We introduce a family of variational quantum algorithms, which we coin as quantum iterative power algorithms (QIPAs), and demonstrate their capabilities as applied to global-optimization numerical experiments. Specifically, we demonstrate the QIPA based on a double exponential oracle as applied to ground state optimization of the H ₂ molecule, search for the transmon qubit ground-state, and biprime factorization. Our results indicate that QIPA outperforms quantum imaginary time evolution (QITE) and requires a polynomial number of queries to reach convergence even with exponentially small overlap between an initial quantum state and the final desired quantum state, under some circumstances. We analytically show that there exists an exponential amplitude amplification at every step of the variational quantum algorithm, provided the initial wavefunction has non-vanishing probability with the desired state and that the unique maximum of the oracle is given by λ1>0 , while all other values are given by the same value 0<λ2<λ1 (here λ can be taken as eigenvalues of the problem Hamiltonian). The generality of the global-optimization method presented here invites further application to other problems that currently have not been explored with QITE-based near-term quantum computing algorithms. Such approaches could facilitate identification of reaction pathways and transition states in chemical physics, as well as optimization in a broad range of machine learning applications. The method also provides a general framework for adaptation of a class of classical optimization algorithms to quantum computers to further broaden the range of algorithms amenable to implementation on current noisy intermediate-scale quantum computers.

中文翻译：

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在变分量子算法中以指数方式提高量子振幅


我们介绍了一系列变分量子算法，我们将其称为量子迭代幂算法（QIPA），并展示了它们应用于全局优化数值实验的能力。具体来说，我们演示了基于双指数预言的 QIPA，应用于 H ₂ 分子的基态优化、搜索 transmon 量子位基态和双素数分解。我们的结果表明，QIPA 优于量子虚时间演化 (QITE)，并且在某些情况下，即使初始量子态和最终所需量子态之间的重叠呈指数级小，也需要多项式查询才能达到收敛。我们分析表明，只要初始波函数具有所需状态的非零概率，并且预言机的唯一最大值由 λ1>0 给出，则变分量子算法的每一步都存在指数幅度放大，而所有其他值由相同的值 0<λ2<λ1 给出（这里 λ 可以视为问题哈密顿量的特征值）。这里提出的全局优化方法的通用性可以进一步应用于目前基于 QITE 的近期量子计算算法尚未探索的其他问题。这些方法可以促进化学物理中反应途径和过渡态的识别，以及广泛的机器学习应用中的优化。该方法还提供了一个通用框架，用于将一类经典优化算法适应量子计算机，以进一步扩大适合在当前嘈杂的中型量子计算机上实现的算法范围。