Southwest Quantum Information and Technology

How efficiently can we simulate local observables in the open system dynamics of Ising models?

Presenting Author: Anupam Mitra, University of New Mexico CQuIC
Contributing Author(s): Philip Daniel Blocher, Tameem Albash, Akimasa Miyake, Ivan H. Deutsch

In the quantum simulation of many-body systems, we are often interested in estimating expectation values of local observable associated with order parameters. It is believed that these observables are likely to be more robust to decoherence, making them more accessible to noisy intermediate scale quantum (NISQ) simulators. Recent work has shown that approximate simulations of NISQ devices can be tractable [Phys. Rev. X 10, 041038], especially in the presence of decoherence [Quantum 4, 318; Phys. Rev. Research 3, 023005]. In this work, we explore estimating local reduced density operators (marginals). We show that the Hilbert-Schmidt distance between appropriate marginals can be used to upper bound the error in estimating expectation values of observables. Focusing on quantum simulation of quench dynamics of Ising spin chains in 1D on a noisy quantum device, we model open quantum system dynamics with single-spin local, unital decoherence map given by a Lindblad master equation, which we solve using quantum trajectories and matrix product state (MPS) time evolution methods. We numerically find that marginals can be well approximated using MPS with modest bond-dimension, giving numerical evidence to show that local observables can be efficiently approximated. Moreover, decoherence permits a more aggressive MPS truncation for approximating local marginals, suggesting that classical simulation of local observables may be tractable and robust to unital decoherence maps.

(Session 5 : Thursday from 12:00pm-2:00 pm)