Efficiency of calculation and robustness of local observables in open-system dynamics of Ising models

In quantum many-body problems, one is often interested in estimating expectation values of local observables associated with order parameters, which are believed to be more robust to decoherence, making them more accessible to noisy intermediate scale quantum (NISQ) simulators. The computational power of NISQ devices remains an open question. Recent work has shown that approximate simulations can be tractable [1], especially in the presence of decoherence [2, 3]. We show that the Hilbert-Schmidt distance between appropriate marginal states 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 a unital Lindblad master equation involving single-spin Lindblad operators. We show that low-order marginals are less sensitive to approximation via truncated tensor network representations and decoherence, suggesting that expectation values of local observables in Ising spin chains are classically tractable and robust against experimental imperfections in NISQ devices. 

[1] Zhou et. al., Phys. Rev. X 10, 041038 (2020)

[2] Noh et. al., Quantum 4, 318 (2020)

[3] Cheng et. al., Phys. Rev. Research 3, 023005 (2021)