论文标题
一个基于查询的量子本素果实
A Query-based Quantum Eigensolver
论文作者
论文摘要
解决特征值问题对于经典和量子应用至关重要。已经开发了许多众所周知的数字本素溶剂，包括QR和古典计算机的功率方法，以及量子相估计（QPE）方法和量子计算机的变分量子质量。在这项工作中，我们提出了一种替代类型的量子方法，该方法使用定点量子搜索来解决II型特征值问题。它是对QPE方法的重要补充，即QPE方法是I型Eigensolver。我们发现，我们方法的有效性取决于最初状态的适当选择，以确保与未知目标特征态的足够大重叠。我们还表明，可以有效地构建基于查询方法的量子甲骨文，以有效地模拟的汉密尔顿人，这对于分析总栅极复杂性至关重要。此外，与QPE方法相比，我们基于查询的方法在解决II型问题时达到了二次加速。
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 an alternative type of quantum method that uses fixed-point quantum search to solve Type II eigenvalue problems. It serves as an important complement to the QPE method, which is a Type I eigensolver. We find that the effectiveness of our method depends crucially on the appropriate choice of the initial state to guarantee a sufficiently large overlap with the unknown target eigenstate. We also show that the quantum oracle of our query-based method can be efficiently constructed for efficiently-simulated Hamiltonians, which is crucial for analyzing the total gate complexity. In addition, compared with the QPE method, our query-based method achieves a quadratic speedup in solving Type II problems.
