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Guifre Vidal

Portrait de Guifre Vidal
Faculty

Areas of Research:
Condensed Matter,
Quantum Information
Phone: x8621

Member of Tensor Networks Initiative

Research Interests

QUANTUM MECHANICS and MANY-BODY PHYSICS

I am interested in the quantum many-body problem: given a large number of quantum mechanical degrees of freedom and a detailed description of their interactions, can we predict their emergent, collective behavior? This question is relevant to a number of research areas, including condensed matter, statistical mechanics, quantum information/computation, quantum chemistry, string theory and quantum gravity.

THE RENORMALIZATION GROUP and ENTANGLEMENT.-- A particular route to addressing this problem is the renormalization group (RG). The goal of the RG is to produce a sequence of effective descriptions of the system, corresponding to increasing length scales, and see how these effective descriptions eventually converge to some fixed point that can be properly characterized. On the other hand, in recent years our understanding of many-body wave-functions has been significantly enriched by the study of their entanglement. For instance, we have learned that in most ground states of local Hamiltonians, entanglement entropy obeys a boundary law (with, at most, logarithmic corrections).

TENSOR NETWORKS.--The multi-scale entanglement renormalization ansatz (MERA) is a modern realization of the RG ideas for quantum systems on a lattice. The MERA is a tensor network that exploits the spatial structure of entanglement to produce an efficient (i.e., computationally tractable) description of ground states. Thanks to its in-built RG flow, the MERA also produces effective descriptions that explicitly identify the degrees of freedom of a many-body system relevant at low energies. Thus, it provides both a computational tool to solve specific many-body problems as well as a natural framework to investigate emergence in quantum systems. More generally, I am interested in other tensor network states, such as matrix product states (MPS) and projected entangled-pair states (PEPS), and their use to classify possible phases of matter.

COLLECTIVE PHENOMENA.--In addition, I also apply tensor network algorithms to learn about new physics. Specifically, I study lattice models (e.g. of frustrated antiferromagnets, interacting fermions, quantum critical system) and aim at characterizing their emergent quantum phenomena (e.g. topological order, high-Tc superconductivity, quantum phase transitions, etc). More broadly, I am also interested in the potential application of these non-perturbative tools to quantum field theories and to quantum gravity.

Positions Held

  • 2011 - present Perimeter Institute for Theoretical Physics Senior Faculty
  • 2005 - 2011 The University of Queensland, Australia Professor in the School of Mathematics and Physics
  • 2002 - 2005 California Institute of Technology, US Postdoctoral fellow
  • 1999 - 2001 University of Innsbruck, Austria Postdoctoral fellow

Awards

  • Simons Foundation Grant, US $835,000 As part of the Tensor Network Group within the "Simons Collaboration on the Many Electron Problem" (http://www.simonsfoundation.org/mathematics-and-physical-science/many-electron-collaboration/), Simons Foundation, 2014-2019.
  • John Templeton Foundation Grant, US $454,000 "Simulating Emergence in Quantum Matter" (with R. Melko) JTF, Sept 2013 -Feb 2016.
  • NSERC Discovery Grant (2012-2017), CAN $305,000, Natural Sciences and Engineering Research Council of Canada, Canada
  • Distinguished Research Chair (2010-2011), Perimeter Institute for Theoretical Physics, Canada
  • ARC Discovery Project (2010-2012), AUS $390,000, Australian Research Council
  • ARC Discovery Project (2008-2010), AUS $575,000, Australian Research Council, Australia
  • ARC Federation Fellowship (2006-2011), AUS$ 1,250,000, Australian Research Council, Australia
  • Sherman Fairchild Postdoctoral Fellowship (2003-2005), United States of America
  • Marie Curie Postdoctoral Fellowship (1999-2001), European Union

Recent Publications

  • Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator, B. Bauer, L. Cincio, B. P. Keller, M. Dolfi, G. Vidal, S. Trebst, A. W. W. Ludwig, Accepted in Nature Communications, arXiv: 1401.3017
  • Entanglement contour, Yangang Chen, Guifre Vidal, Accepted in JStat, arXiv: 1406.1471
  • Glen Evenbly and Guifre Vidal, A real space decoupling transformation for quantum many-body systems, Phys. Rev. Lett. 112, 220502 (2014), arXiv: 1205.0639
  • Scaling of entanglement entropy in the (branching) multi-scale entanglement renormalization ansatz, Glen Evenbly, Guifre Vidal, Phys. Rev. B 89, 235113 (2014), arXiv: 1310.8372
  • Glen Evenbly, Guifre Vidal, A class of highly entangled many-body states that can be efficiently simulated, Phys. Rev. Lett. 112, 240502 (2014), arXiv: 1210.1895
  • Algorithms for entanglement renormalization: boundaries, impurities and interfaces, Glen Evenbly, Guifre Vidal, J Stat Phys, DOI 10.1007/s10955-014-0983-1, arXiv: 1312.0303
  • Sukhwinder Singh, Robert N. C. Pfeifer, Guifre Vidal, Gavin K. Brennen, Matrix product states for anyonic systems and efficient simulation of dynamics, Phys. Rev. B 89, 075112 (2014), arXiv: 1311.0967
  • Sukhwinder Singh, Guifre Vidal, Global symmetries in tensor network states: symmetric tensors versus minimal bond dimension, Phys. Rev. B 88, 115147 (2013), arXiv: 1307.1522
  • Ho N. Phien, Guifré Vidal, and Ian P. McCulloch, Dynamical windows for real-time evolution with matrix product states, Phys. Rev. B 88, 035103 (2013), arXiv: 1207.0678
  • Yirun Arthur Lee, Guifre Vidal, Entanglement negativity and topological order, Phys. Rev. A 88, 042318 (2013), arXiv: 1306.5711
  • Sukhwinder Singh, Guifre Vidal, Symmetry protected entanglement renormalization, Phys. Rev. B 88, 121108(R) (2013), arXiv: 1303.6716
  • L. Cincio, G. Vidal, Characterizing topological order by studying the ground states of an infinite cylinder, Phys. Rev. Lett. 110, 067208 (2013), arXiv: 1208.2623
  • H. N. Phien, G. Vidal, I. McCulloch, Infinite boundary condition for matrix product state calculations, Phys. Rev. B 86, 245107 (2012), arXiv: 1207.0652
  • S. Singh, G. Vidal, Tensor network states and algorithms in the presence of a global SU(2) symmetry, Phys. Rev. B 86, 195114 (2012), arXiv: 1208.3919
  • R. N. C. Pfeifer, O. Buerschaper, S. Trebst, A. W. W. Ludwig, M. Troyer, G. Vidal, Translation invariance, topology, and protection of criticality in chains of interacting anyons, Phys. Rev. B 86(15), 155111 (2012), arXiv: 1005.5486
  • B. Pirvu, G. Vidal, F. Verstraete, L. Tagliacozzo, Matrix product states for critical spin chains: finite size scaling versus finite entanglement scaling, Phys. Rev. B 86, 075117 (2012), arXiv: 1204.3934
  • Andrew J. Ferris, Guifre Vidal, Perfect Sampling with Unitary Tensor Networks, Phys. Rev. B 85, 165146 (2012), arXiv: 1201.3974
  • Andrew J. Ferris, Guifre Vidal, Variational Monte Carlo with the Multi-Scale Entanglement Renormalization Ansatz, Phys. Rev. B 85, 165147 (2012), arXiv: 1201.3975
  • G. Evenbly, G. Vidal, Tensor network states and geometry, J Stat Phys (2011) 145:891-918, arXiv: 1106.1082
  • P. Corboz, S. R. White, G. Vidal, M. Troyer, Stripes in the two-dimensional t-J model with infinite projected entangled-pair states, Phys. Rev. B 84, 041108 (2011), arXiv: 1104.5463
  • Sukhwinder Singh, Robert N. C. Pfeifer, Guifre Vidal, Tensor network states and algorithms in the presence of a global U(1) symmetry, Phys. Rev. B 83, 115125 (2011), arXiv: 1008.4774
  • Philippe Corboz, Jacob Jordan, Guifre Vidal, Simulation of fermionic lattice models in two dimensions with Projected Entangled-Pair States: Next-nearest neighbor Hamiltonians, Phys. Rev. B 82, 245119 (2010), arXiv: 1008.3937
  • Robert N. C. Pfeifer, Philippe Corboz, Oliver Buerschaper, Miguel Aguado, Matthias Troyer, Guifre Vidal, Simulation of anyons with tensor network algorithms, Physical Review B 82, 115126 (2010), arXiv: 1006.3532
  • Philippe Corboz, Roman Orus, Bela Bauer, Guifre Vidal, Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States, Phys. Rev. B 81, 165104 (2010), arXiv: 0912.0646
  • Philippe Corboz, Guifre Vidal, Fermionic multi-scale entanglement renormalization ansatz, Phys. Rev. B 80, 165129 (2009), arXiv: 0907.3184
  • Sukhwinder Singh, Robert N. C. Pfeifer, Guifre Vidal, Tensor network decompositions in the presence of a global symmetry, Phys.Rev.A82:050301,2010, arXiv: 0907.2994
  • Bela Bauer, Guifre Vidal, Matthias Troyer, Assessing the accuracy of projected entangled-pair states on infinite lattices, J. Stat. Mech. (2009) P09006, arXiv: 0905.4880
  • Roman Orus, Guifre Vidal, Simulation of two dimensional quantum systems on an infinite lattice revisited: corner transfer matrix for tensor contraction, Physical Review B 80 094403 (2009), arXiv: 0905.3225
  • Philippe Corboz, Glen Evenbly, Frank Verstraete, Guifre Vidal, Simulation of interacting fermions with entanglement renormalization, Phys. Rev. A 81, 010303(R) (2010), arXiv: 0904.4151
  • Jacob Jordan, Roman Orus, Guifre Vidal, Numerical study of the hard-core Bose-Hubbard Model on an Infinite Square Lattice, Phys. Rev. B 79, 174515 (2009), arXiv: 0901.0420
  • Glen Evenbly, Guifre Vidal, Entanglement renormalization in two spatial dimensions, Phys. Rev. Lett. 102, 180406 (2009), arXiv: 0811.0879
  • Robert N. C. Pfeifer, Glen Evenbly, Guifre Vidal, Entanglement renormalization, scale invariance, and quantum criticality, Physical Review A 79(4), 040301(R) (2009), arXiv: 0810.0580
  • Roman Orus, Andrew C. Doherty, Guifre Vidal, First order phase transition in the anisotropic quantum orbital compass model, Physical Review Letters 102, 077203 (2009), arXiv: 0809.4068
  • Robert Koenig, Ben W. Reichardt, Guifre Vidal, Exact entanglement renormalization for string-net models, Phys. Rev. B 79, 195123 (2009), arXiv: 0806.4583
  • Gregory M. Crosswhite, Andrew C. Doherty, Guifre Vidal, Applying matrix product operators to model systems with long-range interactions, Phys. Rev. B 78, 035116 (2008), arXiv: 0804.2504
  • Miguel Aguado, Guifre Vidal, Entanglement renormalization and topological order, Phys. Rev. Lett. 100, 070404 (2008), arXiv: 0712.0348
  • Roman Orus, Guifre Vidal, The iTEBD algorithm beyond unitary evolution, Phys. Rev. B 78, 155117 (2008), arXiv: 0711.3960
  • Alvaro Perales, Guifre Vidal, Entanglement growth and simulation efficiency in one-dimensional quantum lattice systems, Phys. Rev A 78, 042337 (2008), arXiv: 0711.3676
  • Huan-Qiang Zhou, Roman Orus, Guifre Vidal, Ground state fidelity from tensor network representations, Physical Review Letters 100, 080601 (2008), arXiv: 0709.4596
  • G. Evenbly, G. Vidal, Algorithms for entanglement renormalization, Phys. Rev. B 79, 144108 (2009), arXiv: 0707.1454
  • J. Jordan, R. Orus, G. Vidal, F. Verstraete, J. I. Cirac, Classical simulation of infinite-size quantum lattice systems in two spatial dimensions, Physical Review Letters 101, 250602 (2008), arXiv: cond-mat/0703788
  • Animesh Datta, Guifre Vidal, On the role of entanglement and correlations in mixed-state quantum computation, Phys. Rev. A 75, 042310 (2007), arXiv: quant-ph/0611157
  • G. Vidal, A class of quantum many-body states that can be efficiently simulated, Phys. Rev. Lett. 101, 110501 (2008), arXiv: quant-ph/0610099
  • G. Vidal, Classical simulation of infinite-size quantum lattice systems in one spatial dimension, Phys. Rev. Lett. 98, 070201 (2007), arXiv: cond-mat/0605597
  • Guifre Vidal, Entanglement renormalization, Phys. Rev. Lett. 99, 220405 (2007), arXiv: cond-mat/0512165
  • Yaoyun Shi, Luming Duan, Guifre Vidal, Classical simulation of quantum many-body systems with a tree tensor network, Phys. Rev. A 74, 022320 (2006), arXiv: quant-ph/0511070
  • Michael Zwolak, Guifre Vidal, Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm, Phys. Rev. Lett. 93, 207205 (2004), arXiv: cond-mat/0406440
  • G. Vidal, Efficient simulation of one-dimensional quantum many-body systems, Phys. Rev. Lett. 93, 040502 (2004), arXiv: quant-ph/0310089
  • G. Vidal, C. M. Dawson, A universal quantum circuit for two-qubit transformations with three CNOT gates, Phys. Rev. A 69, 010301 (2004), arXiv: quant-ph/0307177
  • Andrew M. Childs, Debbie W. Leung, Guifre Vidal, Reversible simulation of bipartite product Hamiltonians, IEEE Trans. Inf. Theory Vol. 50, No. 6, 1189-1197 (2004), arXiv: quant-ph/0303097
  • Guifre Vidal, Efficient classical simulation of slightly entangled quantum computations, Phys. Rev. Lett. 91, 147902 (2003), arXiv: quant-ph/0301063
  • A. M. Childs, D. W. Leung, F. Verstraete, G. Vidal, Asymptotic entanglement capacity of the Ising and anisotropic Heisenberg interactions, Quantum Information and Computation 3, 97 (2003), arXiv: quant-ph/0207052
  • E. Jane, G. Vidal, W. Duer, P. Zoller, J.I. Cirac, Simulation of quantum dynamics with quantum optical systems, Quantum Information and Computation, Vol. 3, No. 1, 15-37 (2003), arXiv: quant-ph/0207011
  • G. Vidal, K. Hammerer, J. I. Cirac, Interaction cost of non-local gates, Phys. Rev. Lett. 88 (2002) 237902, arXiv: quant-ph/0112168
  • G. Vidal, J. I. Cirac, Optimal simulation of nonlocal Hamiltonians using local operations and classical communication, Phys. Rev. A 66, 022315 (2002), arXiv: quant-ph/0108076
  • G. Vidal, J. I. Cirac, Catalysis in non--local quantum operations, Phys. Rev. Lett. 88 (2002) 167903, arXiv: quant-ph/0108077
  • G. Vidal, J. I. Cirac, When only two thirds of the entanglement can be distilled, Phys. Rev. A 65, 012323 (2002), arXiv: quant-ph/0107051
  • G. Vidal, R.F. Werner, A computable measure of entanglement, Phys. Rev. A 65, 032314 (2002), arXiv: quant-ph/0102117
  • G. Vidal, L. Masanes, J.I. Cirac, Storing quantum dynamics in quantum states: stochastic programmable gate for U(1) operations, Phys. Rev. Lett. 88, 047905 (2002), arXiv: quant-ph/0102037
  • G. Vidal, J. I. Cirac, Irreversibility in asymptotic manipulations of entanglement, Phys. Rev. Lett. 86, (2001) 5803-5806., arXiv: quant-ph/0102036
  • W. Duer, G. Vidal, J.I. Cirac, Visible compression of commuting mixed states, Phys. Rev. A 64, 022308 (2001), arXiv: quant-ph/0101111
  • G. Vidal, W. Duer, J. I. Cirac, Reversible combination of inequivalent kinds of multipartite entanglement, Phys. Rev. Lett. 85, 658 (2000), arXiv: quant-ph/0004009
  • Guifre Vidal, Daniel Jonathan, M. A. Nielsen, Approximate transformations and robust manipulation of bipartite pure state entanglement, Phys. Rev. A 62, 012304 (2000), arXiv: quant-ph/9910099
  • Rolf Tarrach, Guifre Vidal, Universality of optimal measurements, Phys. Rev. A 60, R3339 (1999), arXiv: quant-ph/9907098
  • Guifre Vidal, Entanglement of pure states for a single copy, Phys.Rev.Lett. 83 (1999) 1046-1049, arXiv: quant-ph/9902033
  • G. Vidal, J.I. Latorre, P. Pascual, R. Tarrach, Optimal minimal measurements of mixed states, Phys.Rev. A60 (1999) 126, arXiv: quant-ph/9812068
  • Guifre Vidal, Entanglement monotones, J.Mod.Opt. 47 (2000) 355, arXiv: quant-ph/9807077
  • Guifre Vidal, Rolf Tarrach, Robustness of entanglement, Phys.Rev. A59 (1999) 141-155, arXiv: quant-ph/9806094
  • Anna Sanpera, Rolf Tarrach, Guifre Vidal, Quantum inseparability as local pseudomixture, Phys.Rev. A58 (1998) 826-830, arXiv: quant-ph/9801024
  • Constructing local integrals of motion in the many-body localized phase, Anushya Chandran, Isaac H. Kim, Guifre Vidal, Dmitry A. Abanin, arXiv: 1407.8480
  • NCON: A tensor network contractor for MATLAB, Robert N. C. Pfeifer, Glen Evenbly, Sukhwinder Singh, Guifre Vidal, arXiv: 1402.0939
  • Disentangling Theorem and Monogamy for Entanglement Negativity, Huan He, Guifre Vidal, arXiv: 1401.5843
  • Glen Evenbly, Guifre Vidal, A theory of minimal updates in holography, arXiv: 1307.0831
  • Quantum Criticality with the Multi-scale Entanglement Renormalization Ansatz, Glen Evenbly and Guifre Vidal, chapter in "Strongly Correlated Systems, Numerical Methods", edited by Adolfo Avella and Ferdinando Mancini (Springer Series in Solid-State Sciences volume 176, Springer 2013); arXiv: 1109.5334
  • Entanglement Renormalization: an introduction, Guifre Vidal, chapter in "Understanding Quantum Phase Transitions", edited by Lincoln D. Carr (Taylor & Francis, Boca Raton, 2010); arXiv: 0912.1651

Seminars

  • "Efficient classical simulation of many-body systems with local integrals of motion", Tensor networks and simulations Simons Institute for the Theory of Computing, UC Berkeley, US, April 2014.
  • "Tensor networks", Simons Collaboration on the Many Electron Problem Simons Foundation, New York, US, March 2014.
  • "Tensor networks for quantum many-body systems", CQIQC seminar, Physics Department, University of Toronto, Toronto, Canada, February 2014.
  • "On the shape of entanglement", Sydney Quantum Information Workshop, Coogee Bay, Sydney, Australia, January 2014.
  • "On the shape of entanglement", Taipei Tensor Network Workshop, Taipei, Taiwan, December 2013.
  • "Many-body entanglement and tensor network states", Colloquium, Institute for Quantum Computing, Waterloo, Canada, October 2013.
  • "Many-body entanglement and tensor network states", Colloquium, Department of Physics and Astronomy, McMaster University, Hamilton, Canada, October 2013.
  • "Characterization of emergent topological order from a microscopic Hamiltonian", Seminar, ICFO, Barcelona, Spain, July 2013.
  • "Tensor Networks", Simons Foundation, New York, US, May 2013.
  • "Towards a complete characterization of emergent topological order from a microscopic Hamiltonian", Sydney Quantum Information Theory Workshop, Coogee, Australia, January 2013.
  • 5. "Towards a complete characterization of emergent topological order from a microscopic Hamiltonian", Quantum Science Seminar, The University of Queensland, Brisbane, Australia, December 2012.
  • "Towards a complete characterization of emergent topological order from a microscopic Hamiltonian", Mini-workshop on recent development in DMRG/TNs, NTU, Taipei, Taiwan, December 2012.
  • "Topological order with tensor networks on infinite cylinders", California Institute of Technology, Pasadena, US, October 2012.
  • "Towards a complete classification of emergent topological order from a microscopic Hamiltonian", Workshop: "Exotic Phases of Frustrated Magnets", KITP, Santa Barbara, October 2012.
  • "Characterizing topological order by studying the ground states of an infinite cylinder", Microsoft Station Q, Santa Barbara, US, September 2012.
  • "Tensor network states that go beyond the boundary law for entanglement entropy", ICFO, Barcelona, Spain, Jun2 2012.
  • "Tensor network states that go beyond the boundary law for entanglement entropy", Workshop: "New states of matter in and out of equilibrium", Galileo Galilei Institute, Florence, Italy, May 2012.
  • "A class of entangling quantum circuits that can be efficiently simulated", Workshop: "Networking tensor networks", Benasque, Spain, May 2012.
  • "Criticality, impurities, and real-space renormalization", Sydney Quantum Information Theory Workshop, Coogee'12 Sydney, Australia, January 2012
  • PIRSA:14040067, 13/14 PSI - Explorations in Condensed Matter - Lecture 15, 2014-04-04,
  • PIRSA:14040040, 13/14 PSI - Explorations in Condensed Matter - Lecture 14, 2014-04-03, 13/14 PSI - Explorations in Condensed Matter
  • PIRSA:14040039, 13/14 PSI - Explorations in Condensed Matter - Lecture 13, 2014-04-02, 13/14 PSI - Explorations in Condensed Matter
  • PIRSA:14040038, 13/14 PSI - Explorations in Condensed Matter - Lecture 12, 2014-04-01, 13/14 PSI - Explorations in Condensed Matter
  • PIRSA:14040037, 13/14 PSI - Explorations in Condensed Matter - Lecture 11, 2014-03-31, 13/14 PSI - Explorations in Condensed Matter
  • PIRSA:14040036, 13/14 PSI - Explorations in Condensed Matter - Lecture 10, 2014-03-28, 13/14 PSI - Explorations in Condensed Matter
  • PIRSA:14040032, 13/14 PSI - Explorations in Condensed Matter - Lecture 9, 2014-03-27, 13/14 PSI - Explorations in Condensed Matter
  • PIRSA:14040031, 13/14 PSI - Explorations in Condensed Matter - Lecture 8, 2014-03-26, 13/14 PSI - Explorations in Condensed Matter
  • PIRSA:14040030, 13/14 PSI - Explorations in Condensed Matter - Lecture 7, 2014-03-25, 13/14 PSI - Explorations in Condensed Matter
  • PIRSA:14040029, 13/14 PSI - Explorations in Condensed Matter - Lecture 6, 2014-03-24, 13/14 PSI - Explorations in Condensed Matter
  • PIRSA:14040026, 13/14 PSI - Explorations in Condensed Matter - Lecture 5, 2014-03-21, 13/14 PSI - Explorations in Condensed Matter
  • PIRSA:14040025, 13/14 PSI - Explorations in Condensed Matter - Lecture 4, 2014-03-20, 13/14 PSI - Explorations in Condensed Matter
  • PIRSA:14040024, 13/14 PSI - Explorations in Condensed Matter - Lecture 3, 2014-03-19, 13/14 PSI - Explorations in Condensed Matter
  • PIRSA:14040023, 13/14 PSI - Explorations in Condensed Matter - Lecture 2, 2014-03-18, 13/14 PSI - Explorations in Condensed Matter
  • PIRSA:14040022, 13/14 PSI - Explorations in Condensed Matter - Lecture 1, 2014-03-17, 13/14 PSI - Explorations in Condensed Matter
  • PIRSA:14020122, Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator, 2014-02-13, Emergence in Complex Systems
  • PIRSA:10100098, Perimeter Institute Pedagogical Introduction: Tensor Networks and Geometry, the Renormalization Group and AdS/CFT , 2011-10-25, Tensor Networks for Quantum Field Theories Conference
  • PIRSA:11100075, Pedagogical Introduction to Tensor Networks: MPS, PEPS and MERA , 2011-10-24, Tensor Networks for Quantum Field Theories Conference
  • PIRSA:11080143, Researcher Presentation: Guifre Vidal, 2011-08-31, 11/12 PSI - Researcher Presentations
  • PIRSA:10050066, Entanglement renormalization and gauge symmetry, 2010-05-25, Emergence and Entanglement
  • PIRSA:08010005, Entanglement Renormalization, Quantum Criticality and Topological Order, 2008-01-23, Perimeter Institute Quantum Discussions
  • PIRSA:05020003, Disentangling quantum systems: a new perspective in computational quantum physics, 2005-02-02, Perimeter Institute Quantum Discussions