为什么要机器学习？ (Why machine learning?)

Machine learning is one of today’s most rapidly cutting-edge growing fields of research, with unprecedented promises to offer solutions to existing engineering and research problems. The powerful combination of recent development and practical progress of computing architectures has made possible a large number of successful machine learning applications, in various fields such as automated translation, image and voice recognition, or game-​playing. Recent advancements in machine learning and deep learning with important applications in diverse fields such as high energy physics, condensed matter, astronomy [1] or industry have deepen the understanding and further the progress of the field, leading to the recent development of result-​driven techniques and advanced algorithms with specific agenda.

机器学习是当今最Swift发展的前沿研究领域之一，其空前的承诺将为现有的工程和研究问题提供解决方案。 计算架构的最新发展和实际进步的有力结合，使得在自动翻译，图像和语音识别或游戏等各个领域中，大量成功的机器学习应用成为可能。 机器学习和深度学习的最新进展以及在高能物理，凝聚态，天文学[1]或工业等各个领域的重要应用已加深了对该领域的理解并进一步发展，从而导致了成果的最新发展。具有特定议程的驱动技术和高级算法。

While traditional computing algorithms are reaching their limits in simulation capabilities and spending computational resources, condensed matter physics and quantum many-body research require alternative techniques of investigation, problem solving, diagnosis and discovery.

尽管传统的计算算法在仿真能力和计算资源方面正达到其极限，但凝聚态物理和量子多体研究需要替代性的研究，问题解决，诊断和发现技术。

Neural networks and machine learning methods in general, have finally reached the next stage of development after several decades of significant progress in diverse fields of science, industry, and technology. What does this mean for condensed-matter physics? The key question here is: how can industry-standard machine learning algorithms help condensed matter physics research? In particular, machine learning techniques are recently employed for studying classical and quantum many-body tasks encountered in condensed matter, quantum information, and related fields of physics. Some of the existing techniques employed today by machine learning methods may lend themselves in the future to fundamental research, to an extent, with specific focus on condensed matter and quantum many-body physics topics.

经过数十年在科学，工业和技术各个领域的重大进步，神经网络和机器学习方法终于进入了下一阶段的发展。 这对凝聚态物理意味着什么？ 这里的关键问题是：行业标准的机器学习算法如何帮助凝聚态物理研究？ 特别是，机器学习技术最近被用于研究在凝聚态，量子信息和相关物理领域中遇到的经典和量子多体任务。 机器学习方法如今采用的某些现有技术将来可能会在一定程度上适合基础研究，尤其是在凝聚态物质和量子多体物理学方面。

Quantum many-body simulations of recent models such as predicting quantum phase transition or exotic emergent phenomena, while conceptually simple, still require a large number of quantum states, leading to an exponentially large number of parameters and therefore becoming computationally difficult, since the solution time can grow exponentially with the size of the task.

最近模型的量子多体模拟(例如，预测量子相变或奇异现象)虽然在概念上很简单，但仍需要大量的量子态，从而导致参数数量呈指数级增长，因此由于求解时间的增加，计算变得困难可以随着任务的大小呈指数增长。

So, why machine learning? Recently, machine learning methods were proven to be extremely useful in diverse areas of condensed matter research, reproducing existing results generated with other techniques with smaller computational cost and less effort. Deep learning also offers a powerful tool to efficiently represent quantum many-body states, including the ground states of many-body Hamiltonians or quantum dynamics states.

那么，为什么要机器学习呢？ 最近，事实证明，机器学习方法在凝聚态研究的各个领域都非常有用，它以较小的计算成本和较少的工作量重现了其他技术产生的现有结果。 深度学习还提供了一个强大的工具，可以有效地表示量子多体状态，包括多体哈密顿量的基态或量子动力学状态。

Condensed matter physics studies microscopic scale interactions of all types of matter at quantum and atom levels, describing them in terms of mesoscopic and macroscopic structure and properties. Condensed matter systems are quite difficult to simulate with traditional computational techniques, predicting approximate solutions hard to test. As condensed matter tasks always deal with massive amounts of interacting particles, these problems become well-suited candidates for solving with machine learning methods, due to big data requirements.

凝聚态物理学研究量子和原子级所有类型物质的微观尺度相互作用，并用介观和宏观结构与性质来描述它们。 浓缩物系统很难用传统的计算技术来模拟，难以预测近似解。 由于凝聚态任务总是要处理大量相互作用的粒子，因此由于大数据需求，这些问题成为解决机器学习方法的合适候选对象。

In the past few years, condensed matter physicists started to employ artificial intelligence techniques and especially machine learning algorithms and neural networks, to recognize patterns in the behavior dynamics of many-body systems. Condensed-matter physics deals with different properties and phases of matter under varying conditions, as well as the behavior of these phases using different laws of physics, especially quantum mechanics. Various constructive connections between these fields can cross-fertilize both machine learning and quantum many-body physics.

在过去的几年中，凝聚态物理学家开始采用人工智能技术，尤其是机器学习算法和神经网络，以识别多体系统行为动力学中的模式。 凝聚态物理处理物质在不同条件下的不同性质和相，以及使用不同的物理定律(尤其是量子力学)处理这些相的行为。 这些领域之间的各种建设性联系可以使机器学习和量子多体物理学交叉应用。

Such methods can be used together with conventional computing algorithms, such as Quantum Monte Carlo algorithms or Tensor networks, like Matrix Product States or MERA, running on supercomputers, for studying collections of particles in a material. Tensor networks are a recent advanced technique that are gaining traction and find new applications in both machine learning (Neural networks, Deep learning) and diverse subfields of physics (MERA, for example) that require identifying and extrapolating patterns from data.

这样的方法可以与在超级计算机上运行的常规计算算法(例如量子蒙特卡洛算法或Tensor网络，例如矩阵乘积状态或MERA)一起使用，以研究材料中的粒子集合。 Tensor网络是一种最新的先进技术，正在获得关注并在机器学习(神经网络，深度学习)和需要识别和推断数据模式的物理子领域(例如，MERA)中找到新的应用。

There are also several classical computer science optimization problems, such as Boolean satisfiability and the travelling salesman problem, which are significantly difficult, having been framed under the generic umbrella term of NP-hard problems. Most optimization problems can be formulated as the problem of finding the ground state of a classical Ising-like Hamiltonian from many-body theory.

还存在一些经典的计算机科学优化问题，例如布尔可满足性和旅行商问题，这在NP-hard问题的总括范围内已非常困难。 可以将大多数优化问题表述为从多体理论中找到经典的类似于Ising的哈密顿量的基态的问题。

Machine learning can find patterns in a black box, as we don’t actually understand how these patterns are detected. Built heavily on statistics, machine learning methods are powerful tools for recognition and search of patterns and regularities in data. With the exponential growth in the volume of data to be transferred, stored or processed, new methods of machine learning become important. The technique of pattern recognition helps detecting arrangements of any potential features or properties that may provide information about a given data set. This is achieved by classifying the data based on the existing knowledge and on the statistical features extracted from different patterns and their representation.

机器学习可以在黑匣子中找到模式，因为我们实际上并不了解如何检测到这些模式。 机器学习方法以统计学为基础，是用于识别和搜索数据模式和规律性的强大工具。 随着要传输，存储或处理的数据量呈指数增长，新的机器学习方法变得越来越重要。 模式识别技术有助于检测可能提供有关给定数据集信息的任何潜在特征或特性的排列。 这是通过根据现有知识以及从不同模式及其表示中提取的统计特征对数据进行分类来实现的。

解决旧问题的新方法 (New solutions to old problems)

There are numerous applications of machine learning and neural networks in condensed matter physics. Important open questions of fundamental interest in quantum many body systems may find their answers and insights into the powerful shallow or deep learning architectures that exhibit a complexity that scales similar to the quantum many-body problem. Recent work also suggested [2] that machine learning algorithms are similar and have a common denominator with the “renormalization group”, an mathematical apparatus used in particle and condensed matter physics that maps a microscopic picture onto a macroscopic one.

机器学习和神经网络在凝聚态物理中有许多应用。 量子多体系统中基本感兴趣的重要开放性问题可能会找到答案，并深入了解强大的浅层或深度学习体系结构，这些体系结构的复杂性与量子多体问题相似。 最近的工作还建议[2]，机器学习算法与“重新归一化组”相似，并且具有相同的分母。“重新归一化组”是一种用于粒子和凝聚态物理的数学设备，可将微观图片映射到宏观图片。

Several approaches that employ supervised, unsupervised and reinforcement learning methods were developed in the recent years [3]. A recent emerging subset of machine learning is deep neural learning or deep neural networks, using neural networks capable of unsupervised learning from data that is unstructured or unlabeled. Examples of such tools are Generative Adversarial Networks, Boltzmann Machines, Variational Autoencoders, and Convolutional Neural Networks [4].

近年来，开发了几种采用监督，无监督和强化学习方法的方法[3]。 机器学习的最新新兴子集是深度神经学习或深度神经网络，它使用能够从非结构化或未标记的数据中进行无监督学习的神经网络。 这样的工具的例子是生成对抗网络，玻尔兹曼机，变分自动编码器和卷积神经网络[4]。

Notably, Restricted Boltzmann machines (RBMs) stand out as as a versatile tool originated in statistical physics and high predictive power for theoretical condensed matter physics models and quantum information theory simulations. RBMs are, indeed, one of the fundamental techniques of deep learning, with various applications in dimensional reduction, feature extraction, and recommender systems through modeling of probability distributions associated with wide variety of datasets [5].

值得注意的是，受限玻尔兹曼机(RBM)作为一种多功能工具而脱颖而出，它起源于统计物理学和理论凝聚态物理模型和量子信息理论模拟的高预测能力。 实际上，RBM是深度学习的基本技术之一，它通过对与各种数据集相关的概率分布进行建模，在降维，特征提取和推荐系统中具有各种应用[5]。

Strongly correlated quantum many-body physics requires challenging, high-demanding computational resources for the study of the many-body quantum wavefunction, which exhibits an exponentially scaling complexity. High-performance computational tools such as quantum Monte Carlo and density matrix renormalization group (DMRG) methods have been employed in the recent years to solve problems in condensed-matter physics[6] [7] [8], with important connections to quantum information sciences [9] [10], ranging from numerical solutions and quantum simulators of simple models to of thermalization and quantum quenches, and much more.

高度相关的量子多体物理学需要具有挑战性的，高要求的计算资源来研究多体量子波函数，该函数显示出指数级的缩放复杂性。 近年来，已使用诸如量子蒙特卡洛和密度矩阵重整化组(DMRG)方法之类的高性能计算工具来解决凝聚态物理中的问题[6] [7] [8]，与量子信息有着重要的联系。科学[9] [10]，范围从简单模型的数值解和量子仿真器到热化和量子猝灭，等等。

A number of efficient algorithms were rigorously developed to quantify and translate RBMs into tensor network states, with the purpose of employing powerful deep learning architectures in future quantum many-body physics research, such as studying the entanglement entropy bound or the area law. Furthermore, RBMs can produce more efficient classical simulations, due to their higher power in representing quantum many-body states [11] with fewer parameters than tensor network states,

为了在未来的量子多体物理学研究中使用强大的深度学习架构，例如研究纠缠熵界或面积定律，我们严格开发了许多有效的算法来量化RBM并将其转换为张量网络状态。 此外，RBM可以产生比张量网络状态更少的参数，从而具有更高的功率来表示量子多体状态[11]，因此可以产生更有效的经典模拟，

期待 (Looking forward)

Condensed matter physics community has already taken advantage, diving into recent explorations of existing predictive algorithms underlying machine learning and neural networks, building an impressive consensus among various predictions and similarities between the two sciences, to steer the next steps in the progress of physics. The currently growing mutually beneficial relation between the fields of condensed matter, statistical physics, and machine learning has opened a new window into future approaches, powerful toy models and computational/data analysis methods being migrated towards the theoretical physics community,

凝聚态物理界已经利用了优势，深入研究了机器学习和神经网络基础上现有的预测算法的最新探索，在两种科学之间的各种预测和相似性之间建立了令人印象深刻的共识，以指导物理学发展的下一步。 凝聚态物质，统计物理学和机器学习领域之间当前日益增长的互利关系为未来的方法，强大的玩具模型和计算/数据分析方法向理论物理学界的迁移打开了新窗口，

The recent predictive, representational and computational power of machine learning in processing and simulating large data sets in quantum many body physics and condensed matter systems, inspired from a range of real-world problems, such as computer vision and natural language processing, offer a successful, compelling high-profile and efficient tool contributing to the advancements of physical sciences and beyond.

机器学习在处理和模拟量子多体物理学和凝聚态系统中的大数据集方面的最新预测，表示和计算能力，受到计算机视觉和自然语言处理等一系列现实问题的启发， ，引人注目的高效工具，为物理科学及其他学科的发展做出了贡献。

[1] E Howard, Holographic renormalization with machine learning, arXiv:1803.11056 [physics.gen-ph] (2018) doi

[1] E霍华德，《通过机器学习实现全息归一化》， arXiv：1803.11056 [physics.gen-ph](2018) doi

[2] E Howard, Machine learning algorithms in Astronomy, Astronomical Data Analysis Software and Systems XXV 512, 245 (2017) doi

[2] E Howard，《天文学中的机器学习算法》，《天文数据分析软件和系统》 XXV 512，245(2017) doi

[3] Lei Wang, Phys. Rev. B 94, 195105 (2016) doi

[3]王磊，物理学。 B 94，195105(2016) doi

[4] J. Carrasquilla and R. Melko, Nature Physics 13, 431–434 (2017) doi

[4] J. Carrasquilla和R. Melko，自然物理学13，431–434(2017) doi

[5] E.P. van Nieuwenburg, Y. Liu, S. Huber, Nature Physics 13, 435–439 (2017) doi

[5] EP van Nieuwenburg，Y。Liu，S。Huber，Nature Physics 13，435–439(2017) doi

[6] Schoenholz et al., Nature 12, 469–471 (2016) doi

[6] Schoenholz等人，Nature 12，469–471(2016) doi

[7] G. Carleo, M. Troyer, Science 355, 602–606 (2017) doi

[7] G. Carleo，M。Troyer，科学355，602–606(2017) doi

[8] A. Hentschel, B.Sanders, Phys. Rev. Lett. 104, 063603 (2010) doi

[8] A. Hentschel，B.Sanders，物理学。 莱特牧师 104，063603(2010) doi

[9] Li Huang and Lei Wang, Phys. Rev. B 95, 035105 (2017) doi

[9]黄莉和王磊，物理学。 B 95，035105(2017) doi

[10] Junwei Liu, Yang Qi, Zi Yang Meng, and Liang Fu, Phys. Rev. B 95, 041101(R) (2017) doi

[10]刘俊伟，杨琦，紫阳萌和梁复，物理。 B 95，041101(R)(2017) doi

[11] Biamonte, Wittek, Pancotti, Rebentrost, Wiebe, Lloyd, Nature 549, 195–202 (2017) doi

[11]比亚蒙特，威特克，潘科蒂，雷本特斯特，威伯，劳埃德，自然549，195–202(2017) doi