Physics Department, Technion, 3200003 Haifa, Israel.
Phys Rev Lett. 2019 Jan 18;122(2):020504. doi: 10.1103/PhysRevLett.122.020504.
Recovering an unknown Hamiltonian from measurements is an increasingly important task for certification of noisy quantum devices and simulators. Recent works have succeeded in recovering the Hamiltonian of an isolated quantum system with local interactions from long-ranged correlators of a single eigenstate. Here, we show that such Hamiltonians can be recovered from local observables alone, using computational and measurement resources scaling linearly with the system size. In fact, to recover the Hamiltonian acting on each finite spatial domain, only observables within that domain are required. The observables can be measured in a Gibbs state as well as a single eigenstate; furthermore, they can be measured in a state evolved by the Hamiltonian for a long time, allowing us to recover a large family of time-dependent Hamiltonians. We derive an estimate for the statistical recovery error due to approximation of expectation values using a finite number of samples, which agrees well with numerical simulations.
从测量中恢复未知哈密顿量对于噪声量子设备和模拟器的认证是一项越来越重要的任务。最近的工作已经成功地从单个本征态的长程相关函数中恢复出具有局部相互作用的孤立量子系统的哈密顿量。在这里，我们表明，仅使用与系统大小成线性比例的计算和测量资源，就可以从局部可观测量中恢复出这种哈密顿量。实际上，要恢复作用于每个有限空间域的哈密顿量，仅需要该域内的可观测量。可观测量可以在吉布斯态以及单个本征态中进行测量；此外，它们可以在由哈密顿量长时间演化的态中进行测量，这使我们能够恢复一大类时变哈密顿量。我们推导出了由于使用有限数量的样本近似期望值而导致的统计恢复误差的估计，该估计与数值模拟吻合得很好。
