论文标题
使用离域催化的量子绝热算法的加速
Speedup of the Quantum Adiabatic Algorithm using Delocalization Catalysis
论文作者
论文摘要
我们提出了一种使用多体脱位催化的方法来加快量子绝热算法的速度。这适用于随机场抗磁磁性自旋模型。该算法的催化方式使得进化在过程中间近似于亨森伯格模型，并且该模型处于离域阶段。我们以数字方式显示，我们可以使用此想法加快标准算法来查找随机场ISING模型的基态。我们还证明，即使基础模型并非没有挫败感，速度也是由于差距扩增。跨界速度大致出现在相互作用的值中，这被称为离域转变的关键。我们还将参与率和纠缠熵计算为时间的函数：它们的时间依赖性表明该系统正在探索更多的状态，并且它们比没有催化剂时更纠缠。总之，所有这些证据都表明加速与离域有关。即使只能研究相对较小的系统，证据表明，该方法的缩放尺寸是有利的。一台小型在线IBM量子计算机的实验结果说明了我们的方法，这表明了如何随着这些机器的改善来验证该方法。与标准算法相比，催化方法的成本只是一个恒定的因素。
We propose a method to speed up the quantum adiabatic algorithm using catalysis by many-body delocalization. This is applied to random-field antiferromagnetic Ising spin models. The algorithm is catalyzed in such a way that the evolution approximates a Heisenberg model in the middle of its course, and the model is in a delocalized phase. We show numerically that we can speed up the standard algorithm for finding the ground state of the random-field Ising model using this idea. We also demonstrate that the speedup is due to gap amplification, even though the underlying model is not frustration-free. The crossover to speedup occurs at roughly the value of the interaction which is known to be the critical one for the delocalization transition. We also calculate the participation ratio and entanglement entropy as a function of time: their time dependencies indicate that the system is exploring more states and that they are more entangled than when there is no catalyst. Together, all these pieces of evidence demonstrate that the speedup is related to delocalization. Even though only relatively small systems can be investigated, the evidence suggests that the scaling of the method with system size is favorable. Our method is illustrated by experimental results from a small online IBM quantum computer, showing how to verify the method in future as such machines improve. The cost of the catalytic method compared to the standard algorithm is only a constant factor.
