Guifre Vidal

Research Interests

QUANTUM MECHANICS + 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

• 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

• 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, Variational Monte Carlo with the Multi-Scale Entanglement Renormalization Ansatz, Phys. Rev. B 85, 165147 (2012), arxiv: 1201.3975
• Andrew J. Ferris, Guifre Vidal, Perfect Sampling with Unitary Tensor Networks, Phys. Rev. B 85, 165146 (2012), arxiv: 1201.3974
• 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
• Tensor network states and algorithms in the presence of a global SU(2) symmetry, Sukhwinder Singh, Guifre Vidal, arxiv: 1208.3919
• Characterizing topological order by studying the ground states of an infinite cylinder, Lukasz Cincio, Guifre Vidal, arxiv: 1208.2623
• Infinite boundary conditions for matrix product state calculations, Ho N. Phien, Guifre Vidal, Ian P. McCulloch arxiv: 1207.0678
• Dynamical windows for real-time evolution with matrix product states, Ho N. Phien, Guifre Vidal, Ian P. McCulloch arxiv: 1207.0678
• A real space decoupling transformation for quantum many-body systems, Glen Evenbly, Guifre Vidal arxiv: 1205.0639
• 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

• "Tensor network states that go beyond the boundary law for entanglement entropy", ICFO, Barcelona, Spain
• "A class of entangling quantum circuits that can be efficiently simulated", Workshop: "Networking tensor networks", Benasque, Spain
• "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.
• "Criticality, impurities, and real-space renormalization", Sydney Quantum Information Theory Workshop, Coogee'12 Sydney, Australia
• "Quantum criticality with entanglement renormalization", Forum of Physics, Hong Kong, China
• "Criticality, impurities, and real-space renormalization", Workshop on Quantum Information in Quantum Many-Body Physics, CRM Montreal, Canada
• "A class of entangling quantum circuits that can be efficiently simulated", Sydney Quantum Information Theory Workshop, Coogee'11, Sydney, Australia
• 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