We introduce NetKet, a comprehensive open source framework for the study of many-body quantum systems using machine learning techniques. The framework is built around a general and flexible implementation of neural-network quantum states, which are used as a variational ansatz for quantum wavefunctions. NetKet provides algorithms for several key tasks in quantum many-body physics and quantum technology, namely quantum state tomography, supervised learning from wavefunction data, and ground state searches for a wide range of customizable lattice models. Our aim is to provide a common platform for open research and to stimulate the collaborative development of computational methods at the interface of machine learning and many-body physics. I. MOTIVATION AND SIGNIFICANCERecent years have seen a tremendous activity around the development of physics-oriented numerical techniques based on machine learning (ML) tools [1]. In the context of many-body quantum physics, one of the main goals of these approaches is to tackle complex quantum problems using compact representations of many-body states based on artificial neural networks. These representations, dubbed neural-network quantum states (NQS) [2], can be used for several applications. In the supervised learning setting, they can be used, e.g., to learn existing quantum states for which a non-NQS representation is available [3]. In the unsupervised setting, they can be used to reconstruct complex quantum states from experimental measurements, a task known as quantum state tomography [4]. Finally, in the context of purely variational applications, NQS can be used to find approximate ground-and excited-state solutions of the Schrödinger equation [2, 5-9], as well as to describe unitary [2, 10, 11] and dissipative [12-15] many-body dynamics. Despite the increasing methodological and theoretical interest in NQS and their applications, a set of comprehensive, easyto-use tools for research applications is still lacking. This is particularly pressing as the complexity of NQS-related approaches and algorithms is expected to grow rapidly given these first successes, steepening the learning curve.The goal of NetKet is to provide a set of primitives and flexible tools to ease the development of cuttingedge ML applications for quantum many-body physics. NetKet also wants to help bridge the gap between the latest and technically demanding developments in the field and those scholars and students who approach the subject for the first time. Pedagogical tutorials are provided to this aim. Serving as a common platform for future research, the NetKet project is meant to stimulate the open and easy-to-certify development of new methods and to provide a common set of tools to reproduce published results.A central philosophy of the NetKet framework is to provide tools that are as simple as possible to use for the end user. Given the huge popularity of the Python programming language and of the many accompanying tools gravitating around the Python ecosystem, we have built NetKet as a full...

Neural quantum states (NQS) attract a lot of attention due to their potential to serve as a very expressive variational ansatz for quantum many-body systems. Here we study the main factors governing the applicability of NQS to frustrated magnets by training neural networks to approximate ground states of several moderately-sized Hamiltonians using the corresponding wave function structure on a small subset of the Hilbert space basis as training dataset. We notice that generalization quality, i.e. the ability to learn from a limited number of samples and correctly approximate the target state on the rest of the space, drops abruptly when frustration is increased. We also show that learning the sign structure is considerably more difficult than learning amplitudes. Finally, we conclude that the main issue to be addressed at this stage, in order to use the method of NQS for simulating realistic models, is that of generalization rather than expressibility.

Recent progress in the fabrication of materials has made it possible to create arbitrary non-periodic two-dimensional structures in the quantum plasmon regime. This paves the way for exploring the plasmonic properties of electron gases in complex geometries such as fractals. In this work, we study the plasmonic properties of Sierpinski carpets and gaskets, two prototypical fractals with different ramification, by fully calculating their dielectric functions. We show that the Sierpinski carpet has a dispersion comparable to a square lattice, but the Sierpinski gasket features highly localized plasmon modes with a flat dispersion. This strong plasmon confinement in finitely ramified fractals can provide a novel setting for manipulating light at the quantum scale.

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