1.8k citations · 31.8k across the 228 of their papers we have counts for
124 papers · 1 filter
Gauge-covariant projected entangled paired states for interacting systems in a magnetic field
Wei Tang, Gunnar Möller, Frank Verstraete +1
The Hamiltonian for a system of itinerant particles on a two-dimensional lattice in a uniform magnetic field reduces the translational symmetry to a magnetic translation group, bec…
Fermionic tensor network methods
Quinten Mortier, Lukas Devos, Lander Burgelman +5
We show how fermionic statistics can be naturally incorporated in tensor networks on arbitrary graphs through the use of graded Hilbert spaces. This formalism allows to use tensor…
Dualities in one-dimensional quantum lattice models: topological sectors
Laurens Lootens, Clement Delcamp, Frank Verstraete
It has been a long-standing open problem to construct a general framework for relating the spectra of dual theories to each other. Here, we solve this problem for the case of one-d…
Generative modeling with projected entangled-pair states
Tom Vieijra, Laurens Vanderstraeten, Frank Verstraete
We argue and demonstrate that projected entangled-pair states (PEPS) outperform matrix product states significantly for the task of generative modeling of datasets with an intrinsi…
Mapping between Morita equivalent string-net states with a constant depth quantum circuit
Laurens Lootens, Bram Vancraeynest-De Cuiper, Norbert Schuch +1
We construct a constant depth quantum circuit that maps between Morita equivalent string-net models. Due to its constant depth and unitarity, the circuit cannot alter the topologic…
Dualities in one-dimensional quantum lattice models: symmetric Hamiltonians and matrix product operator intertwiners
Laurens Lootens, Clement Delcamp, Gerardo Ortiz +1
We present a systematic recipe for generating and classifying duality transformations in one-dimensional quantum lattice systems. Our construction emphasizes the role of global sym…
A scaling hypothesis for projected entangled-pair states
Bram Vanhecke, Juraj Hasik, Frank Verstraete +1
We introduce a new paradigm for scaling simulations with projected entangled-pair states (PEPS) for critical strongly-correlated systems, allowing for reliable extrapolations of PE…
Quantum error correction thresholds for the universal Fibonacci Turaev-Viro code
Alexis Schotte, Guanyu Zhu, Lander Burgelman +1
We consider a two-dimensional quantum memory of qubits on a torus which encode the extended Fibonaccistring-net code, and devise strategies for error correction when those qubits a…
Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
Ignacio Cirac, David Perez-Garcia, Norbert Schuch +1
The theory of entanglement provides a fundamentally new language for describing interactions and correlations in many body systems. Its vocabulary consists of qubits and entangled…
Matrix product operator symmetries and intertwiners in string-nets with domain walls
Laurens Lootens, Jürgen Fuchs, Jutho Haegeman +2
We provide a description of virtual non-local matrix product operator (MPO) symmetries in projected entangled pair state (PEPS) representations of string-net models. Given such a P…
Variational optimization of continuous matrix product states
Benoît Tuybens, Jacopo De Nardis, Jutho Haegeman +1
Just as matrix product states represent ground states of one-dimensional quantum spin systems faithfully, continuous matrix product states (cMPS) provide faithful representations o…
Efficient variational contraction of two-dimensional tensor networks with a non-trivial unit cell
A. Nietner, B. Vanhecke, F. Verstraete +2
Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor n…
Uncertainty and Trade-offs in Quantum Multiparameter Estimation
Ilya Kull, Philippe Allard Guérin, Frank Verstraete
Uncertainty relations in quantum mechanics express bounds on our ability to simultaneously obtain knowledge about expectation values of non-commuting observables of a quantum syste…
Tangent-space methods for truncating uniform MPS
Bram Vanhecke, Maarten Van Damme, Jutho Haegeman +2
A central primitive in quantum tensor network simulations is the problem of approximating a matrix product state with one of a lower bond dimension. This problem forms the central…
Symmetric cluster expansions with tensor networks
Bram Vanhecke, Laurens Vanderstraeten, Frank Verstraete
Cluster expansions for the exponential of local operators are constructed using tensor networks. In contrast to other approaches, the cluster expansion does not break any spatial o…
Simulating Lattice Gauge Theories within Quantum Technologies
M. C. Bañuls, R. Blatt, J. Catani +17
Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum…
Galois conjugated tensor fusion categories and non-unitary CFT
Laurens Lootens, Robijn Vanhove, Jutho Haegeman +1
We provide a generalisation of the matrix product operator (MPO) formalism for string-net projected entangled pair states (PEPS) to include non-unitary solutions of the pentagon eq…
Mapping topological to conformal field theories through strange correlators
Matthias Bal, Dominic J. Williamson, Robijn Vanhove +3
We extend the concept of strange correlators, defined for symmetry-protected phases in [You et al., Phys. Rev. Lett. 112, 247202 (2014)], to topological phases of matter by taking…
Symmetry-enriched topological order in tensor networks: Defects, gauging and anyon condensation
Dominic J. Williamson, Nick Bultinck, Frank Verstraete
We study symmetry-enriched topological order in two-dimensional tensor network states by using graded matrix product operator algebras to represent symmetry-induced domain walls. A…
Thermal States as Convex Combinations of Matrix Product States
Mario Berta, Fernando G. S. L. Brandao, Jutho Haegeman +2
We study thermal states of strongly interacting quantum spin chains and prove that those can be represented in terms of convex combinations of matrix product states. Apart from rev…
Variational optimization algorithms for uniform matrix product states
V. Zauner-Stauber, L. Vanderstraeten, M. T. Fishman +2
We combine the Density Matrix Renormalization Group (DMRG) with Matrix Product State tangent space concepts to construct a variational algorithm for finding ground states of one di…
Continuous matrix product states with periodic boundary conditions and an application to atomtronics
Damian Draxler, Jutho Haegeman, Frank Verstraete +1
We introduce a time evolution algorithm for one-dimensional quantum field theories with periodic boundary conditions. This is done by applying the Dirac-Frenkel time-dependent vari…
Fermionic Matrix Product Operators and Topological Phases of Matter
Dominic J. Williamson, Nick Bultinck, Jutho Haegeman +1
We introduce the concept of fermionic matrix product operators, and show that they provide a natural representation of fermionic fusion tensor categories. This allows for the class…
Matrix Product Density Operators: Renormalization Fixed Points and Boundary Theories
J. I. Cirac, D. Perez-Garcia, N. Schuch +1
We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced by F. Verstraete…