State preparation and measurement in a quantum simulation of the O(3) sigma model
Abstract
Recently, Singh and Chandrasekharan showed 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. In a paper by the NuQS collaboration, the proposal is made to simulate such field theories on a quantum computer using the universal properties of a similar model. In this paper, following that direction, we demonstrate how to prepare the ground state of the model from and measure a dynamical quantity of interest, the O(3) Noether charge, on a quantum computer. In particular, we apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes and use shadow tomography to measure the dynamics of local observables. We then present and analyze a quantum algorithm based on non-unitary randomized simulation methods that may yield an approach suitable for intermediate-term noisy quantum devices.
Keywords
Cite
@article{arxiv.2006.15746,
title = {State preparation and measurement in a quantum simulation of the O(3) sigma model},
author = {Alexander J. Buser and Tanmoy Bhattacharya and Lukasz Cincio and Rajan Gupta},
journal= {arXiv preprint arXiv:2006.15746},
year = {2021}
}
Comments
14 pages, 11 figures. Rev. 3: Corrected typos, updated title, revised abstract and introduction