We propose a quantum inverse iteration algorithm, which can be used to estimate ground state properties of a programmable quantum device. The method relies on the inverse power iteration technique, where the sequential application of the Hamiltonian inverse to an initial state prepares the approximate ground state. To apply the inverse Hamiltonian operation, we write it as a sum of unitary evolution operators using the Fourier approximation approach. This allows to reformulate the protocol as separate measurements for the overlap of initial and propagated wavefunction. The algorithm thus crucially depends on the ability to run Hamiltonian dynamics with an available quantum device, and can be used for analog quantum simulators. We benchmark the performance using paradigmatic examples of quantum chemistry, corresponding to molecular hydrogen and beryllium hydride. Finally, we show its use for studying the ground state properties of relevant material science models, which can be simulated with existing devices, considering an example of the Bose-Hubbard atomic simulator.

我们提出了一种量子逆迭代算法，该算法可用于估计可编程量子器件的基态属性。该方法依赖于逆功率迭代技术，在该技术中，将汉密尔顿逆的顺序应用到初始状态会准备近似的基态。为了应用哈密顿逆运算，我们使用傅立叶逼近法将其写为of演化算子的​​总和。这允许将协议重新制定为针对初始和传播波函数重叠的单独测量。因此，该算法至关重要地取决于使用可用量子设备运行哈密顿动力学的能力，并且可用于模拟量子模拟器。我们使用量子化学的范例对性能进行基准测试，对应于分子氢和氢化铍。最后，我们以Bose-Hubbard原子模拟器为例，说明了其在研究相关材料科学模型的基态特性中的应用，这些材料可以使用现有设备进行模拟。