Critical behavior of lattice gauge theory Rydberg simulators from effective Hamiltonians

• URL: http://arxiv.org/abs/2312.04436v2
• Date: Thu, 25 Jan 2024 15:10:52 GMT
• Title: Critical behavior of lattice gauge theory Rydberg simulators from effective Hamiltonians
• Authors: Jin Zhang, Shan-Wen Tsai, Yannick Meurice
• Abstract summary: We consider multileg ladders of Rydberg atoms which have been proposed as quantum simulators for the compact Abelian Higgs model (CAHM) in 1+1 dimensions. Using numerical methods, we demonstrate the close correspondence between the physical simulator and the effective description for the ground state energy and real-time evolution.
• Score: 2.9780372446425627
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider multileg ladders of Rydberg atoms which have been proposed as quantum simulators for the compact Abelian Higgs model (CAHM) in 1+1 dimensions [Y. Meurice, Phys. Rev. D 104, 094513 (2021)] and modified versions of theses simulators such as triangular prisms. Starting with the physical Hamiltonian for the analog simulator, we construct translation-invariant effective Hamiltonians by integrating over the simulator high-energy states produced by the blockade mechanism when some of the atoms are sufficiently close to each others. Remarkably, for all the simulators considered, the effective Hamiltonians have the three types of terms present for the CAHM (Electric field, matter charge and currents energies) but, in addition, terms quartic in the electric field. For the two leg ladder, these additional terms cannot be removed by fine-tuning the adjustable parameters of currently available devices. For positive detuning, the new terms create highly-degenerate vacua resulting in a very interesting phase diagram. Using numerical methods, we demonstrate the close correspondence between the physical simulator and the effective description for the ground state energy and real-time evolution. We discuss the phase diagram at fixed geometry with variable Rabi frequency and detuning and show that a rich variety of phases can be reached with potential interest in the context of QCD at finite density. We illustrate how the effective description can be used to design simulators with desirable properties from the point of view of constructing hybrid event generators.

Related papers

• Simulating Schwinger model dynamics with quasi-one-dimensional qubit arrays [0.0]
  We develop a strategy to run Schwinger model dynamics on synthetic quantum spin lattices. We show that global magnetic field patterns can drive coherent quantum dynamics of the interface equivalent to the lattice Schwinger Hamiltonian. This work opens up a path for near-term quantum simulators to address questions of immediate relevance to particle physics.
  arXiv  Detail & Related papers  (2024-09-22T17:58:25Z)
• Quantum emulation of the transient dynamics in the multistate Landau-Zener model [50.591267188664666]
  We study the transient dynamics in the multistate Landau-Zener model as a function of the Landau-Zener velocity. Our experiments pave the way for more complex simulations with qubits coupled to an engineered bosonic mode spectrum.
  arXiv  Detail & Related papers  (2022-11-26T15:04:11Z)
• Fermionic approach to variational quantum simulation of Kitaev spin models [50.92854230325576]
  Kitaev spin models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.
  arXiv  Detail & Related papers  (2022-04-11T18:00:01Z)
• Variational Adiabatic Gauge Transformation on real quantum hardware for effective low-energy Hamiltonians and accurate diagonalization [68.8204255655161]
  We introduce the Variational Adiabatic Gauge Transformation (VAGT) VAGT is a non-perturbative hybrid quantum algorithm that can use nowadays quantum computers to learn the variational parameters of the unitary circuit. The accuracy of VAGT is tested trough numerical simulations, as well as simulations on Rigetti and IonQ quantum computers.
  arXiv  Detail & Related papers  (2021-11-16T20:50:08Z)
• Theoretical methods to design and test quantum simulators for the compact Abelian Higgs model [0.0]
  In 1+1 dimensions, the Abelian Higgs model can be quantum simulated using a ladder-shaped optical lattice with Rydberg-dressed atoms. We show that the building blocks of the Hamiltonian calculations are models with one and two spins. We argue that near-term technology could be used to quantum simulate models with two or more spins.
  arXiv  Detail & Related papers  (2021-07-23T17:33:34Z)
• Quantum Simulation of the Bosonic Creutz Ladder with a Parametric Cavity [5.336258422653554]
  We use a multimode superconducting parametric cavity as a hardware-efficient analog quantum simulator. We realize a lattice in synthetic dimensions with complex hopping interactions. The complex-valued hopping interaction further allows us to simulate, for instance, gauge potentials and topological models.
  arXiv  Detail & Related papers  (2021-01-11T14:46:39Z)
• Engineering analog quantum chemistry Hamiltonians using cold atoms in optical lattices [69.50862982117127]
  We benchmark the working conditions of the numerically analog simulator and find less demanding experimental setups. We also provide a deeper understanding of the errors of the simulation appearing due to discretization and finite size effects.
  arXiv  Detail & Related papers  (2020-11-28T11:23:06Z)
• Quantum simulations with complex geometries and synthetic gauge fields in a trapped ion chain [0.0]
  We introduce a technique that can substantially extend the reach of quantum simulators using an external field gradient along the ion chain and a global, uniform driving field. The technique can be used to generate both static and time-varying synthetic gauge fields in a linear chain of trapped ions. It enables continuous simulation of geometries of a variety of coupling and topologies, including periodic boundary conditions and high dimensional Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-04T16:48:09Z)
• State preparation and measurement in a quantum simulation of the O(3) sigma model [65.01359242860215]
  We show that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. We apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes. We present and analyze a quantum algorithm based on non-unitary randomized simulation methods.
  arXiv  Detail & Related papers  (2020-06-28T23:44:12Z)
• Kink dynamics and quantum simulation of supersymmetric lattice Hamiltonians [0.0]
  We propose a quantum simulation of a supersymmetric lattice model using atoms trapped in a 1D configuration and interacting through a Rydberg dressed potential. We provide an analytical description of the kink/skink dynamics and propose a protocol to prepare and detect these excitations in the quantum simulator.
  arXiv  Detail & Related papers  (2020-05-01T21:01:35Z)
• Quantum Simulation of 2D Quantum Chemistry in Optical Lattices [59.89454513692418]
  We propose an analog simulator for discrete 2D quantum chemistry models based on cold atoms in optical lattices. We first analyze how to simulate simple models, like the discrete versions of H and H$+$, using a single fermionic atom. We then show that a single bosonic atom can mediate an effective Coulomb repulsion between two fermions, leading to the analog of molecular Hydrogen in two dimensions.
  arXiv  Detail & Related papers  (2020-02-21T16:00:36Z)

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.