Spectral gaps in interacting quantum systems

Project Information

GAPS

Grant agreement ID: 648913

DOI 10.3030/648913

Project closed

EC signature date 23 March 2015

Start date 1 September 2015

End date 28 February 2022

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost € 1 462 750,00

EU contribution € 1 462 750,00

Coordinated by

UNIVERSIDAD COMPLUTENSE DE MADRID
Spain

Publications

Peer reviewed articles (50)

Observers of quantum systems cannot agree to disagree

Author(s): Patricia Contreras-Tejada, Giannicola Scarpa, Aleksander M. Kubicki, Adam Brandenburger, Pierfrancesco La Mura
Published in: Nature Communications, Issue 12, 2021, Page(s) 7021, ISSN 2041-1723
Publisher: Nature Publishing Group
DOI: 10.1038/s41467-021-27134-6

Efficient training of energy-based models via spin-glass control

Author(s): Alejandro Pozas-Kerstjens, Gorka Muñoz-Gil, Eloy Piñol, Miguel Ángel García-March, Antonio Acín, Maciej Lewenstein, Przemysław R Grzybowski
Published in: Machine Learning: Science and Technology, Issue 2/2, 2021, Page(s) 025026, ISSN 2632-2153
Publisher: IOP Publishing
DOI: 10.1088/2632-2153/abe807

Quantum Inflation: A General Approach to Quantum Causal Compatibility

Author(s): Elie Wolfe, Alejandro Pozas-Kerstjens, Matan Grinberg, Denis Rosset, Antonio Acín, Miguel Navascués
Published in: Physical Review X, Issue 11/2, 2021, ISSN 2160-3308
Publisher: American Physical Society
DOI: 10.1103/physrevx.11.021043

Correlation Length in Random MPS and PEPS

Author(s): Cécilia Lancien, David Pérez-García
Published in: Annales Henri Poincaré, 2021, ISSN 1424-0637
Publisher: Birkhauser Verlag
DOI: 10.1007/s00023-021-01087-4

Random Private Quantum States

Author(s): Matthias Christandl, Roberto Ferrara, Cecilia Lancien
Published in: IEEE Transactions on Information Theory, Issue 66/7, 2020, Page(s) 4621-4640, ISSN 0018-9448
Publisher: Institute of Electrical and Electronics Engineers
DOI: 10.1109/tit.2020.2973155

String order parameters for symmetry fractionalization in an enriched toric code

Author(s): José Garre-Rubio, Mohsin Iqbal, David T. Stephen
Published in: Physical Review B, Issue 103/12, 2021, ISSN 2469-9950
Publisher: American Physical Society
DOI: 10.1103/physrevb.103.125104

Full Network Nonlocality

Author(s): Alejandro Pozas-Kerstjens, Nicolas Gisin, Armin Tavakoli
Published in: Physical Review Letters, Issue 128, 2022, Page(s) 010403, ISSN 0031-9007
Publisher: American Physical Society
DOI: 10.1103/physrevlett.128.010403

Undecidability of the Spectral Gap in One Dimension

Author(s): Johannes Bausch, Toby S. Cubitt, Angelo Lucia, David Perez-Garcia
Published in: Physical Review X, Issue 10/3, 2020, ISSN 2160-3308
Publisher: American Physical Society
DOI: 10.1103/physrevx.10.031038

Matrix product states and projected entangled pair states: Concepts, symmetries, theorems

Author(s): J. Ignacio Cirac, David Pérez-García, Norbert Schuch, Frank Verstraete
Published in: Reviews of Modern Physics, Issue 93, 2021, Page(s) 045003, ISSN 0034-6861
Publisher: American Physical Society
DOI: 10.1103/revmodphys.93.045003

Subsystem symmetry enriched topological order in three dimensions

Author(s): David T. Stephen, José Garre-Rubio, Arpit Dua, Dominic J. Williamson
Published in: Physical Review Research, Issue 2/3, 2020, ISSN 2643-1564
Publisher: American Physical Society
DOI: 10.1103/physrevresearch.2.033331

Projected Entangled Pair States: Fundamental Analytical and Numerical Limitations

Author(s): G. Scarpa, A. Molnár, Y. Ge, J. J. García-Ripoll, N. Schuch, D. Pérez-García, S. Iblisdir
Published in: Physical Review Letters, Issue 125/21, 2020, ISSN 0031-9007
Publisher: American Physical Society
DOI: 10.1103/physrevlett.125.210504

Inaccessible entanglement in symmetry protected topological phases

Author(s): Caroline de Groot, David T Stephen, Andras Molnar, Norbert Schuch
Published in: Journal of Physics A: Mathematical and Theoretical, Issue 53/33, 2020, Page(s) 335302, ISSN 1751-8113
Publisher: Institute of Physics Publishing
DOI: 10.1088/1751-8121/ab98c7

On the modified logarithmic Sobolev inequality for the heat-bath dynamics for 1D systems

Author(s): Ivan Bardet, Ángela Capel, Angelo Lucia, David Pérez-García, Cambyse Rouzé
Published in: Journal of Mathematical Physics, Issue 62/6, 2021, Page(s) 061901, ISSN 0022-2488
Publisher: American Institute of Physics
DOI: 10.1063/1.5142186

Single-photon nonlocality in quantum networks

Author(s): Paolo Abiuso, Tamás Kriváchy, Emanuel-Cristian Boghiu, Marc-Olivier Renou, Alejandro Pozas-Kerstjens, Antonio Acín
Published in: Physical Review Research, Issue 4, 2022, Page(s) L012041, ISSN 2643-1564
Publisher: American Physical Society
DOI: 10.1103/physrevresearch.4.l012041

Defence against adversarial attacks using classical and quantum-enhanced Boltzmann machines †

Author(s): Aidan Kehoe, Peter Wittek, Yanbo Xue, Alejandro Pozas-Kerstjens
Published in: Machine Learning: Science and Technology, Issue 2/4, 2021, Page(s) 045006, ISSN 2632-2153
Publisher: IOP Publishing
DOI: 10.1088/2632-2153/abf834

Bell nonlocality in networks

Author(s): Armin Tavakoli, Alejandro Pozas-Kerstjens, Ming-Xing Luo, Marc-Olivier Renou
Published in: Reports on Progress in Physics, 2022, ISSN 0034-4885
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6633/ac41bb

Geometry of Banach spaces: a new route towards Position Based Cryptography

Author(s): Marius Junge, Aleksander M. Kubicki, Carlos Palazuelos, David Pérez-García
Published in: Communications in Mathematical Physics, Issue provisionally accepted, 2021, ISSN 0010-3616
Publisher: Springer Verlag

Superadditivity of Quantum Relative Entropy for General States

Author(s): Angela Capel, Angelo Lucia, David Perez-Garcia
Published in: IEEE Transactions on Information Theory, Issue 64/7, 2018, Page(s) 4758-4765, ISSN 0018-9448
Publisher: Institute of Electrical and Electronics Engineers
DOI: 10.1109/tit.2017.2772800

A contour for the entanglement entropies in harmonic lattices

Author(s): Andrea Coser, Cristiano De Nobili, Erik Tonni
Published in: Journal of Physics A: Mathematical and Theoretical, Issue 50/31, 2017, Page(s) 314001, ISSN 1751-8113
Publisher: Institute of Physics Publishing
DOI: 10.1088/1751-8121/aa7902

Size-driven quantum phase transitions

Author(s): Johannes Bausch, Toby S. Cubitt, Angelo Lucia, David Perez-Garcia, Michael M. Wolf
Published in: Proceedings of the National Academy of Sciences, Issue 115/1, 2018, Page(s) 19-23, ISSN 0027-8424
Publisher: National Academy of Sciences
DOI: 10.1073/pnas.1705042114

Symmetry reduction induced by anyon condensation: A tensor network approach

Author(s): José Garre-Rubio, Sofyan Iblisdir, David Pérez-García
Published in: Physical Review B, Issue 96/15, 2017, ISSN 1098-0121
Publisher: American Physical Society
DOI: 10.1103/PhysRevB.96.155123

Matrix product unitaries: structure, symmetries, and topological invariants

Author(s): J Ignacio Cirac, David Perez-Garcia, Norbert Schuch, Frank Verstraete
Published in: Journal of Statistical Mechanics: Theory and Experiment, Issue 2017/8, 2017, Page(s) 083105, ISSN 1742-5468
Publisher: Institute of Physics
DOI: 10.1088/1742-5468/aa7e55

Irreducible forms of matrix product states: Theory and applications

Author(s): Gemma De las Cuevas, J. Ignacio Cirac, Norbert Schuch, David Perez-Garcia
Published in: Journal of Mathematical Physics, Issue 58/12, 2017, Page(s) 121901, ISSN 0022-2488
Publisher: American Institute of Physics
DOI: 10.1063/1.5000784

Memory effects can make the transmission capability of a communication channel uncomputable

Author(s): David Elkouss, David Pérez-García
Published in: Nature Communications, Issue 9/1, 2018, ISSN 2041-1723
Publisher: Nature Publishing Group
DOI: 10.1038/s41467-018-03428-0

Quantum conditional relative entropy and quasi-factorization of the relative entropy

Author(s): Ángela Capel, Angelo Lucia, David Pérez-García
Published in: Journal of Physics A: Mathematical and Theoretical, 2018, ISSN 1751-8113
Publisher: Institute of Physics Publishing
DOI: 10.1088/1751-8121/aae4cf

Constructing topological models by symmetrization: A projected entangled pair states study

Author(s): Carlos Fernández-González, Roger S. K. Mong, Olivier Landon-Cardinal, David Pérez-García, Norbert Schuch
Published in: Physical Review B, Issue 94/15, 2016, ISSN 2469-9950
Publisher: American Physical Society
DOI: 10.1103/PhysRevB.94.155106

Fundamental limitations in the purifications of tensor networks

Author(s): G. De las Cuevas, T. S. Cubitt, J. I. Cirac, M. M. Wolf, D. Pérez-García
Published in: Journal of Mathematical Physics, Issue 57/7, 2016, Page(s) 071902, ISSN 0022-2488
Publisher: American Institute of Physics
DOI: 10.1063/1.4954983

Matrix product density operators: Renormalization fixed points and boundary theories

Author(s): J.I. Cirac, D. Pérez-García, N. Schuch, F. Verstraete
Published in: Annals of Physics, Issue 378, 2017, Page(s) 100-149, ISSN 0003-4916
Publisher: Academic Press
DOI: 10.1016/j.aop.2016.12.030

Area law for fixed points of rapidly mixing dissipative quantum systems

Author(s): Fernando G. S. L. Brandão, Toby S. Cubitt, Angelo Lucia, Spyridon Michalakis, David Perez-Garcia
Published in: Journal of Mathematical Physics, Issue 56/10, 2015, Page(s) 102202, ISSN 0022-2488
Publisher: American Institute of Physics
DOI: 10.1063/1.4932612

Undecidability of the spectral gap

Author(s): Toby S. Cubitt, David Perez-Garcia, Michael M. Wolf
Published in: Nature, Issue 528/7581, 2015, Page(s) 207-211, ISSN 0028-0836
Publisher: Nature Publishing Group
DOI: 10.1038/nature16059

Entanglement negativity in a two dimensional harmonic lattice: area law and corner contributions

Author(s): Cristiano De Nobili, Andrea Coser, Erik Tonni
Published in: Journal of Statistical Mechanics: Theory and Experiment, Issue 2016/8, 2016, Page(s) 083102, ISSN 1742-5468
Publisher: Institute of Physics
DOI: 10.1088/1742-5468/2016/08/083102

Conformal energy currents on the edge of a topological superconductor

Author(s): Chris N. Self, Jiannis K. Pachos, James R. Wootton, Sofyan Iblisdir
Published in: Physical Review B, Issue 95/11, 2017, ISSN 2469-9950
Publisher: American Physical Society
DOI: 10.1103/PhysRevB.95.115141

Resource Quantification for the No-Programing Theorem

Author(s): Aleksander M. Kubicki, Carlos Palazuelos, David Pérez-García
Published in: Physical Review Letters, Issue 122/8, 2019, ISSN 0031-9007
Publisher: American Physical Society
DOI: 10.1103/PhysRevLett.122.080505

Local order parameters for symmetry fractionalization

Author(s): José Garre-Rubio, Sofyan Iblisdir
Published in: New Journal of Physics, Issue 21/11, 2019, Page(s) 113016, ISSN 1367-2630
Publisher: Institute of Physics Publishing
DOI: 10.1088/1367-2630/ab4fff

Locality at the Boundary Implies Gap in the Bulk for 2D PEPS

Author(s): Michael J. Kastoryano, Angelo Lucia, David Perez-Garcia
Published in: Communications in Mathematical Physics, Issue 366/3, 2019, Page(s) 895-926, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-019-03404-9

Classification of phases for mixed states via fast dissipative evolution

Author(s): Andrea Coser, David Pérez-García
Published in: Quantum, Issue 3, 2019, Page(s) 174, ISSN 2521-327X
Publisher: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
DOI: 10.22331/q-2019-08-12-174

Thermally induced metallic phase in a gapped quantum spin liquid: Monte Carlo study of the Kitaev model with parity projection

Author(s): Chris N. Self, Johannes Knolle, Sofyan Iblisdir, Jiannis K. Pachos
Published in: Physical Review B, Issue 99/4, 2019, ISSN 2469-9950
Publisher: American Physical Society
DOI: 10.1103/physrevb.99.045142

Localization with random time-periodic quantum circuits

Author(s): Christoph Sünderhauf, David Pérez-García, David A. Huse, Norbert Schuch, J. Ignacio Cirac
Published in: Physical Review B, Issue 98/13, 2018, ISSN 2469-9950
Publisher: American Physical Society
DOI: 10.1103/physrevb.98.134204

Normal projected entangled pair states generating the same state

Author(s): Andras Molnar, José Garre-Rubio, David Pérez-García, Norbert Schuch, J Ignacio Cirac
Published in: New Journal of Physics, Issue 20/11, 2018, Page(s) 113017, ISSN 1367-2630
Publisher: Institute of Physics Publishing
DOI: 10.1088/1367-2630/aae9fa

An entropic invariant for 2D gapped quantum phases

Author(s): Kohtaro Kato, Pieter Naaijkens
Published in: Journal of Physics A: Mathematical and Theoretical, Issue 53/8, 2020, Page(s) 085302, ISSN 1751-8113
Publisher: Institute of Physics Publishing
DOI: 10.1088/1751-8121/ab63a5

Probing Thermalization through Spectral Analysis with Matrix Product Operators

Author(s): Yilun Yang, Sofyan Iblisdir, J. Ignacio Cirac, Mari Carmen Bañuls
Published in: Physical Review Letters, Issue 124/10, 2020, ISSN 0031-9007
Publisher: American Physical Society
DOI: 10.1103/physrevlett.124.100602

On the Stability of Charges in Infinite Quantum Spin Systems

Author(s): Matthew Cha, Pieter Naaijkens, Bruno Nachtergaele
Published in: Communications in Mathematical Physics, Issue 373/1, 2020, Page(s) 219-264, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-019-03630-1

Continuum limits of matrix product states

Author(s): Gemma De las Cuevas, Norbert Schuch, David Perez-Garcia, J. Ignacio Cirac
Published in: Physical Review B, Issue 98/17, 2018, ISSN 2469-9950
Publisher: American Physical Society
DOI: 10.1103/physrevb.98.174303

High-Dimensional Entanglement in States with Positive Partial Transposition

Author(s): Marcus Huber, Ludovico Lami, Cécilia Lancien, Alexander Müller-Hermes
Published in: Physical Review Letters, Issue 121/20, 2018, ISSN 0031-9007
Publisher: American Physical Society
DOI: 10.1103/PhysRevLett.121.200503

Mathematical open problems in projected entangled pair states

Author(s): Juan Ignacio Cirac, José Garre-Rubio, David Pérez-García
Published in: Revista Matemática Complutense, Issue 32/3, 2019, Page(s) 579-599, ISSN 1139-1138
Publisher: Universidad Complutense de Madrid
DOI: 10.1007/s13163-019-00318-x

Undecidability of the spectral gap

Author(s): Toby Cubitt, David Perez-Garcia, Michael M. Wolf
Published in: Forum of Mathematics, Pi, Issue accepted, 2022, ISSN 2050-5086
Publisher: Cambridge University Press

Approximate Tensorization of the Relative Entropy for Noncommuting Conditional Expectations

Author(s): Ivan Bardet, Ángela Capel, Cambyse Rouzé
Published in: Annales Henri Poincaré, 2021, ISSN 1424-0637
Publisher: Birkhauser Verlag
DOI: 10.1007/s00023-021-01088-3

Locality of temperature and correlations in the presence of non-zero-temperature phase transitions

Author(s): Senaida Hernández Santana, Andras Molnar, Christian Gogolin, J. Ignacio Cirac, Antonio Acín
Published in: New Journal of Physics, Issue 23, 2021, Page(s) 073052, ISSN 1367-2630
Publisher: Institute of Physics Publishing
DOI: 10.1088/1367-2630/ac14a9

Genuine Network Multipartite Entanglement

Author(s): Miguel Navascués, Elie Wolfe, Denis Rosset, Alejandro Pozas-Kerstjens
Published in: Physical Review Letters, Issue 125/24, 2020, ISSN 0031-9007
Publisher: American Physical Society
DOI: 10.1103/physrevlett.125.240505

Efficient Description of Many-Body Systems with Matrix Product Density Operators

Author(s): Jiří Guth Jarkovský, András Molnár, Norbert Schuch, J. Ignacio Cirac
Published in: PRX Quantum, Issue 1/1, 2020, ISSN 2691-3399
Publisher: American Physical Society
DOI: 10.1103/prxquantum.1.010304

Other (8)

Proofs of network quantum nonlocality aided by machine learning

Author(s): Alejandro Pozas-Kerstjens, Nicolas Gisin, Marc-Olivier Renou
Published in: 2022
Publisher: arXiv preprint

Entropy decay for Davies semigroups of a one dimensional quantum lattice

Author(s): Ivan Bardet, Ángela Capel, Li Gao, Angelo Lucia, David Pérez-García, Cambyse Rouzé
Published in: 2021
Publisher: arXiv preprint

Matrix product operator algebras I: representations of weak Hopf algebras and projected entangled pair states

Author(s): Andras Molnar, Alberto Ruiz de Alarcón, José Garre-Rubio, Norbert Schuch, J. Ignacio Cirac, David Pérez-García
Published in: 2022
Publisher: arXiv preprint

Locality estimates for complex time evolution in 1D

Author(s): David Pérez-García, Antonio Pérez-Hernández
Published in: 2020
Publisher: arXiv preprint

Matrix Product Operator Algebras II: Phases of Matter for 1D Mixed States

Author(s): Alberto Ruiz de Alarcón, José Garre-Rubio, András Molnár, David Pérez-García
Published in: 2022
Publisher: arXiv preprint

Rapid thermalization of spin chain commuting Hamiltonians

Author(s): Ivan Bardet, Ángela Capel, Li Gao, Angelo Lucia, David Pérez-García, Cambyse Rouzé
Published in: 2021
Publisher: arXiv preprint

Physics solutions for machine learning privacy leaks

Author(s): Alejandro Pozas-Kerstjens, Senaida Hernández-Santana, José Ramón Pareja Monturiol, Marco Castrillón López, Giannicola Scarpa, Carlos E. González-Guillén, David Pérez-García
Published in: 2022
Publisher: Arxiv preprint

Thermalization in Kitaev's quantum double models via Tensor Network techniques

Author(s): Angelo Lucia, David Pérez-García, Antonio Pérez-Hernández
Published in: 2021
Publisher: arXiv preprint