Jaksch Peter, Papageorgiou Anargyros
Department of Computer Science, Columbia University, New York, New York 10027-6902, USA.
Phys Rev Lett. 2003 Dec 19;91(25):257902. doi: 10.1103/PhysRevLett.91.257902.
We present an efficient method for preparing the initial state required by the eigenvalue approximation quantum algorithm of Abrams and Lloyd. Our method can be applied when solving continuous Hermitian eigenproblems, e.g., the Schrödinger equation, on a discrete grid. We start with a classically obtained eigenvector for a problem discretized on a coarse grid, and we efficiently construct, quantum mechanically, an approximation of the same eigenvector on a fine grid. We use this approximation as the initial state for the eigenvalue estimation algorithm, and show the relationship between its success probability and the size of the coarse grid.
我们提出了一种有效的方法来制备艾布拉姆斯和劳埃德的特征值近似量子算法所需的初始状态。当在离散网格上求解连续厄米特特征值问题（例如薛定谔方程）时，我们的方法可以应用。我们从在粗网格上离散化问题的经典获得的特征向量开始，并用量子力学方法有效地在细网格上构造同一特征向量的近似。我们将此近似用作特征值估计算法的初始状态，并展示其成功概率与粗网格大小之间的关系。
