具有非随机哈密顿量的量子退火的消息传递算法
Message-passing algorithm of quantum annealing with nonstoquastic Hamiltonian
摘要：
量子退火（QA）是一种利用虚拟量子涨落求解优化问题的通用方法。目前执行QA的设备涉及控制横向场;它是通过使用将量子自旋系统映射到经典自旋系统的标准技术来经典模拟的。从这个意义上说，目前的QA系统虽然利用了量子涨落，但并不强大。因此，我们开发了一个系统与时间相关的哈密顿量的组合制定的伊辛模型和“司机”的哈密顿量只有量子涨落。在以前的研究中，对于一个完全连接的自旋模型，量子涨落可以以一种相对简单的方式解决。我们证明了全连通反铁磁相互作用可以转化为一个起伏的横向场，因此在足够低的温度下是经典模拟的。利用涨落横场，我们建立了几种在经典计算机上模拟部分非随机哈密顿量的方法。在本研究中，我们制定了一个消息传递算法。该算法能够评估QA的性能与部分的非随机哈密顿具有大量的自旋。换句话说，我们开发了一种不同的方法来模拟非随机哈密顿量，而不使用量子蒙特卡罗技术。我们的研究结果进行了验证，通过比较得到的结果，通过复制的方法。
英文摘要：
Quantum annealing (QA) is a generic method for solving optimization problems using fictitious quantum fluctuation. The current device performing QA involves controlling the transverse field; it is classically simulatable by using the standard technique for mapping the quantum spin systems to the classical ones. In this sense, the current system for QA is not powerful despite utilizing quantum fluctuation. Hence, we developed a system with a time-dependent Hamiltonian consisting of a combination of the formulated Ising model and the "driver" Hamiltonian with only quantum fluctuation. In the previous study, for a fully connected spin model, quantum fluctuation can be addressed in a relatively simple way. We proved that the fully connected antiferromagnetic interaction can be transformed into a fluctuating transverse field and is thus classically simulatable at sufficiently low temperatures. Using the fluctuating transverse field, we established several ways to simulate part of the nonstoquastic Hamiltonian on classical computers. We formulated a message-passing algorithm in the present study. This algorithm is capable of assessing the performance of QA with part of the nonstoquastic Hamiltonian having a large number of spins. In other words, we developed a different approach for simulating the nonstoquastic Hamiltonian without using the quantum Monte Carlo technique. Our results were validated by comparison to the results obtained by the replica method.
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