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Given a set of vectors (the data) in a Hilbert space H, we prove the existence of an optimal collection of subspaces minimizing the sum of the square of the distances between each vector and its closest subspace in the collection. This…

Classical Analysis and ODEs · Mathematics 2008-02-07 Akram Aldroubi , Carlos Cabrelli , Ursula Molter

Tree tensor network (TTN) provides an essential theoretical framework for the practical simulation of quantum many-body systems, where the network structure defined by the connectivity of the isometry tensors plays a crucial role in…

Statistical Mechanics · Physics 2023-01-24 Toshiya Hikihara , Hiroshi Ueda , Kouichi Okunishi , Kenji Harada , Tomotoshi Nishino

Particle transport and localization phenomena in condensed-matter systems can be modeled using a tight-binding lattice Hamiltonian. The ideal experimental emulation of such a model utilizes simultaneous, high-fidelity control and readout of…

With the increasing adoption of machine learning tools like neural networks across several domains, interesting connections and comparisons to concepts from other domains are coming to light. In this work, we focus on the class of Tensor…

Machine Learning · Computer Science 2020-04-22 Raghavendra Selvan , Erik B Dam

We introduce structured random matrix ensembles, constructed to model many-body quantum systems with local interactions. These ensembles are employed to study equilibration of isolated many-body quantum systems, showing that rather complex…

Quantum Physics · Physics 2020-07-01 Daniel Nickelsen , Michael Kastner

Tensor networks (TNs) are one of the best available tools to study many-body quantum systems. TNs are particularly suitable for one-dimensional local Hamiltonians, while their performance for generic geometries is mainly limited by two…

Quantum Physics · Physics 2026-04-08 Apimuk Sornsaeng , Itai Arad , Dario Poletti

Ground-state properties are central to our understanding of quantum many-body systems. At first glance, it seems natural and essential to obtain the ground state before analyzing its properties; however, its exponentially large Hilbert…

Strongly Correlated Electrons · Physics 2022-09-26 Pei-Lin Zheng , Si-Jing Du , Yi Zhang

High-dimensional Hilbert spaces possess large information encoding and transmission capabilities. Characterizing exactly the real potential of high-dimensional entangled systems is a cornerstone of tomography and quantum imaging. The…

Quantum Physics · Physics 2017-10-10 Laszlo Gyongyosi

We show that a simple artificial neural network trained on entanglement spectra of individual states of a many-body quantum system can be used to determine the transition between a many-body localized and a thermalizing regime.…

Disordered Systems and Neural Networks · Physics 2017-07-04 Frank Schindler , Nicolas Regnault , Titus Neupert

In the tensor-network framework, the expectation values of two-dimensional quantum states are evaluated by contracting a double-layer tensor network constructed from initial and final tensor-network states. The computational cost of…

Strongly Correlated Electrons · Physics 2017-07-24 Z. Y. Xie , H. J. Liao , R. Z. Huang , H. D. Xie , J. Chen , Z. Y. Liu , T. Xiang

We present a high-accuracy procedure for electronic structure calculations of strongly correlated materials. To address limitations in current electronic structure methods, we employ density functional theory in combination with the…

Due to the exponential growth of the Hilbert space dimension with system size, the simulation of quantum many-body systems has remained a persistent challenge until today. Here, we review a relatively new class of variational states for the…

Disordered Systems and Neural Networks · Physics 2024-07-29 Hannah Lange , Anka Van de Walle , Atiye Abedinnia , Annabelle Bohrdt

An active area of investigation in the search for quantum advantage is Quantum Machine Learning. Quantum Machine Learning, and Parameterized Quantum Circuits in a hybrid quantum-classical setup in particular, could bring advancements in…

Quantum Physics · Physics 2020-09-01 Thomas Hubregtsen , Josef Pichlmeier , Patrick Stecher , Koen Bertels

Discovering and categorizing quantum orders in mixed many-body systems are currently one of the most important problems. Specific types of decoherence applied to typical quantum many-body states can induce a novel kind of mixed state…

Quantum Physics · Physics 2025-05-06 Takahiro Orito , Yoshihito Kuno , Ikuo Ichinose

In this work we apply deep neural networks to find the non-equilibrium steady state solution to correlated open quantum many-body systems. Motivated by the ongoing search to find more powerful representations of (mixed) quantum states, we…

Quantum Physics · Physics 2025-01-13 Johannes Mellak , Enrico Arrigoni , Wolfgang von der Linden

We develop a novel framework for sparse multiscale kernel approximation of large scattered data problems based on a samplet representation. Samplets form a multiresolution analysis of localized discrete signed measures and enable…

Numerical Analysis · Mathematics 2026-04-03 Sara Avesani , Gaia Fumagalli , Michael Multerer , Chiara Segala

We study Hilbert space fragmentation and quantum scars in quantum spin systems with Ising interactions. The system consists of two sets of quantum spins, A and B. As the parent system, set A is an Ising model on arbitrary lattices with a…

Strongly Correlated Electrons · Physics 2026-04-06 E. S. Ma , Z. Song

We have developed an efficient tensor network algorithm for spin ladders, which generates ground-state wave functions for infinite-size quantum spin ladders. The algorithm is able to efficiently compute the ground-state fidelity per lattice…

Statistical Mechanics · Physics 2011-05-17 Sheng-Hao Li , Yao-Heng Su , Yan-Wei Dai , Huan-Qiang Zhou

Classical simulations of quantum circuits play a vital role in the development of quantum computers and for taking the temperature of the field. Here, we classically simulate various physically-motivated circuits using 2D tensor network…

Quantum Physics · Physics 2025-09-16 Manuel S. Rudolph , Joseph Tindall

Within the reduced basis methods approach, an effective low-dimensional subspace of a quantum many-body Hilbert space is constructed in order to investigate, e.g., the ground-state phase diagram. The basis of this subspace is built from…

Quantum Physics · Physics 2023-08-31 Paul Brehmer , Michael F. Herbst , Stefan Wessel , Matteo Rizzi , Benjamin Stamm