Efficient variational contraction of two-dimensional tensor networks with a non-trivial unit cell

• URL: http://arxiv.org/abs/2003.01142v4
• Date: Mon, 26 Sep 2022 08:10:37 GMT
• Title: Efficient variational contraction of two-dimensional tensor networks with a non-trivial unit cell
• Authors: A. Nietner, B. Vanhecke, F. Verstraete, J. Eisert, L. Vanderstraeten
• Abstract summary: tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems. We generalize a recently proposed variational uniform matrix product state algorithm for capturing one-dimensional quantum lattices. A key property of the algorithm is a computational effort that scales linearly rather than exponentially in the size of the unit cell.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the description of such complex many-body systems, close to optimal variational principles based on such states are less obvious to come by. In this work, we generalize a recently proposed variational uniform matrix product state algorithm for capturing one-dimensional quantum lattices in the thermodynamic limit, to the study of regular two-dimensional tensor networks with a non-trivial unit cell. A key property of the algorithm is a computational effort that scales linearly rather than exponentially in the size of the unit cell. We demonstrate the performance of our approach on the computation of the classical partition functions of the antiferromagnetic Ising model and interacting dimers on the square lattice, as well as of a quantum doped resonating valence bond state.

Related papers

• Tensor Network Representation and Entanglement Spreading in Many-Body Localized Systems: A Novel Approach [0.0]
  A novel method has been devised to compute the Local Integrals of Motion for a one-dimensional many-body localized system. A class of optimal unitary transformations is deduced in a tensor-network formalism to diagonalize the Hamiltonian of the specified system. The efficiency of the method was assessed and found to be both fast and almost accurate.
  arXiv  Detail & Related papers  (2023-12-13T14:28:45Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory [44.99833362998488]
  We introduce quantum algorithms that can efficiently simulate certain classes of interactions consisting of correlated changes in multiple quantum numbers. The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions. The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories.
  arXiv  Detail & Related papers  (2022-12-28T18:56:25Z)
• Solving the nuclear pairing model with neural network quantum states [58.720142291102135]
  We present a variational Monte Carlo method that solves the nuclear many-body problem in the occupation number formalism. A memory-efficient version of the reconfiguration algorithm is developed to train the network by minimizing the expectation value of the Hamiltonian.
  arXiv  Detail & Related papers  (2022-11-09T00:18:01Z)
• Efficient calculation of three-dimensional tensor networks [5.652290685410878]
  We have proposed an efficient algorithm to calculate physical quantities in the translational invariant three-dimensional tensor networks. For the three-dimensional Ising model, the calculated internal energy and spontaneous magnetization agree with the published results in the literature.
  arXiv  Detail & Related papers  (2022-10-18T14:40:09Z)
• Say NO to Optimization: A Non-Orthogonal Quantum Eigensolver [0.0]
  A balanced description of both static and dynamic correlations in electronic systems with nearly degenerate low-lying states presents a challenge for multi-configurational methods on classical computers. We present here a quantum algorithm utilizing the action of correlating cluster operators to provide high-quality wavefunction ans"atze.
  arXiv  Detail & Related papers  (2022-05-18T16:20:36Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Quantum-Classical Hybrid Algorithm for the Simulation of All-Electron Correlation [58.720142291102135]
  We present a novel hybrid-classical algorithm that computes a molecule's all-electron energy and properties on the classical computer. We demonstrate the ability of the quantum-classical hybrid algorithms to achieve chemically relevant results and accuracy on currently available quantum computers.
  arXiv  Detail & Related papers  (2021-06-22T18:00:00Z)
• Joint Network Topology Inference via Structured Fusion Regularization [70.30364652829164]
  Joint network topology inference represents a canonical problem of learning multiple graph Laplacian matrices from heterogeneous graph signals. We propose a general graph estimator based on a novel structured fusion regularization. We show that the proposed graph estimator enjoys both high computational efficiency and rigorous theoretical guarantee.
  arXiv  Detail & Related papers  (2021-03-05T04:42:32Z)
• Dynamics of two-dimensional open quantum lattice models with tensor networks [0.0]
  We develop a tensor network method, based on an infinite Projected Entangled Pair Operator (iPEPO) ansatz, applicable directly in the thermodynamic limit. We consider dissipative transverse quantum Ising and driven-dissipative hard core boson models in non-mean field limits. Our method enables to study regimes which are accessible to current experiments but lie well beyond the applicability of existing techniques.
  arXiv  Detail & Related papers  (2020-12-22T18:24:20Z)
• Variational classical networks for dynamics in interacting quantum matter [0.0]
  We introduce a variational class of wavefunctions based on complex networks of classical spins akin to artificial neural networks. We show that our method can be applied to any quantum many-body system with a well-defined classical limit.
  arXiv  Detail & Related papers  (2020-07-31T14:03:37Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.