Quantum optimization of complex systems with a quantum annealer
Quantum optimization of complex systems with a quantum annealer
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DOI：
10.1103/physreva.106.042607
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发表时间：
2022-10-10
影响因子：
2.9
通讯作者：
Spannowsky, Michael
中科院分区：
文献类型：
--
作者：
Abel, Steve;Blance, Andrew;Spannowsky, Michael
我们对量子退火与几种经典的优化技术进行了深入的比较，即热退火、Nelder-Mead和梯度下降。我们研究的重点是大的准连续的潜力，必须使用域壁编码编码。要做到这一点，重要的是首先要了解离散编码到退火机上的系统的量子相特性，以及热效应与量子效应的重要性。因此，我们开始与量子退火机上的二维伊辛模型的直接研究，并比较其性质直接与热的二维伊辛模型。这些性质包括一个类似伊辛的相变，它可以通过改变理论的“量子性”（通过退火机上的横向场分量），或者通过放大或缩小伊辛耦合来诱导。这种行为与量子系统的物理理解所预期的是雅阁的。然后，我们继续证明量子退火器在最小化几个越来越硬的二维势的功效。对于所有的潜力，我们发现的一般行为，Nelder-Mead和梯度下降法是非常容易陷入虚假的最小值，而热退火方法是有点更好地发现真正的最小值。然而，尽管目前的限制，其大小，量子退火机执行最小化非常显着优于任何这些经典技术。可以设计量子退火，使系统几乎不会陷入错误的最小值，并迅速成功地使电势最小化。
We perform an in-depth comparison of quantum annealing with several classical optimization techniques, namely, thermal annealing, Nelder-Mead, and gradient descent. The focus of our study is large quasicontinuous potentials that must be encoded using a domain wall encoding. To do this, it is important to first understand the properties of a system that is discretely encoded onto an annealer, in terms of its quantum phases, and the importance of thermal versus quantum effects. We therefore begin with a direct study of the 2D Ising model on a quantum annealer, and compare its properties directly with those of the thermal 2D Ising model. These properties include an Ising-like phase transition that can be induced by either a change in "quantumness" of the theory (by way of the transverse field component on the annealer), or by scaling the Ising couplings up or down. This behavior is in accord with what is expected from the physical understanding of the quantum system. We then go on to demonstrate the efficacy of the quantum annealer at minimizing several increasingly hard two-dimensional potentials. For all potentials, we find the general behavior that Nelder-Mead and gradient descent methods are very susceptible to becoming trapped in false minima, while the thermal anneal method is somewhat better at discovering the true minimum. However, and despite current limitations on its size, the quantum annealer performs a minimization very markedly better than any of these classical techniques. A quantum anneal can be designed so the system almost never gets trapped in a false minimum, and rapidly and successfully minimizes the potentials.