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A query-based quantum eigensolver

机译：基于查询的量子eigensolver

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摘要

Solving eigenvalue problems is crucially important for both classical and quantum applications. Many well-known numerical eigensolvers have been developed, including the QR and the power methods for classical computers, as well as the quantum phase estimation (QPE) method and the variational quantum eigensolver for quantum computers. In this work, we present a different type of quantum method that uses fixed-point quantum search to solve Type II eigenvalue problems. This method serves as an important complement to the QPE method, which is a Type I eigensolver. We show that the quantum oracle of our query-based method can be efficiently constructed from the QPE gate, which is crucial for analyzing the total gate complexity of our method. In addition, compared with the QPE method, our query-based method achieves a quadratic speedup in solving Type II problems. As two applications, we then discuss how to apply our method to solve Type II eigenvalue problems for the Heisenberg model and the hydrogen molecule.
机译：求解特征值问题是至关重要的经典和量子的应用程序。著名的数值eigensolvers发展,包括QR和力量的方法经典计算机,以及量子相位估计(QPE)方法和变分量子eigensolver量子计算机。这项工作中,我们提出一个不同类型的量子使用定点量子搜索方法解决II型特征值问题。QPE作为一个重要的补充方法,该方法是一种我eigensolver。量子甲骨文的基于查询的方法可以有效地由QPE门口,这是分析的关键总门我们的方法的复杂性。QPE方法,基于查询的方法实现二次加速解决II型问题。如何运用我们的方法解决II型海森堡模型和特征值问题氢分子。

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