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A 2-year postdoctoral position in Quantum Information Science is opening in the Department of Physics and Astronomy at the University of British Columbia in Spring 2012, in the group of Dr. Robert Raussendorf. Possible areas of research include - but are not restricted to - models of quantum computation, quantum error-correction and quantum algorithms. The application deadline is December 15, 2011. For details, click here.
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.
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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.
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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 J. Harrington, Fault-tolerant quantum computation with high threshold in two dimensions, arXiv:quant-ph/0610082, Phys. Rev. Lett. 98, 150504 (2007).
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.
AKLT states as computational resources. [Posted February 24, 2011] We show that the ground state of an isotropic quantum antiferromagnet in two spatial dimensions, a so-called Affleck-Kennedy-Lieb-Tasaki (AKLT) state, is a universal resource for measurement-based quantum computation. This may become useful in two ways: (1) It may bring closer to experimental reality the possibility of creating computational resource states by cooling, and (2) More generally, it strengthens the overlap between the field of measurement-based quantum compuation and condensed matter physics. Could this overlap generate novel ideas and approaches for the classification of all computationally universal resource states?
An initial highly entangled resource state is the key ingredient in measurement-based quantum computation, where the process of computation itself is driven by single-spin measurements. Universal resource states are known to be rare. Recent quests for them have turned to ground states of short-ranged, preferably two-body interacting Hamiltonians, as they may be created by cooling. In particular, success has been obtained in the family of the AKLT models, in which single-qubit operations are shown to be possible. However, it remained open whether any state in the AKLT family can provide the full capability for universal quantum computation. Our results show that this is indeed the case for the two-dimensional spin-3/2 AKLT state supported on the honeycomb lattice.
The AKLT state was originally constructed in 1987 to understand the low-energy phenomenology of rotationally invariant spin Hamiltonians, a question at the center of condensed matter physics but outside the realm of quantum information. Amazingly, however, this happened not long after the notion of quantum computation started to develop, through the works of Feynman (1982) and Deutsch (1985).
[Journal Reference: Tzu-Chieh Wei, Ian Affleck, Robert Raussendorf, Physical Review Letters 106, 070501 (2011). An analogous result has been obtained independently by A. Miyake; See arXiv:1009.3491.]
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AKLT states as universal computational resources. At the techical level, our constructions proceeds by reducing the 2D AKLT state to a 2D cluster state through local operations (POVMs and projective measurements). The 2D cluster is the standard universal resource. The mapping requires three steps. (1) We devise a suitable generalized local measurement (local POVM) which breaks the rotational symmetry of the AKLT state. (2) We show that the resulting state is an encoded graph state on a random planar graph. Therein, the planar graph depends on the random but short-range correlated POVM outcomes. The encoding can be undone by local measurements. (3) A planar graph state can be further reduced to a 2D cluster state if it is large and has traversing paths, i.e., is in the supercritical phase of percolation (a). We show that this is indeed the case for typical graph states resulting from the POVM in Step 1, by Monte-Carlo simulation (b). |
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. From 2003 to 2006 I was postdoc at Caltech and from 2006 to 2007 at the Perimeter Institute for Theoretical Physics in Waterloo, Canada. I am Assistant Professor at the Department of Physics and Astronomy of the University of British Columbia since January 2008. Scholar of the Cifar Quantum Information program and Sloan Research Fellow 2009 - 2011.