论文标题
一类广义特征值问题的量子相估计
Quantum phase estimation for a class of generalized eigenvalue problems
论文作者
论文摘要
量子相估计提供了量子计算的途径，以对遗传学特征值问题进行量子计算$ hv =λv$，例如量子化学中发生的方法。自然要问是否可以将相同的技术应用于广义特征值问题$ av =λbv $，这在科学和工程的许多领域都会出现。我们肯定地回答了这个问题。可以像标准特征值问题一样有效地解决一类限制的广义特征值问题。 Sturm-Liouville问题提供了一个范式的例子。另一个示例来自线性理想磁流失动力学，其中相位估计可用于确定融合反应器中磁性粘附的等离子体的稳定性。
Quantum phase estimation provides a path to quantum computation of solutions to Hermitian eigenvalue problems $Hv = λv$, such as those occurring in quantum chemistry. It is natural to ask whether the same technique can be applied to generalized eigenvalue problems $Av = λB v$, which arise in many areas of science and engineering. We answer this question affirmatively. A restricted class of generalized eigenvalue problems could be solved as efficiently as standard eigenvalue problems. A paradigmatic example is provided by Sturm--Liouville problems. Another example comes from linear ideal magnetohydrodynamics, where phase estimation could be used to determine the stability of magnetically confined plasmas in fusion reactors.
