Efficient Tensor Network ansatz for high-dimensional quantum many-body problems

• URL: http://arxiv.org/abs/2011.08200v1
• Date: Mon, 16 Nov 2020 19:00:04 GMT
• Title: Efficient Tensor Network ansatz for high-dimensional quantum many-body problems
• Authors: Timo Felser, Simone Notarnicola and Simone Montangero
• Abstract summary: We introduce a novel tensor network structure augmenting the well-established Tree Network representation of a quantum many-body wave function. We benchmark this novel approach against paradigmatic two-dimensional spin models demonstrating unprecedented precision and system sizes.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a novel tensor network structure augmenting the well-established Tree Tensor Network representation of a quantum many-body wave function. The new structure satisfies the area law in high dimensions remaining efficiently manipulatable and scalable. We benchmark this novel approach against paradigmatic two-dimensional spin models demonstrating unprecedented precision and system sizes. Finally, we compute the ground state phase diagram of two-dimensional lattice Rydberg atoms in optical tweezers observing non-trivial phases and quantum phase transitions, providing realistic benchmarks for current and future two-dimensional quantum simulations.

Related papers

• From $SU(2)$ holonomies to holographic duality via tensor networks [0.0]
  We construct a tensor network representation of the spin network states, which correspond to $SU(2)$ gauge-invariant discrete field theories. The spin network states play a central role in the Loop Quantum Gravity (LQG) approach to the Planck scale physics.
  arXiv  Detail & Related papers  (2024-10-24T14:59:35Z)
• Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems [77.88054335119074]
  We use FNOs to model the evolution of random quantum spin systems. We apply FNOs to a compact set of Hamiltonian observables instead of the entire $2n$ quantum wavefunction.
  arXiv  Detail & Related papers  (2024-09-05T07:18:09Z)
• Simulating 2D topological quantum phase transitions on a digital quantum computer [3.727382912998531]
  Efficient preparation of many-body ground states is key to harnessing the power of quantum computers in studying quantum many-body systems. We propose a simple method to design exact linear-depth parameterized quantum circuits which prepare a family of ground states across topological quantum phase transitions in 2D. We show that the 2D isoTNS can also be efficiently simulated by a holographic quantum algorithm requiring only an 1D array of qubits.
  arXiv  Detail & Related papers  (2023-12-08T15:01:44Z)
• A Floquet-Rydberg quantum simulator for confinement in $\mathbb{Z}_2$ gauge theories [44.99833362998488]
  Recent advances in the field of quantum technologies have opened up the road for the realization of small-scale quantum simulators. We present a scalable Floquet scheme for the quantum simulation of the real-time dynamics in a $mathbbZ$ LGT. We show that an observation of gauge-invariant confinement dynamics in the Floquet-Rydberg setup is at reach of current experimental techniques.
  arXiv  Detail & Related papers  (2023-11-28T13:01:24Z)
• Highly resolved spectral functions of two-dimensional systems with neural quantum states [0.0]
  We develop a versatile approach using neural quantum states to obtain spectral properties based on simulations of excitations initially localized in real or momentum space. Our approach is broadly applicable to interacting quantum lattice models in two dimensions and opens up a route to compute spectral properties of correlated quantum matter in yet inaccessible regimes.
  arXiv  Detail & Related papers  (2023-03-14T19:00:27Z)
• Towards Neural Variational Monte Carlo That Scales Linearly with System Size [67.09349921751341]
  Quantum many-body problems are central to demystifying some exotic quantum phenomena, e.g., high-temperature superconductors. The combination of neural networks (NN) for representing quantum states, and the Variational Monte Carlo (VMC) algorithm, has been shown to be a promising method for solving such problems. We propose a NN architecture called Vector-Quantized Neural Quantum States (VQ-NQS) that utilizes vector-quantization techniques to leverage redundancies in the local-energy calculations of the VMC algorithm.
  arXiv  Detail & Related papers  (2022-12-21T19:00:04Z)
• Neural network enhanced measurement efficiency for molecular groundstates [63.36515347329037]
  We adapt common neural network models to learn complex groundstate wavefunctions for several molecular qubit Hamiltonians. We find that using a neural network model provides a robust improvement over using single-copy measurement outcomes alone to reconstruct observables.
  arXiv  Detail & Related papers  (2022-06-30T17:45:05Z)
• Neural-Network Quantum States for Periodic Systems in Continuous Space [66.03977113919439]
  We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of periodicity. For one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods.
  arXiv  Detail & Related papers  (2021-12-22T15:27:30Z)
• Efficient Simulation of Dynamics in Two-Dimensional Quantum Spin Systems with Isometric Tensor Networks [0.0]
  We investigate the computational power of the recently introduced class of isometric tensor network states (isoTNSs) We discuss several technical details regarding the implementation of isoTNSs-based algorithms and compare different disentanglers. We compute the dynamical spin structure factor of 2D quantum spin systems for two paradigmatic models.
  arXiv  Detail & Related papers  (2021-12-15T19:00:05Z)
• Solving Quantum Master Equations with Deep Quantum Neural Networks [0.0]
  We use deep quantum feedforward neural networks capable of universal quantum computation to represent the mixed states for open quantum many-body systems. Owning to the special structure of the quantum networks, this approach enjoys a number of notable features, including the absence of barren plateaus.
  arXiv  Detail & Related papers  (2020-08-12T18:00:08Z)
• Hyperentanglement in structured quantum light [50.591267188664666]
  Entanglement in high-dimensional quantum systems, where one or more degrees of freedom of light are involved, offers increased information capacities and enables new quantum protocols. Here, we demonstrate a functional source of high-dimensional, noise-resilient hyperentangled states encoded in time-frequency and vector-vortex structured modes. We generate highly entangled photon pairs at telecom wavelength that we characterise via two-photon interference and quantum state tomography, achieving near-unity visibilities and fidelities.
  arXiv  Detail & Related papers  (2020-06-02T18:00:04Z)

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.