be implemented in a topological fashion. The present experiment demonstrates the fault-tolerance properties, not yet the encoded quantum gates. For the latter, larger cluster states will be required in future experiments. The smallest possible setting to demonstrate topological error-correction with cluster states requires 8 qubits, which was just in reach of the present photon-based experiment.
Journal Reference: Xing-Can Yao et al, Experimental demonstration of topological error correction, Nature 482, 489 (2012).
Also see James D. Franson, Quantum computing: A topological route to error correction, Nature 482, News and Views, (2012).
Topological error correction with cluster states. (left) Measurement of the error in the topologically protected correlation of the cluster state (0: perfect correlation, 0.5: no correlation, 1: perfect anti-correlation), vs. the one qubit error rate. The local errors are subjected to the cluster state on purpose, with varying strength. The black curve is the theory prediction for the strength of the correlation vs local error rate, if no error correction is performed, and the red dashed curve is for the same correlation with error correction performed. The dots represent the measured data. For small error probabilities, topological error correction significantly reduces logical error. (right) What do the 8-qubit cluster state used in the experiment and a large 3D cluster state have in common? - Both can be described by an underlying three-dimensional chain complex. Their topological error protection derives from the homology properties of these complexes.
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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 measurement-based quantum computation. I was postdoc at Caltech (2003-06) and at the Perimeter Institute for Theoretical Physics (2006-07), 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.
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