This work proposes a protocol for Fermionic Hamiltonian learning. For the Hubbard model defined on a bounded-degree graph, the Heisenberg-limited scaling is achieved while allowing for state preparation and measurement errors. To achieve $\epsilon$-accurate estimation for all parameters, only $\tilde{\mathcal{O}}(\epsilon^{-1})$ total evolution time is needed, and the constant factor is independent of the system size. Moreover, our method only involves simple one or two-site Fermionic manipulations, which is desirable for experiment implementation.

翻译：本文提出了一种费米子汉密尔顿量学习的协议。对于定义在有界度图上的哈伯德模型，该方法实现了海森堡极限标度，同时容许态制备与测量误差。为获得所有参数的$\epsilon$精度估计，仅需$\tilde{\mathcal{O}}(\epsilon^{-1})$总演化时间，且常数因子与系统规模无关。此外，本方法仅涉及简单的单格点或双格点费米子操控，这有利于实验实现。