Constructing neural stationary states for open quantum many-body systems

Yoshioka, Nobuyuki; Hamazaki, Ryusuke

doi:10.1103/physrevb.99.214306

Cited by 192 publications

(128 citation statements)

References 71 publications

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“…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][6][7][8][9], as well as to describe unitary [2,10,11] and dissipative [12][13][14][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.…”

Section: Motivation and Significancementioning

confidence: 99%

NetKet: A machine learning toolkit for many-body quantum systems

et al. 2019

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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...

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Section: Motivation and Significancementioning

confidence: 99%

NetKet: A machine learning toolkit for many-body quantum systems

et al. 2019

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“…This feature makes RBMs attractive for a variety of quantum variational optimization problems [18], which require finding a quantum state that best satisfies a certain criterion. Examples of such problems, in addition to quantum tomography [19], include searching ground states of Hamiltonians in quantum chemistry tasks [20], investigating tensor network states [21] and topological states [22], and simulating open quantum many-body systems [23][24][25][26][27].…”

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confidence: 99%

Experimental quantum homodyne tomography via machine learning

Tiunov¹,

Tiunova²,

Ulanov³

et al. 2020

Optica

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Complete characterization of states and processes that occur within quantum devices is crucial for understanding and testing their potential to outperform classical technologies for communications and computing. However, solving this task with current state-of-the-art techniques becomes unwieldy for large and complex quantum systems. Here we realize and experimentally demonstrate a method for complete characterization of a quantum harmonic oscillator based on an artificial neural network known as the restricted Boltzmann machine. We apply the method to optical homodyne tomography and show it to allow full estimation of quantum states based on a smaller amount of experimental data compared to state-of-the-art methods. We link this advantage to reduced overfitting. Although our experiment is in the optical domain, our method provides a way of exploring quantum resources in a broad class of large-scale physical systems, such as superconducting circuits, atomic and molecular ensembles, and optomechanical systems.

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“…Refs. [42][43][44][45][46][47][48][49][50]). However, in what follows we mainly refer to the results shown in Ref.…”

Section: A Magnetic Properties Of the Xyz Modelmentioning

confidence: 99%

Complexity of the steady state of weakly symmetric open quantum lattices

Nigro

2020

Phys. Rev. A

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We investigate the properties of Lindblad equations on d-dimensional lattices supporting a unique steady-state configuration. We consider the case of a time evolution weakly symmetric under the action of a finite group G, which is also a symmetry group for the lattice structure. We show that in such case the steady-state belongs to a relevant subspace, and provide an explicit algorithm for constructing an orthonormal basis of such set. As explicitly shown for a spin-1/2 system, the dimension of such subspace is extremely smaller than the dimension of the set of square operators. As a consequence, by projecting the dynamics within such set, the steady-state configuration can be determined with a considerably reduced amount of resources. We demonstrate the validity of our theoretical results by determinining the exact structure of the steady-state configuration of the two dimensional XYZ model in the presence of uniform dissipation, with and without magnetic fields, up to a number of sites equal to 12. As far as we know, this is the first time one is capable of determining the steady-state structure of such model for the 12 sites cluster exactly. Altough in this work we consider explicitly only spin-1/2 systems, our approach can be exploited in the characterisation of arbitrary spin systems, fermion and boson systems (with truncated Fock space), as well as many-particle systems with degrees of freedom having different statistical properties.

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Constructing neural stationary states for open quantum many-body systems

Cited by 192 publications

References 71 publications

NetKet: A machine learning toolkit for many-body quantum systems

NetKet: A machine learning toolkit for many-body quantum systems

Experimental quantum homodyne tomography via machine learning

Complexity of the steady state of weakly symmetric open quantum lattices

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