饰Andrew Hodges
Reply to Andrew Hodges
摘要：
我们把Hodges \cite{Hodges2005}和其他人的批评分为对算法本身的批评和对物理实现的批评。然后我们指出，{ \em all}那些反对该算法是误导或误解，该算法是自洽的。另一方面，反对该算法的物理实现的唯一核心论点是基于一个假设，即由于缺乏无限精度，它的哈密顿量不能有效地构造。然而，到目前为止，还没有已知的物理原理来说明为什么不能这样做。为了表明批评可能不是一个放弃的结论，我们指出几乎未知的事实，相反，简单的例子丢番图方程显然{ \em无限精确}整数系数已{ \em已经}在实验中实现某些量子相变。我们还推测如何统计中心极限定理可能是一些帮助有效实施所需的哈密顿量。
英文摘要：
We separate the criticisms of Hodges \cite{Hodges2005} and others into those against the algorithm itself and those against its physical implementation. We then point out that {\em all} those against the algorithm are either misleading or misunderstanding, and that the algorithm is self consistent. The only central argument against physical implementations of the algorithm, on the other hand, is based on an assumption that its Hamiltonians cannot be effectively constructed due to a lack of infinite precision. However, so far there is no known physical principle dictating why that cannot be done. To show that the criticism may not be a forgone conclusion, we point out the virtually unknown fact that, on the contrary, simple instances of Diophantine equations with apparently {\em infinitely precisely} integer coefficients have {\em already} been realised in experiments for certain quantum phase transitions. We also speculate on how central limit theorem of statistics might be of some help in the effective implementation of the required Hamiltonians.
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