Abstract The capacity for solving eigenstates with a quantum computer is key for ultimately simulating physical systems. Here we propose inverse iteration quantum eigensolvers, which exploit the power of quantum computing for the classical inverse power iteration method. A key ingredient is constructing an inverse Hamiltonian as a linear combination of coherent Hamiltonian evolution. We first consider a continuous-variable quantum mode (qumode) for realizing such a linear combination as an integral, with weights being encoded into a qumode resource state. We demonstrate the quantum algorithm with numerical simulations under finite squeezing for various physical systems, including molecules and quantum many-body models. We also discuss a hybrid quantum–classical algorithm that directly sums up Hamiltonian evolution with different durations for comparison. It is revealed that continuous-variable resources are valuable for reducing the coherent evolution time of Hamiltonians in quantum algorithms.

中文翻译：

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逆迭代量子本征求解器辅助连续变量

摘要 用量子计算机求解本征态的能力是最终模拟物理系统的关键。在这里，我们提出了逆迭代量子特征求解器，它利用量子计算的能力来实现经典的逆幂迭代方法。一个关键因素是将逆哈密顿量构建为相干哈密顿量演化的线性组合。我们首先考虑一种连续变量量子模式（qumode），用于实现积分这样的线性组合，权重被编码为qumode资源状态。我们通过有限压缩下的数值模拟演示了各种物理系统的量子算法，包括分子和量子多体模型。我们还讨论了一种混合量子经典算法，该算法直接总结了不同持续时间的哈密顿演化以进行比较。揭示了连续变量资源对于减少量子算法中哈密顿量的相干演化时间很有价值。