Hermite矩阵的量子对角化
Quantum Diagonalization of Hermitean Matrices
摘要：
测量一个量子力学系统的一个可观测量，使它处于它的一个本征态，测量的结果就是它的一个本征值。这个过程被证明是一个计算资源。它允许一个，在原则上，对角化厄米（N乘N）矩阵的量子力学测量。为此，我们将给定的矩阵视为具有适当长度s=（N-1）/2的单个自旋的可观测量，其可以使用广义Stern-Gerlach装置测量。然后，每次运行提供一个特征值的观察。由于它是以与测量有关的“波函数的坍缩”为基础的，因此这一过程既不是数字计算，也不是模拟计算-因此它定义了一种新的量子力学计算方法。
英文摘要：
To measure an observable of a quantum mechanical system leaves it in one of its eigenstates and the result of the measurement is one of its eigenvalues. This process is shown to be a computational resource. It allows one, in principle, to diagonalize hermitean (N by N) matrices by quantum mechanical measurements only. To do so, one considers the given matrix as an observable of a single spin with appropriate length s=(N-1)/2, which can be measured using a generalized Stern-Gerlach apparatus. Then, each run provides one eigenvalue of the observable. As it is based on the `collapse of the wave function' associated with a measurement, the procedure is neither a digital nor an analog calculation--it defines thus a new quantum mechanical method of computation.
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