通过量子蒙特卡罗模拟理解量子隧穿
Understanding Quantum Tunneling through Quantum Monte Carlo Simulations
摘要：
伊辛铁磁体的两个基态之间的隧穿是两个局部极小值之间的多体隧穿过程的典型例子，因为它们发生在量子退火期间。通过量子Monte Carlo（QMC）模拟，我们发现QMC隧穿率与非相干隧穿率一样，随系统尺寸的变化具有相同的标度。两种情况下的缩放都是$O(Δ^2)$，其中$Δ$是隧道分裂。一个重要的结果是，QMC模拟可以用来预测量子退火器的性能，通过势垒隧穿。此外，通过在虚时间中使用开放而不是周期性边界条件，相当于投影QMC算法，我们获得了二次加速QMC，并实现了线性缩放$Δ$。我们提供了一个物理的理解，这些结果和它们的适用范围的基础上的瞬子图片。
英文摘要：
The tunneling between the two ground states of an Ising ferromagnet is a typical example of many-body tunneling processes between two local minima, as they occur during quantum annealing. Performing quantum Monte Carlo (QMC) simulations we find that the QMC tunneling rate displays the same scaling with system size, as the rate of incoherent tunneling. The scaling in both cases is $O(Δ^2)$, where $Δ$ is the tunneling splitting. An important consequence is that QMC simulations can be used to predict the performance of a quantum annealer for tunneling through a barrier. Furthermore, by using open instead of periodic boundary conditions in imaginary time, equivalent to a projector QMC algorithm, we obtain a quadratic speedup for QMC, and achieve linear scaling in $Δ$. We provide a physical understanding of these results and their range of applicability based on an instanton picture.
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