Curriculum vitae Maarten Van den Nest

Transcription

1 Curriculum vitae Maarten Van den Nest August 28, Personal data and contact details Date of birth: December 10th, 1978 Place of birth: Aalst, Belgium Nationality: Belgian Office address: Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, Garching, Germany Office phone: maarten.vandennest@mpq.mpg.de 2 Education September June 2001, Katholieke Universiteit Leuven, Belgium. Master in Theoretical Physics (high energy physics). September May 2005, Katholieke Universiteit Leuven, Belgium. PhD in Applied Sciences, department of electrical engineering, group SISTA-SCD. Topic: quantum information theory. Title: Local equivalence of stabilizer states and codes. Supervisors : Prof. Bart De Moor and Prof. Mark Fannes. 3 Fields of specialization Quantum information theory and quantum computation 4 Professional experience January 1st March 31st Postdoctoral researcher in Prof. Hans Briegel s group at the Institute for Quantum Optics and Quantum Information (IQOQI), Austrian academy of Sciences, Innsbruck, Austria. April 1st present: Postdoctoral researcher in Prof. Ignacio Cirac s group, Max-Planck-Institut für Quantenoptik, Garching, Germany. 1

2 5 Teaching experience Linear algebra, tutorial sessions and examination for undergraduate course in the Department of Applied Sciences, Katholieke Universiteit Leuven, Belgium, Quantum information and quantum computation, introductory course for computer scientists at undergraduate level (full course, tutorials, examination and lecture notes), University of Innsbruck, Austria, summer semester Lecture notes freely available on request. Prof. Hans Briegel (cf. References section) may be contacted for a statement regarding my teaching skills and experience. 6 International research collaboration, participation in projects In my scientific activities I have formed collaborations and contacts with several international research groups. This includes the Institute for Quantum Optics and Quantum Information (Innsbruck, Austria), the Max Planck Institute for Quantum Optics (Garching, Germany), the Perimeter Institute (Waterloo, Canada), the University College London (London, United Kingdom), the University of Queensland (Queensland, Australia), the University of British Columbia (Vancouver, Canada), the Bristol University (Bristol, United Kingdom), and others. During my stay as a postdoctoral researcher in Innsbruck I was involved in a large European project on Foundational structures for quantum information and computation (QICS, ). This ongoing project has several research centers as partners (University of Bristol, University of Oxford, Technical University of Braunschweig (Germany), CNRS France, McGill University (Montreal, Canada), University of York (York, United Kingdom), University of Paris (France)). I contributed in writing the proposal for this QICS project. 7 Referee activities I act as a referee for the following journals: Physical Review Letters, Physical Review A, New Journal of Physics, Quantum information and Computation, Communications in Mathematical Physics, Journal of Mathematical Physics. 8 Research interests Quantum information theory and quantum computation; Measurement-based quantum computation; Classical simulation of quantum computation; Statistical physics and its connections to quantum information; Theoretical computer science, complexity theory; Graph states and the stabilizer formalism; Discrete mathematics. 2

3 9 Research highlights (selected papers + abstracts) H. J. Briegel, D. E. Browne, W. Dür, R. Raussendorf, M. Van den Nest, Measurement-based quantum computation, Nature Physics 5 1, (2009). Quantum computation offers a promising new kind of information processing, where the non-classical features of quantum mechanics are harnessed and exploited. A number of models of quantum computation exist. These models have been shown to be formally equivalent, but their underlying elementary concepts and the requirements for their practical realization can differ significantly. A particularly exciting paradigm is that of measurement-based quantum computation, where the processing of quantum information takes place by rounds of simple measurements on qubits prepared in a highly entangled state. We review recent developments in measurement-based quantum computation with a view to both fundamental and practical issues, in particular the power of quantum computation, the protection against noise (fault tolerance) and steps towards experimental realization. Finally, we highlight a number of connections between this field and other branches of physics and mathematics. M. Van den Nest, W. Dür, H. J. Briegel, Completeness of the classical 2D Ising model and universal quantum computation, Phys. Rev. Lett. 100, (2008). We prove that the 2D Ising model is complete in the sense that the partition function of any classical q- state spin model (on an arbitrary graph) can be expressed as a special instance of the partition function of a 2D Ising model with complex inhomogeneous couplings and external fields. In the case where the original model is an Ising or Potts-type model, we find that the corresponding 2D square lattice requires only polynomially more spins w.r.t the original one, and we give a constructive method to map such models to the 2D Ising model. For more general models the overhead in system size may be exponential. The results are established by connecting classical spin models with measurement-based quantum computation and invoking the universality of the 2D cluster states. M. Van den Nest, W. Dür, H. J. Briegel, Classical spin models and the quantum stabilizer formalism, Phys. Rev. Lett. 98, (2007). We relate a large class of classical spin models, including the inhomogeneous Ising, Potts, and clock models of q-state spins on arbitrary graphs, to problems in quantum physics. More precisely, we show how to express partition functions as inner products between certain quantum stabilizer states and product states. This connection allows us to use powerful techniques developed in quantum information theory, such as the stabilizer formalism and classical simulation techniques, to gain general insights into these models in a unified way. We recover and generalize several symmetries and highlow temperature dualities, and we provide an efficient classical evaluation of partition functions for all interaction graphs with a bounded tree-width. M. Van den Nest, W. Dür, G. Vidal, H. J. Briegel, Classical simulation versus universality in measurement based quantum computation, Phys. Rev. A 75, (2007). We investigate for which resource states an efficient classical simulation of measurement based quantum computation is possible. We show that the Schmidt rank width, a measure recently introduced to assess universality of resource states, plays a crucial role in this context as well. We relate Schmidt rank width to the optimal description of states in terms of tree tensor networks and show that an efficient classical simulation of measurement based quantum computation is possible for all states with logarithmically bounded Schmidt-rank width (with respect to the system size). For graph states where the Schmidt rank width scales in this way, we efficiently construct the optimal tree tensor network descriptions, and provide several examples. We highlight parallels in the efficient description of complex systems in quantum information theory and graph theory. 3

4 M. Van den Nest, A. Miyake, W. Dür, H. J. Briegel, Universal resources for measurement-based quantum computation, Phys. Rev. Lett. 97, (2006). We investigate which entanglement resources allow universal measurement-based quantum computation via single-qubit operations. We find that any entanglement feature exhibited by the 2D cluster state must also be present in any other universal resource. We obtain a powerful criterion to assess universality of graph states, by introducing an entanglement measure which necessarily grows unboundedly with the system size for all universal resource states. Furthermore, we prove that graph states associated with 2D lattices such as the hexagonal and triangular lattice are universal, and obtain the first example of a universal non-graph state. M. Hein, W. Dür, J. Eisert, R. Raussendorf, M. Van den Nest, H. J. Briegel, Entanglement in graph states and its applications, International School of Physics Enrico Fermi (Varenna, Italy), Quantum computers, algorithms and chaos 162 (Eds.: P. Zoller, G. Casati, D. Shepelyansky, G. Benenti) (2006). Graph states form a rich class of entangled states that exhibit important aspects of multi-partite entanglement. At the same time, they can be described by a number of parameters that grows only moderately with the system size. They have a variety of applications in quantum information theory, most prominently as algorithmic resources in the context of the one-way quantum computer, but also in other fields such as quantum error correction and multi-partite quantum communication, as well as in the study of foundational issues such as non-locality and decoherence. In this review, we give a tutorial introduction into the theory of graph states. We introduce various equivalent ways how to define graph states, and discuss the basic notions and properties of these states. The focus of this review is on their entanglement properties. These include aspects of non-locality, bi-partite and multi-partite entanglement and its classification in terms of the Schmidt measure, the distillability properties of mixed entangled states close to a pure graph state, as well as the robustness of their entanglement under decoherence. We review some of the known applications of graph states, as well as proposals for their experimental implementation. 10 Research visits L.M.U Munich, Germany, June 2-6th QIPC Workshop Rome, Italy, September 20-24th Techn. Un. Innsbruck, Austria, December 6-10th Laboratoire Leibniz-IMAG, Grenoble, France, January 5-7th California Institute of Technology, Pasadena, USA, November 14-18th QUIC, Université libre de Bruxelles, Belgium, December QIP2006 workshop, Paris, France, January 16-20th Laboratoire Leibniz-IMAG, Grenoble, France, June 5-9th CKC Oxford workshop, UK, July 17th-21st QCMC2006, Tsukuba, Japan, November 28th - December 1st MBQC 2007 Oxford, UK, March 29-23th Technical university of Lisbon, Portugal, April 9-13th

5 Summer school Jacobs University Bremen, Germany, June 13-15th Perimeter Institute, Waterloo, CA, September 10-14th University of Calgary, CA, September 17th-21st Max-Planck Institute for quantum optics, Garching, Germany, September 24-26th QIPC2007 Conference, Barcelona, Spain, October 15-19th SFB 2008 Meeting, Innsbruck, Austria, January 31st University of Bristol, UK, June 9-13th ICALP 2008, 35th International Colloquium on Automata, Languages and Programming, Reykjavik, Iceland, July 6-13th MPQ / Barcelona Research Centers: workshop on Quantum Information, Sant Benet, Spain, December 3-6th, QUROPE09 International School Quantum Information and Many-Body Systems, Cortona, Italy, May 3-17th University of Innsbruck, Austria, May 25-28th Benasque meeting on quantum information, Benasque, Spain, June 7-13th Oral presentations Invited talks (conferences, schools) Workshop on Quantum Information and Graph Theory: emerging connections, Perimeter Institute, Waterloo, Canada, April 28 - May , Quantum computation and statistical mechanics. QICS workshop on Foundational Structures for Quantum Information and Computation, September 14th - 20th 2008, Obergurgl, Austria, Quantum computation and statistical mechanics. QUROPE09 International School Quantum Information and Many-Body Systems, May 3rd - 17th 2009, Cortona, Italy, Statistical mechanics and quantum information theory (3 hours). Contributed conference talks and seminar talks L.M.U Munich, Germany, June 6th 2003, group of H. Briegel, Equivalence of stabilizer states under local Clifford operations and algebra over GF(2). QIPC Workshop Rome, Italy, September 21st 2004, Local Clifford equivalence of graph states and graph operations. Techn. Un. Innsbruck, Austria, December 7th 2004, group of H. Briegel, Local equivalence of stabilizer states. Laboratoire Leibniz-IMAG, Grenoble, France, January 6th 2005, group of P. Jorrand, Graph states, LC equivalence and local complementation. PhD defense, K.U. Leuven, Belgium, May 30th 2005, Local Equivalence of stabilizer states and codes. 5

6 California Institute of Technology, Pasadena, USA, November 16th 2005, group of J. Preskill, Local Equivalence of stabilizer states. QUIC, Université libre de Bruxelles, Belgium, December 2005, group of N. Cerf, Local Equivalence of stabilizer states. Laboratoire Leibniz-IMAG, Grenoble, France, June 11th 2006, group of P. Jorrand, Investigating graph problems with quantum information techniques. CKC Oxford, UK, July 17th 2006, Classical simulation versus universality in measurement based quantum computation. MBQC 2007 Oxford, UK, March 20th 2007, Measurement-based quantum computation and undecidable logic. QICS 2007, Oxford, UK, March 15th 2007, Universality in one-way quantum computation. Technical university of Lisbon, Portugal, April 13th 2007, Measurement-based quantum computation and undecidable logic. Jacobs University Bremen, Germany, June 14th 2007, Interfaces between physics and computer science, An introduction to graph states and their connections to statistical physics. Perimeter Institute, Waterloo, CA, September 12th 2007, Mapping classical spin models to the graph state formalism. University of Waterloo, Dept. of combinatorics and optimization (Tutte seminar), Waterloo, CA, September 14th 2007, Width parameters of graphs and codes, and tree tensor networks. University of Calgary, CA, September 19th 2007, Mapping classical spin models to the graph state formalism. Max-Planck Institute for quantum optics, Garching, Germany, September 25th 2007, Mapping classical spin models to the graph state formalism. QIPC2007 Conference, Barcelona, Spain, October 19th 2007, Mapping classical spin models to the graph state formalism. SFB 2008 Meeting, Innsbruck, Austria, January 31st 2008, Recent progress in measurement-based quantum computation. University of Bristol, UK, June 11th 2008, Quantum computation and statistical mechanics. ICALP 2008, 35th International Colloquium on Automata, Languages and Programming, Reykjavik, Iceland, July 6th - 13th 2008, Measurement-based quantum computation and undecidable logic. 12 Publications Published and accepted papers (peer reviewed) J.-M. Cai, W. Dür, M. Van den Nest, A. Miyake, H. J. Briegel, Quantum computation in correlation space and extremal entanglement, Phys. Rev. Lett. 103, (2009). 6

7 20. R. Hübener, M. Van den Nest, W. Dür, H. J. Briegel, Classical spin systems and the quantum stabilizer formalism: general mappings and applications, J. Math. Phys. 50, (2009). 19. H. J. Briegel, D. E. Browne, W. Dür, R. Raussendorf, M. Van den Nest, Measurement-based quantum computation, Nature Physics 5 1, (2009). 18. G. De las Cuevas, W. Dür, M. Van den Nest, H. J. Briegel, Completeness of classical spin models and universal quantum computation, J. Stat. Mech. (2009) P M. Van den Nest, W. Dür, H. J. Briegel, Completeness of the classical 2D Ising model and universal quantum computation, Phys. Rev. Lett. 100, (2008). 16. M. Van den Nest, H. J. Briegel, Measurement-based quantum computation and undecidable logic, Foundations of Physics 38 5, (2008). 15. D. Gross and M. Van den Nest, The LU-LC conjecture, diagonal local operations and quadratic forms over GF(2), Quantum Inf. Comput. 8, 263 (2008). 14. M. Van den Nest, K. Luttmer, W. Dür, H. J. Briegel, Graph states as ground states of many-body spin-1/2 Hamiltonians, Phys. Rev. A 77, (2008) M. Van den Nest, W. Dür, H. J. Briegel, Classical spin models and the quantum stabilizer formalism, Phys. Rev. Lett. 98, (2007). 12. M. Van den Nest, W. Dür, A. Miyake, H. J. Briegel, Fundamentals of universality in one-way quantum computation, New J. Phys. 9, 204 (2007). 11. M. Van den Nest, W. Dür, G. Vidal, H. J. Briegel, Classical simulation versus universality in measurement based quantum computation, Phys. Rev. A 75, (2007) M. Van den Nest, A. Miyake, W. Dür, H. J. Briegel, Universal resources for measurement-based quantum computation, Phys. Rev. Lett. 97, (2006) M. Hein, W. Dür, J. Eisert, R. Raussendorf, M. Van den Nest, H. J. Briegel, Entanglement in graph states and its applications, International School of Physics Enrico Fermi (Varenna, Italy), Quantum computers, algorithms and chaos 162 (Eds.: P. Zoller, G. Casati, D. Shepelyansky, G. Benenti) (2006). 8. M. Van den Nest, J. Dehaene, B. De Moor, Invariants of the local Clifford group, Phys. Rev. A. 71, (2005). 7. M. Van den Nest, J. Dehaene, B. De Moor, Local unitary versus local Clifford equivalence of stabilizer states, Phys. Rev. A 71, (2005). 6. M. Van den Nest, J. Dehaene, B. De Moor, Finite set of invariants to characterize local Clifford equivalence of stabilizer states, Phys. Rev. A 72, (2005). 7

8 M. Van den Nest, J. Dehaene, B. De Moor, Graphical description of the action of local Clifford operations on graph states, Phys. Rev. A 69, (2004). 4. M. Van den Nest, J. Dehaene, B. De Moor, Local invariants of stabilizer codes, Phys. Rev. A (2004). 3. M. Van den Nest, J. Dehaene, B. De Moor, Efficient algorithm to recognize local Clifford equivalence of graph states, Phys. Rev. A. 70, (2004). 2. M. Van den Nest, J. Dehaene, B. De Moor, Local equivalence of stabilizer states, Proceedings of the 16th International Symposium of Mathematical Theory of Networks and Systems (MTNS2004), K.U. Leuven (2004). 1. J. Dehaene, M. Van den Nest, B. De Moor, F. Verstraete, Local permutations of products of Bell states and entanglement distillation, Phys. Rev. A 67, (2003). Preprints and submitted papers C. E. Mora, M. Piani, A. Miyake, M. Van den Nest, W. Dür, H. J. Briegel, Universal resources for approximate and stochastic measurement-based quantum computation, arxiv: M. Van den Nest, Classical simulation of quantum computation, the Gottesman-Knill theorem, and slightly beyond, arxiv: M. Van den Nest, W. Dür, R. Raussendorf, H. J. Briegel, Quantum algorithms for spin models and simulable gate sets for quantum computation, arxiv: M. Van den Nest, B. De Moor, Edge-local equivalence of graphs, preprint, 2005; see math/ Personal interests I enjoy spending time with my wife and daughter, travelling, going out with friends, dining out in a fine restaurant, playing squash, writing short pieces of fiction, going to concerts. 8

9 References For a statement about my research skills, please contact: Prof. Hans J. Briegel, Institut für Quantenoptik und Quanteninformation, Technikerstraße 21a A Innsbruck, Austria. Tel: , Hans.Briegel@uibk.ac.at. Prof. Ignacio Cirac, Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, Garching, Germany. Tel: , ignacio.cirac@mpq.mpg.de. 9