N. Schuch

发表

Computational complexity of projected entangled pair states.

F. Verstraete, J. Cirac, M. Wolf, 2007, Physical review letters.

Spontaneous symmetry breaking in projected entangled pair state models

B. Terhal, N. Schuch, M. Rispler, 2017 .

Matrix Product Density Operators: Renormalization Fixed Points and Boundary Theories

D. Perez-Garcia, J. I. Cirac, F. Verstraete, 2016, 1606.00608.

Computational complexity of interacting electrons and fundamental limitations of density functional theory

F. Verstraete, N. Schuch, 2007, 0712.0483.

Measurement-based quantum computation beyond the one-way model

D. Gross, J. Eisert, D. Pérez-García, 2007, 0706.3401.

Natural two-qubit gate for quantum computation using the XY interaction

J. Siewert, N. Schuch, 2002, quant-ph/0209035.

PEPS as ground states: Degeneracy and topology

D. Pérez-García, I. Cirac, N. Schuch, 2010, 1001.3807.

Quantum entanglement theory in the presence of superselection rules (15 pages)

J. Ignacio Cirac, Norbert Schuch, Frank Verstraete, 2004 .

Nonlocal resources in the presence of superselection rules.

J I Cirac, F. Verstraete, J. Cirac, 2003, Physical review letters.

Simulation of quantum many-body systems with strings of operators and Monte Carlo tensor contractions.

Norbert Schuch, Frank Verstraete, F. Verstraete, 2008, Physical review letters.

Ground-state properties of quantum many-body systems: entangled-plaquette states and variational Monte Carlo

J. Ignacio Cirac, Norbert Schuch, Massimo Boninsegni, 2009, 0905.3898.

Fermionic projected entangled pair states

J. Ignacio Cirac, Norbert Schuch, Frank Verstraete, 2009, 0904.4667.

Entanglement spectrum and boundary theories with projected entangled-pair states

J. Ignacio Cirac, Norbert Schuch, Frank Verstraete, 2011, 1103.3427.

Purifications of multipartite states: limitations and constructive methods

J. Ignacio Cirac, Norbert Schuch, Gemma De las Cuevas, 2013, 1308.1914.

Implementation of quantum algorithms with Josephson charge qubits

N. Schuch, 2002 .

Chiral topological spin liquids with projected entangled pair states

J. Ignacio Cirac, Norbert Schuch, Didier Poilblanc, 2015, 1504.05236.

On entropy growth and the hardness of simulating time evolution

Michael M. Wolf, J. Ignacio Cirac, Norbert Schuch, 2008, 0801.2078.

Inaccessible entanglement in symmetry protected topological phases

David T. Stephen, N. Schuch, C. de Groot, 2020, Journal of Physics A: Mathematical and Theoretical.

Condensed Matter Applications of Entanglement Theory

N. Schuch, 2013, 1306.5551.

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

J. Cirac, N. Schuch, José Garre-Rubio, 2022, 2204.05940.

Entanglement spectra of non-chiral topological (2+1)-dimensional phases with strong time-reversal breaking, Li-Haldane state counting, and PEPS

A. Ludwig, N. Schuch, Mark J. Arildsen, 2022, 2207.03246.

Quantum States on Harmonic Lattices

J. Cirac, M. Wolf, N. Schuch, 2005, quant-ph/0509166.

Quantum entanglement theory in the presence of superselection rules (15 pages)

F. Verstraete, J. Cirac, N. Schuch, 2004, quant-ph/0404079.

Programmable networks for quantum algorithms.

J. Siewert, N. Schuch, 2003, Physical review letters.

Complete characterization of non-Abelian topological phase transitions and detection of anyon splitting with projected entangled pair states

N. Schuch, José Garre-Rubio, Wen-Tao Xu, 2022, 2208.13200.

Locality optimization for parent Hamiltonians of tensor networks

J. Cirac, N. Schuch, G. Giudici, 2022, Physical Review B.

Preparation and verification of tensor network states

J. Cirac, N. Schuch, Jordi Tura i Brugués, 2021, Physical Review Research.

Long-range order and symmetry breaking in projected entangled-pair state models

N. Schuch, M. Rispler, K. Duivenvoorden, 2015, 1505.04217.

Chiral projected entangled-pair state with topological order.

J. Cirac, N. Schuch, T. Wahl, 2014, Physical review letters.

Symmetries and boundary theories for chiral projected entangled pair states

J. Cirac, N. Schuch, T. Wahl, 2014, 1405.0447.

Edge theories in projected entangled pair state models.

F. Verstraete, J. Cirac, N. Schuch, 2013, Physical review letters.

Topological order in the projected entangled-pair states formalism: transfer operator and boundary Hamiltonians.

J. Cirac, D. Pérez-García, N. Schuch, 2013, Physical review letters.

Simulation of quantum many-body systems with strings of operators and Monte Carlo tensor contractions.

F. Verstraete, J. Cirac, M. Wolf, 2007, Physical review letters.

Detecting subsystem symmetry protected topological order via entanglement entropy

David T. Stephen, N. Schuch, Henrik Dreyer, 2019, Physical Review B.

Resonating-valence-bond superconductors with fermionic projected entangled pair states

J. Cirac, N. Schuch, P. Corboz, 2014, 1404.5268.

Gapped Z2 spin liquid in the breathing kagome Heisenberg antiferromagnet

N. Schuch, D. Poilblanc, Mohsin Iqbal, 2019, Physical Review B.

Frustration Free Gapless Hamiltonians for Matrix Product States

J. Cirac, M. Wolf, D. Pérez-García, 2014, Communications in Mathematical Physics.

Symmetry Protected Topological Order in Open Quantum Systems

N. Schuch, Alex Turzillo, Caroline de Groot, 2021, Quantum.

Detecting emergent continuous symmetries at quantum criticality

N. Schuch, B. Vanhecke, Ming-Jing Yang, 2022, 2210.17539.

Information propagation for interacting-particle systems

J. Eisert, T. Osborne, N. Schuch, 2010, 1010.4576.

Classifying quantum phases using Matrix Product States and PEPS

D. Pérez-García, I. Cirac, N. Schuch, 2010, 1010.3732.

Lower Bounds on Ground-State Energies of Local Hamiltonians through the Renormalization Group

N. Schuch, B. Dive, I. Kull, 2022, Physical Review X.

Complete characterization of non-Abelian topological phase transitions and detection of anyon splitting with projected entangled pair states

N. Schuch, José Garre-Rubio, Wen-Tao Xu, 2022, Physical Review B.

Fractional chiral hinge insulator

N. Regnault, N. Schuch, B. Bernevig, 2020, 2010.09728.

Computational complexity of projected entangled pair states.

F. Verstraete, J. Cirac, M. Wolf, 2006, Physical review letters.

Order parameters and critical exponents for topological phase transitions through tensor networks

N. Schuch, Mohsin Iqbal, 2020 .

Entanglement order parameters and critical behavior for topological phase transitions and beyond

N. Schuch, Mohsin Iqbal, 2020, 2011.06611.

Topological spin liquids: Robustness under perturbations

N. Schuch, Helena Casademunt, Mohsin Iqbal, 2019, Physical Review B.

A generalization of the injectivity condition for Projected Entangled Pair States

J. Ignacio Cirac, Norbert Schuch, Yimin Ge, 2017, 1706.07329.

Transfer matrices and excitations with matrix product states

F. Verstraete, J. Haegeman, N. Schuch, 2014, 1408.5140.

Localization with random time-periodic quantum circuits

D. Huse, J. Cirac, N. Schuch, 2018, Physical Review B.

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

F. Verstraete, D. Pérez-García, I. Cirac, 2020, Reviews of Modern Physics.

Classifying quantum phases using matrix product states and projected entangled pair states

David Pérez-García, J. Ignacio Cirac, Norbert Schuch, 2011 .

Entropy scaling and simulability by matrix product states.

Norbert Schuch, Frank Verstraete, F. Verstraete, 2007, Physical review letters.

Robustness of critical U(1) spin liquids and emergent symmetries in tensor networks

N. Schuch, Ji-Yao Chen, L. Vanderstraeten, 2020, 2008.04833.

Quantum chaos in the Brownian SYK model with large finite N : OTOCs and tripartite information

J. Cirac, N. Schuch, X. Qi, 2019, Journal of High Energy Physics.

Frustration Free Gapless Hamiltonians for Matrix Product States

D. Pérez-García, J. I. Cirac, J. Cirac, 2012, 1210.6613.

Approximating Gibbs states of local Hamiltonians efficiently with projected entangled pair states

J. Ignacio Cirac, Norbert Schuch, Frank Verstraete, 2014, 1406.2973.

On the stability of topological order in tensor network states

F. Verstraete, N. Schuch, C. Delcamp, 2020, Physical Review B.

Characterizing Topological Order with Matrix Product Operators

Norbert Schuch, Frank Verstraete, Dominic Williamson, 2014, Annales Henri Poincaré.

Study of anyon condensation and topological phase transitions from a Z4 topological phase using the projected entangled pair states approach

N. Schuch, K. Duivenvoorden, Mohsin Iqbal, 2017, 1712.04021.

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

D. Pérez-García, O. Landon-Cardinal, N. Schuch, 2016 .

Shadows of anyons and the entanglement structure of topological phases

F. Verstraete, J. Haegeman, N. Schuch, 2014, Nature Communications.

Gauging Quantum States: From Global to Local Symmetries in Many-Body Systems

F. Verstraete, J. Cirac, J. Haegeman, 2014, 1407.1025.

Elementary excitations in gapped quantum spin systems.

F. Verstraete, T. Osborne, J. Haegeman, 2013, Physical review letters.

SU(3)_{1} Chiral Spin Liquid on the Square Lattice: A View from Symmetric Projected Entangled Pair States.

N. Schuch, M. Mambrini, S. Capponi, 2019, Physical review letters.

Bridging Perturbative Expansions with Tensor Networks.

F. Verstraete, J. Vidal, J. Haegeman, 2017, Physical review letters.

Entanglement phases as holographic duals of anyon condensates

Norbert Schuch, Kasper Duivenvoorden, Frank Verstraete, 2017, 1702.08469.

SU(2)1 chiral edge modes of a critical spin liquid

I. Affleck, N. Schuch, D. Poilblanc, 2016, 1602.05969.

Projected entangled-pair states can describe chiral topological states.

J I Cirac, J. Cirac, N. Schuch, 2013, Physical review letters.

Characterization of topological phase transitions from a non-Abelian topological state and its Galois conjugate through condensation and confinement order parameters

N. Schuch, Wen-Tao Xu, 2021, Physical Review B.

Interplay of SU(2), point group, and translational symmetry for projected entangled pair states: Application to a chiral spin liquid

N. Schuch, A. Sterdyniak, Anna Hackenbroich, 2018, Physical Review B.

Projected entangled pair states with continuous virtual symmetries

J. Ignacio Cirac, Norbert Schuch, Henrik Dreyer, 2018, Physical Review B.

On tensor network representations of the (3+1)d toric code

N. Schuch, C. Delcamp, 2020, Quantum.

Generating function for tensor network diagrammatic summation

N. Schuch, N. Kawashima, Ji-Yao Chen, 2021, Physical Review B.

Simulating two- and three-dimensional frustrated quantum systems with string-bond states

J. Cirac, N. Schuch, A. Sfondrini, 2009, 0908.4036.

Interacting electrons, Density Functional Theory, and Quantum Merlin Arthur

F. Verstraete, N. Schuch, 2007 .

Quantum Entanglement: Theory and Applications

Norbert Schuch, N. Schuch, 2007 .

Limitations of passive protection of quantum information

J. Ignacio Cirac, Norbert Schuch, Fernando Pastawski, 2009, Quantum Inf. Comput..

One-shot entanglement generation over long distances in noisy quantum networks

M. D. Lukin, S. Perseguers, J. I. Cirac, 2008, 0807.0208.

Detecting emergent continuous symmetries at quantum criticality

N. Schuch, B. Vanhecke, Ming-Jing Yang, 2022, 2210.17539.

C 4 Condensed Matter Applications of Entanglement Theory 1

N. Schuch, 2013 .

Fermionic tensor networks for higher-order topological insulators from charge pumping

N. Regnault, N. Schuch, B. Bernevig, 2019, Physical Review B.

Mapping between Morita-equivalent string-net states with a constant depth quantum circuit

F. Verstraete, N. Schuch, Laurens Lootens, 2021, Physical Review B.

Quantum trimer models and topological SU(3) spin liquids on the kagome lattice

N. Schuch, Sven Jandura, Mohsin Iqbal, 2020, 2006.08646.

Study of anyon condensation and topological phase transitions from a Z 4 topological phase using Projected Entangled Pair States

N. Schuch, K. Duivenvoorden, Mohsin Iqbal, 2018 .

Complexity of commuting Hamiltonians on a square lattice of qubits

Norbert Schuch, N. Schuch, 2011, Quantum Inf. Comput..

Quantum proofs can be verified using only single qubit measurements pdf

Tomoyuki Morimae, Norbert Schuch, Daniel Nagaj, 2015, ArXiv.

Resonating valence bond states in the PEPS formalism

J. Cirac, D. Pérez-García, N. Schuch, 2012, 1203.4816.

Topological and entanglement properties of resonating valence bond wave functions

J. Cirac, N. Schuch, D. Poilblanc, 2012, 1202.0947.

Classification of Matrix-Product Unitaries with Symmetries.

J. Cirac, N. Schuch, Z. Gong, 2018, Physical review letters.

Matrix product unitaries: structure, symmetries, and topological invariants

David Perez-Garcia, J. Ignacio Cirac, Norbert Schuch, 2017, 1703.09188.

Gapless Hamiltonians for the toric code using the projected entangled pair state formalism.

David Pérez-García, Norbert Schuch, J. Cirac, 2011, Physical review letters.

Gapped SU(3) spin liquid with Z3 topological order

N. Schuch, L. Vanderstraeten, Ivana Kurečić, 2018, Physical Review B.

Computational difficulty of finding matrix product ground states.

Norbert Schuch, Frank Verstraete, Ignacio Cirac, 2008, Physical review letters.

Entanglement of the Antisymmetric State

Matthias Christandl, Norbert Schuch, Andreas Winter, 2009, 0910.4151.

Implementation of the Four-Bit Deutsch-Jozsa Algorithm with Josephson Charge Qubits

Jens Siewert, Norbert Schuch, J. Siewert, 2002 .

Normal projected entangled pair states generating the same state

J. Ignacio Cirac, Norbert Schuch, Jos'e Garre-Rubio, 2018, New Journal of Physics.

Irreducible forms of matrix product states: Theory and applications

David Perez-Garcia, J. Ignacio Cirac, Norbert Schuch, 2017, 1708.00029.

Order parameter for symmetry-protected phases in one dimension.

David Pérez-García, Norbert Schuch, Ignacio Cirac, 2012, Physical review letters.

Matrix product state algorithms for Gaussian fermionic states

Norbert Schuch, Bela Bauer, B. Bauer, 2019, Physical Review B.

The Computational Complexity of Density Functional Theory

F. Verstraete, J. Whitfield, N. Schuch, 2013, 1306.1259.

Projected Entangled Pair States: Fundamental Analytical and Numerical Limitations.

N. Schuch, G. Scarpa, D. Perez-Garcia, 2020, Physical review letters.

Generating function for projected entangled-pair states

N. Schuch, Hyun-Yong Lee, N. Kawashima, 2023, 2307.08083.

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

J. Cirac, N. Schuch, A. Molnár, 2020, 2003.12418.

Computational complexity of PEPS zero testing

D. Perez-Garcia, J. J. Garcia-Ripoll, G. Scarpa, 2018, 1802.08214.

Computational Difficulty of Computing the Density of States

Steven T. Flammia, Norbert Schuch, Brielin Brown, 2010, Physical review letters.

ZN symmetry breaking in projected entangled pair state models

N. Schuch, M. Rispler, K. Duivenvoorden, 2017, 1703.04137.

Computational Difficulty of Computing the Density of States

S. Flammia, N. Schuch, B. Brown, 2010, Physical review letters.