Southwest Quantum Information and Technology

Robustness and complexity of estimating local observables in quench dynamics of 1D Ising models

Presenting Author: Anupam Mitra, University of New Mexico CQuIC

In non-equilibrium dynamics of quantum many-body problems, a common objective is estimating expectation values of local (few-body) observables associated with dynamical order parameters. It is hoped that these quantities are more robust to implementation errors and decoherence and yet still inaccessible by classical simulation, making them suitable for quantum simulators in the noisy intermediate scale quantum (NISQ) era. Here we demonstrate that this hope is not always justified by focusing on the case of quench dynamics of Ising spin chains in 1D in the presence of decoherence. We first show that the Hilbert-Schmidt distance between the ideal and realized reduced density matrix upper-bounds the error in estimating the expectation values of local observables. This allows us to focus on how accurately we can approximate the reduced density matrix. We show that the few-body reduced density matrices of Ising spin chains are less sensitive to approximation via truncated tensor network representations and decoherence through evolution under a unital Lindblad master equation involving single-spin Lindblad operators. Our results suggests that expectation values of local observables in Ising spin chains are classically tractable and robust against experimental imperfections in NISQ devices. [1] Preskill, Quantum 2, 79 (2018) [2] Zhou et. al., Phys. Rev. X 10, 041038 (2020) [3] Noh et. al., Quantum 4, 318 (2020) [4] Cheng et. al., Phys. Rev. Research 3, 023005 (2021)

(Session 5 : Thursday from 5:00 pm - 7:00 pm)