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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).
A complete list of my publications can be found here.
Wigner Function Negativity and Contextuality in Quantum Computation on Rebits. [Posted May 4, 2015] We describe a universal scheme of quantum computation by state injection on rebits (states with real density matrices). For this scheme, we establish contextuality and Wigner function negativity as computational resources, extending results of M. Howard et al. [Nature (London) 510, 351 (2014)] to two-level systems. For this purpose, we define a Wigner function suited to systems of multiple rebits and prove a corresponding discrete Hudson's theorem. We introduce contextuality witnesses for rebit states and discuss the compatibility of our result with state-independent contextuality.
Journal Reference: Nicolas Delfosse, Philippe Allard Guerin, Jacob Bian, and Robert Raussendorf, Wigner Function Negativity and Contextuality in Quantum Computation on Rebits, Phys. Rev. X 5, 021003 (2015).
Negativity and contextuality for rebits. Left: Rebit Wigner function of a three-qubit graph state. This state is local unitary equivalent to a Greenberger-Horne-Zeilinger (GHZ) state. Negativity of the Wigner function for the three-qubit graph state indicates non-classicality. Contrary to qudits in odd prime dimension, for rebits negativity is not synonymous wit contextuality. Nevertheless, the negativity in the Wigner function for the three-qubit graph state is strong enough to witness contextuality. Right: From the perspective of contextuality in quantum computation with magic states, Mermin's square and star, and all their cousins, are ``little monsters''. For explanation, see below.
State-independent contextuality, as exhibited by Mermin's square and star, provides beautifully simple proofs for the Kochen-Specker theorem in dimension 4 and higher. However, for establishing contextuality as a resource only posessed by magic states, state-independent contextuality poses a problem: If ``cheap'' Pauli measurements already have contextuality, then how can one say that contextuality is a key resource provided by the magic states? For qudits, the problem doesn't exist because there is no state-independent contextuality w.r.t. Pauli measurements. For rebits, the problem is overcome by the operational restriction to CSS-ness preserving gates and measurements.
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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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