Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Entanglement clustering for ground-stateable quantum many-body states

Michael Matty, Yi Zhang, T. Senthil, Eun-Ah Kim

Published Jan 1, 2021• 2 citations
OpenAlex

Abstract

Despite their fundamental importance in dictating the quantum-mechanical properties of a system, ground states of many-body local quantum Hamiltonians form a set of measure zero in the many-body Hilbert space. Hence determining whether a given many-body quantum state is ground-stateable is a challenging task. Here we propose an unsupervised machine learning approach, dubbed Entanglement Clustering (“EntanCl”), to separate out ground-stateable wave functions from those that must be excited-state wave functions using entanglement structure information. EntanCl uses snapshots of an ensemble of swap operators as input and projects these high-dimensional data to two dimensions, preserving important topological features of the data associated with distinct entanglement structure using the uniform manifold approximation and projection. The projected data are then clustered using K-means clustering with k=2. By applying EntanCl to two examples, a one-dimensional free fermion model and the two-dimensional toric code, we demonstrate that EntanCl can successfully separate ground states from excited states with high computational efficiency. Being independent of a Hamiltonian and associated energy estimates, EntanCl offers a new paradigm for addressing quantum many-body wave functions in a computationally efficient manner.Received 15 May 2020Accepted 29 April 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.023212Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEntanglement entropyEntanglement measuresMachine learningQuantum entanglementTechniquesVariational wave functional methodsCondensed Matter, Materials & Applied PhysicsQuantum Information

Related papers

Entanglement clustering for ground-stateable quantum many-body states

Michael Matty, Yi Zhang, T. Senthil +1 more

Despite their fundamental importance in dictating the quantum-mechanical properties of a system, ground states of many-body local quantum Hamiltonians form a set of measure zero in the many-body Hilbert space. Hence determining whether a given many-body quantum state is ground-stateable is a challenging task. Here we propose an unsupervised machine learning approach, dubbed Entanglement Clustering ("EntanCl"), to separate out ground-stateable wave functions from those that must be excited-state wave functions using entanglement structure information. EntanCl uses snapshots of an ensemble of swap operators as input and projects these high-dimensional data to two dimensions, preserving important topological features of the data associated with distinct entanglement structure using the uniform manifold approximation and projection. The projected data are then clustered using K-means clustering with k = 2. By applying EntanCl to two examples, a one-dimensional free fermion model and the two-dimensional toric code, we demonstrate that EntanCl can successfully separate ground states from excited states with high computational efficiency. Being independent of a Hamiltonian and associated energy estimates, EntanCl offers a new paradigm for addressing quantum many-body wave functions in a computationally efficient manner.

arXiv:2004.06141•Physical Review Research•Jun 16, 2021•1 citation

Exponentially improved efficient machine learning for quantum many-body states with provable guarantees

Yanming Che, Clemens Gneiting, Franco Nori

Solving the ground state and the ground-state properties of quantum many-body systems is generically a hard task for classical algorithms. For a family of Hamiltonians defined on an m -dimensional space of physical parameters, the ground state and its properties at an arbitrary parameter configuration can be predicted via a machine learning protocol up to a prescribed prediction error ɛ , provided that a sample set (of size N ) of the states can be efficiently prepared and measured. In a recent work [Huang , ], a rigorous guarantee for such a generalization was proved. Unfortunately, an exponential scaling for the provable sample complexity, N = m O ( 1 ɛ ) , was found to be universal for generic gapped Hamiltonians. This result applies to the situation where the dimension of the parameter space is large, while the scaling with the accuracy is not an urgent factor, not entering the realm of more precise learning and prediction. In this work, we consider an alternative relevant scenario, where the effective dimension m is a finite, not necessarily large constant, while the scaling with the prediction error becomes the central concern. By jointly preserving the fundamental properties of density matrices in the learning protocol and utilizing the continuity of quantum states in the parameter range of interest, we rigorously obtain a polynomial sample complexity for predicting quantum many-body states and their properties, with respect to the prediction error ɛ and the number of qubits, n , with N = poly ( ɛ − 1 , n , ln 1 δ ) , where poly denotes a polynomial function, and ( 1 − δ ) is the probability of success. Moreover, if restricted to learning local quantum-state properties, the number of samples can be further reduced to N = poly ( ɛ − 1 , ln n δ ) . Numerical demonstrations confirm our findings, and an alternative approach utilizing statistical learning theory with reproducing kernel Hilbert space achieves consistent results. The mere continuity assumption indicates that our results are not restricted to gapped Hamiltonian systems and properties within the same phase. Published by the American Physical Society 2024

arXiv:2304.04353•Physical Review Research•Jul 8, 2024•8 citations

Publisher’s Note: Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods [Phys. Rev. X 7 , 031059 (2017)]

Mário Motta, David M. Ceperley, Garnet Kin‐Lic Chan +18 more

Received 18 March 2021DOI:https://doi.org/10.1103/PhysRevX.11.029901Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.© 2021 American Physical SocietyPhysics Subject Headings (PhySH)Physical Systems1-dimensional systemsStrongly correlated systemsTechniquesElectronic structureFirst-principles calculationsNumerical techniquesQuantum chemistry methodsCondensed Matter & Materials Physics

Physical Review X•Apr 6, 2021•2 citations

Finding Quantum Many-Body Ground States with Artificial Neural Network

Jiaxin Wu, Wenjuan Zhang

Solving ground states of quantum many-body systems has been a long-standing problem in condensed matter physics. Here, we propose a new unsupervised machine learning algorithm to find the ground state of a general quantum many-body system utilizing the benefits of artificial neural network. Without assuming the specific forms of the eigenvectors, this algorithm can find the eigenvectors in an unbiased way with well controlled accuracy. As examples, we apply this algorithm to 1D Ising and Heisenberg models, where the results match very well with exact diagonalization.

arXiv:1906.11216•Jun 26, 2019•0 citations

Bound entangled singlet-like states for quantum metrology

Károly F. Pál, Géza Tóth, Erika Bene +1 more

Bipartite entangled quantum states with a positive partial transpose (PPT), i.e., PPT entangled states, are usually considered very weakly entangled. Since no pure entanglement can be distilled from them, they are also called bound entangled. In this paper, we present two classes of (2d×2d)-dimensional PPT entangled states for any d≥2 which outperform all separable states in metrology significantly. We present strong evidence that our states provide the maximal metrological gain achievable by PPT states for a given system size. When the dimension d goes to infinity, the metrological gain of these states becomes maximal and equals the metrological gain of a pair of maximally entangled qubits. Thus, we argue that our states could be called "PPT singlets."Received 16 November 2020Revised 18 March 2021Accepted 29 March 2021Corrected 8 June 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.023101Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEntanglement detectionEntanglement manipulationQuantum metrologyGeneral PhysicsQuantum Information

•Jan 1, 2021•2 citations

Preparation of Entangled Many-Body States with Machine Learning

Kim, Donggyu, Eun-Gook Moon

Preparation of a target quantum many-body state on quantum simulators is one of the significant steps in quantum science and technology. With a small number of qubits, a few quantum states, such as the Greenberger-Horne-Zeilinger state, have been prepared, but fundamental difficulties in systems with many qubits remain, including the Lieb-Robinson bounds for the number of quantum operations. Here, we provide one algorithm with an implementation of a deep learning process and achieve to prepare the target ground states with many qubits. Our strategy is to train a machine-learning model and predict parameters with many qubits by utilizing a pattern of quantum states from the corresponding quantum states with small numbers of qubits. For example, we demonstrate that our algorithm with the Quantum Approximate Optimization Ansatz can effectively generate the ground state for a 1D XY model with 64 spins. We also demonstrate that the reduced density operator of two qubits can be utilized to capture the pattern of quantum many-body states such as correlation lengths even for quantum critical states.

arXiv:2307.14627•Jul 27, 2023•1 citation
Despite their fundamental importance in dictating the quantum-mechanical properties of a system, ground states of many-body local quantum Hamiltonians form a set of measure zero in the many-body Hilbert space. Hence determining whether a given many-body quantum state is ground-stateable is a challenging task. Here we propose an unsupervised machine learning approach, dubbed Entanglement Clustering (“EntanCl”), to separate out ground-stateable wave functions from those that must be excited-state wave functions using entanglement structure information. EntanCl uses snapshots of an ensemble of swap operators as input and projects these high-dimensional data to two dimensions, preserving important topological features of the data associated with distinct entanglement structure using the uniform manifold approximation and projection. The projected data are then clustered using K-means clustering with k=2. By applying EntanCl to two examples, a one-dimensional free fermion model and the two-dimensional toric code, we demonstrate that EntanCl can successfully separate ground states from excited states with high computational efficiency. Being independent of a Hamiltonian and associated energy estimates, EntanCl offers a new paradigm for addressing quantum many-body wave functions in a computationally efficient manner.Received 15 May 2020Accepted 29 April 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.023212Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEntanglement entropyEntanglement measuresMachine learningQuantum entanglementTechniquesVariational wave functional methodsCondensed Matter, Materials & Applied PhysicsQuantum Information
Despite their fundamental importance in dictating the quantum-mechanical properties of a system, ground states of many-body local quantum Hamiltonians form a set of measure zero in the many-body Hilbert space. Hence determining whether a given many-body quantum state is ground-stateable is a challenging task. Here we propose an unsupervised machine learning approach, dubbed Entanglement Clustering ("EntanCl"), to separate out ground-stateable wave functions from those that must be excited-state wave functions using entanglement structure information. EntanCl uses snapshots of an ensemble of swap operators as input and projects these high-dimensional data to two dimensions, preserving important topological features of the data associated with distinct entanglement structure using the uniform manifold approximation and projection. The projected data are then clustered using K-means clustering with k = 2. By applying EntanCl to two examples, a one-dimensional free fermion model and the two-dimensional toric code, we demonstrate that EntanCl can successfully separate ground states from excited states with high computational efficiency. Being independent of a Hamiltonian and associated energy estimates, EntanCl offers a new paradigm for addressing quantum many-body wave functions in a computationally efficient manner.
Solving the ground state and the ground-state properties of quantum many-body systems is generically a hard task for classical algorithms. For a family of Hamiltonians defined on an m -dimensional space of physical parameters, the ground state and its properties at an arbitrary parameter configuration can be predicted via a machine learning protocol up to a prescribed prediction error ɛ , provided that a sample set (of size N ) of the states can be efficiently prepared and measured. In a recent work [Huang , ], a rigorous guarantee for such a generalization was proved. Unfortunately, an exponential scaling for the provable sample complexity, N = m O ( 1 ɛ ) , was found to be universal for generic gapped Hamiltonians. This result applies to the situation where the dimension of the parameter space is large, while the scaling with the accuracy is not an urgent factor, not entering the realm of more precise learning and prediction. In this work, we consider an alternative relevant scenario, where the effective dimension m is a finite, not necessarily large constant, while the scaling with the prediction error becomes the central concern. By jointly preserving the fundamental properties of density matrices in the learning protocol and utilizing the continuity of quantum states in the parameter range of interest, we rigorously obtain a polynomial sample complexity for predicting quantum many-body states and their properties, with respect to the prediction error ɛ and the number of qubits, n , with N = poly ( ɛ − 1 , n , ln 1 δ ) , where poly denotes a polynomial function, and ( 1 − δ ) is the probability of success. Moreover, if restricted to learning local quantum-state properties, the number of samples can be further reduced to N = poly ( ɛ − 1 , ln n δ ) . Numerical demonstrations confirm our findings, and an alternative approach utilizing statistical learning theory with reproducing kernel Hilbert space achieves consistent results. The mere continuity assumption indicates that our results are not restricted to gapped Hamiltonian systems and properties within the same phase. Published by the American Physical Society 2024
Received 18 March 2021DOI:https://doi.org/10.1103/PhysRevX.11.029901Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.© 2021 American Physical SocietyPhysics Subject Headings (PhySH)Physical Systems1-dimensional systemsStrongly correlated systemsTechniquesElectronic structureFirst-principles calculationsNumerical techniquesQuantum chemistry methodsCondensed Matter & Materials Physics
Solving ground states of quantum many-body systems has been a long-standing problem in condensed matter physics. Here, we propose a new unsupervised machine learning algorithm to find the ground state of a general quantum many-body system utilizing the benefits of artificial neural network. Without assuming the specific forms of the eigenvectors, this algorithm can find the eigenvectors in an unbiased way with well controlled accuracy. As examples, we apply this algorithm to 1D Ising and Heisenberg models, where the results match very well with exact diagonalization.
Bipartite entangled quantum states with a positive partial transpose (PPT), i.e., PPT entangled states, are usually considered very weakly entangled. Since no pure entanglement can be distilled from them, they are also called bound entangled. In this paper, we present two classes of (2d×2d)-dimensional PPT entangled states for any d≥2 which outperform all separable states in metrology significantly. We present strong evidence that our states provide the maximal metrological gain achievable by PPT states for a given system size. When the dimension d goes to infinity, the metrological gain of these states becomes maximal and equals the metrological gain of a pair of maximally entangled qubits. Thus, we argue that our states could be called "PPT singlets."Received 16 November 2020Revised 18 March 2021Accepted 29 March 2021Corrected 8 June 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.023101Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEntanglement detectionEntanglement manipulationQuantum metrologyGeneral PhysicsQuantum Information
Preparation of a target quantum many-body state on quantum simulators is one of the significant steps in quantum science and technology. With a small number of qubits, a few quantum states, such as the Greenberger-Horne-Zeilinger state, have been prepared, but fundamental difficulties in systems with many qubits remain, including the Lieb-Robinson bounds for the number of quantum operations. Here, we provide one algorithm with an implementation of a deep learning process and achieve to prepare the target ground states with many qubits. Our strategy is to train a machine-learning model and predict parameters with many qubits by utilizing a pattern of quantum states from the corresponding quantum states with small numbers of qubits. For example, we demonstrate that our algorithm with the Quantum Approximate Optimization Ansatz can effectively generate the ground state for a 1D XY model with 64 spins. We also demonstrate that the reduced density operator of two qubits can be utilized to capture the pattern of quantum many-body states such as correlation lengths even for quantum critical states.