Ground state preparation with shallow variational warm-start

• URL: http://arxiv.org/abs/2303.11204v1
• Date: Mon, 20 Mar 2023 15:36:23 GMT
• Title: Ground state preparation with shallow variational warm-start
• Authors: Youle Wang, Chenghong Zhu, Mingrui Jing, Xin Wang
• Abstract summary: This work provides a quantum ground state preparation scheme with shallow variational warm-start to tackle the bottlenecks of current algorithms. We demonstrate the effectiveness of our methods via extensive numerical simulations on spin-$1/2$ Heisenberg models. We extend research on the Hubbard model, demonstrating superior performance compared to the prevalent variational quantum algorithms.
• Score: 5.526775342940154
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Preparing the ground states of a many-body system is essential for evaluating physical quantities and determining the properties of materials. This work provides a quantum ground state preparation scheme with shallow variational warm-start to tackle the bottlenecks of current algorithms, i.e., demand for prior ground state energy information and lack of demonstration of efficient initial state preparation. Particularly, our methods would not experience the instability for small spectral gap $\Delta$ during pre-encoding the phase factors since our methods involve only $\widetilde{O}(1)$ factors while $\widetilde{O}(\Delta^{-1})$ is requested by the near-optimal methods. We demonstrate the effectiveness of our methods via extensive numerical simulations on spin-$1/2$ Heisenberg models. We also show that the shallow warm-start procedure can process chemical molecules by conducting numerical simulations on the hydrogen chain model. Moreover, we extend research on the Hubbard model, demonstrating superior performance compared to the prevalent variational quantum algorithms.

Related papers

• Phase Diagram of the Schwinger Model by Adiabatic Preparation of States on a Quantum Simulator [6.2210196243454075]
  We argue the feasibility to study the phase structure of a quantum physical system on quantum devices via adiabatic preparation of states. We introduce a novel method and successfully test it in application to the Schwinger model in the presence of a topological $theta$-term.
  arXiv  Detail & Related papers  (2024-07-12T12:44:49Z)
• Near-Term Quantum Spin Simulation of the Spin-$\frac{1}{2}$ Square $J_{1}-J_{2}$ Heisenberg Model [0.0]
  This study focuses on the $J_1-J_2$ Heisenberg model, renowned for its rich phase behavior on the square lattice. We conducted the first experimental quantum computing study of this model using the 127-qubit IBM Rensselear Eagle processor.
  arXiv  Detail & Related papers  (2024-06-26T16:33:40Z)
• Critical behavior of Ising model by preparing thermal state on quantum computer [3.570760625392093]
  We simulate the critical behavior of the Ising model utilizing a thermal state prepared using quantum computing techniques. We calculate the specific heat and susceptibility of the long-range interacting Ising model and observe indications of the Ising criticality on a small lattice size.
  arXiv  Detail & Related papers  (2023-02-28T03:29:19Z)
• Entropic Neural Optimal Transport via Diffusion Processes [105.34822201378763]
  We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions. Our algorithm is based on the saddle point reformulation of the dynamic version of EOT which is known as the Schr"odinger Bridge problem. In contrast to the prior methods for large-scale EOT, our algorithm is end-to-end and consists of a single learning step.
  arXiv  Detail & Related papers  (2022-11-02T14:35:13Z)
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics [62.997667081978825]
  We show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality. We show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators.
  arXiv  Detail & Related papers  (2022-06-03T18:00:02Z)
• Phenomenological Theory of Variational Quantum Ground-State Preparation [0.0]
  The variational quantum eigensolver (VQE) algorithm aims to prepare the ground state of a Hamiltonian exploiting parametrized quantum circuits. We show that the algorithm's success crucially depends on other parameters such as the learning rate. We propose a symmetry-enhanced simulation protocol that should be used if the gap closes.
  arXiv  Detail & Related papers  (2022-05-12T18:00:04Z)
• Quantum simulation and ground state preparation for the honeycomb Kitaev model [23.87373187143897]
  We propose a quantum protocol that allows preparing a ground state (GS) of the honeycomb Kitaev model. We demonstrate the high fidelity preparation of spin liquid ground states for the original Kitaev model. We then extend the variational procedure to non-zero magnetic fields, studying observables and correlations that reveal the phase transition.
  arXiv  Detail & Related papers  (2021-09-28T17:13:53Z)
• Hybridized Methods for Quantum Simulation in the Interaction Picture [69.02115180674885]
  We provide a framework that allows different simulation methods to be hybridized and thereby improve performance for interaction picture simulations. Physical applications of these hybridized methods yield a gate complexity scaling as $log2 Lambda$ in the electric cutoff. For the general problem of Hamiltonian simulation subject to dynamical constraints, these methods yield a query complexity independent of the penalty parameter $lambda$ used to impose an energy cost.
  arXiv  Detail & Related papers  (2021-09-07T20:01:22Z)
• Benchmarking adaptive variational quantum eigensolvers [63.277656713454284]
  We benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves. We find both methods provide good estimates of the energy and ground state. gradient-based optimization is more economical and delivers superior performance than analogous simulations carried out with gradient-frees.
  arXiv  Detail & Related papers  (2020-11-02T19:52:04Z)
• Preparation of excited states for nuclear dynamics on a quantum computer [117.44028458220427]
  We study two different methods to prepare excited states on a quantum computer. We benchmark these techniques on emulated and real quantum devices. These findings show that quantum techniques designed to achieve good scaling on fault tolerant devices might also provide practical benefits on devices with limited connectivity and gate fidelity.
  arXiv  Detail & Related papers  (2020-09-28T17:21:25Z)
• A Near-Optimal Gradient Flow for Learning Neural Energy-Based Models [93.24030378630175]
  We propose a novel numerical scheme to optimize the gradient flows for learning energy-based models (EBMs) We derive a second-order Wasserstein gradient flow of the global relative entropy from Fokker-Planck equation. Compared with existing schemes, Wasserstein gradient flow is a smoother and near-optimal numerical scheme to approximate real data densities.
  arXiv  Detail & Related papers  (2019-10-31T02:26:20Z)

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.