Trotter Errors from Dynamical Structural Instabilities of Floquet Maps in Quantum Simulation
Trotter Errors from Dynamical Structural Instabilities of Floquet Maps in Quantum Simulation
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DOI：
10.1103/prxquantum.3.010351
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发表时间：
2022-03-28
期刊：
影响因子：
9.7
通讯作者：
Poggi, Pablo M.
中科院分区：
文献类型：
--
作者：
Chinni, Karthik;Munoz-Arias, Manuel H.;Poggi, Pablo M.
我们研究的行为错误的自旋系统的量子模拟与远程多体相互作用产生的Trotter-Suzuki分解的时间演化算子。我们确定了一个政权，其中Floquet运营商的基础Trotter分解经历了急剧的变化，即使是小的变化，在模拟步长。这导致时间演化算子与目标哈密顿量生成的动力学非常不同，这导致量子模拟中的错误激增。Floquet算子中的这些急剧变化的区域，被称为结构不稳定区域，通常出现在中间Trotter步长和弱相互作用区域中，因此与最近揭示的Trotterized演化的量子混沌区域互补[L. M. Sieberer et al. npj Quantum Inf. 5，78（2019）; M. Heyl，P. Hauke和P. Zoller，Sci. Adv. 5，eaau8342（2019）]。我们在p -自旋模型，横场伊辛模型与所有的p -体相互作用的特点，这些结构的不稳定性制度，并分析预测其发生的基础上酉微扰理论。我们进一步表明，有效的哈密顿与Trotter分解的酉时间演化算子，当Trotter步长被选择为在结构不稳定区域，是非常不同的目标哈密顿，这解释了大的错误，可以发生在模拟中的不稳定区域。这些结果对近期基于门的量子模拟器的可靠性具有影响，并揭示了误差与被模拟系统的物理特性之间的重要相互作用。
We study the behavior of errors in the quantum simulation of spin systems with long-range multibody interactions resulting from the Trotter-Suzuki decomposition of the time-evolution operator. We identify a regime where the Floquet operator underlying the Trotter decomposition undergoes sharp changes even for small variations in the simulation step size. This results in a time evolution operator that is very different from the dynamics generated by the targeted Hamiltonian, which leads to a proliferation of errors in the quantum simulation. These regions of sharp change in the Floquet operator, referred to as structural instability regions, appear typically at intermediate Trotter step sizes and in the weakly interacting regime, and are thus complementary to recently revealed quantum chaotic regimes of the Trotterized evolution [L. M. Sieberer et al. npj Quantum Inf. 5, 78 (2019); M. Heyl, P. Hauke, and P. Zoller, Sci. Adv. 5, eaau8342 (2019)]. We characterize these structural instability regimes in p -spin models, transverse-field Ising models with all-to-all p -body interactions, and analytically predict their occurrence based on unitary perturbation theory. We further show that the effective Hamiltonian associated with the Trotter decomposition of the unitary time-evolution operator, when the Trotter step size is chosen to be in the structural instability region, is very different from the target Hamiltonian, which explains the large errors that can occur in the simulation in the regions of instability. These results have implications for the reliability of near-term gate-based quantum simulators, and reveal an important interplay between errors and the physical properties of the system being simulated.