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

arXiv:1906.10155 · Physical Review A

Machine learning phase transitions with a quantum processor

Alexey Uvarov, Andrey Kardashin, Jacob Biamonte

Published Jul 15, 2020• 69 citations
arXivHTMLPDF

Abstract

Machine learning has emerged as a promising approach to unveil properties of many-body systems. Recently proposed as a tool to classify phases of matter, the approach relies on classical simulation methods---such as Monte Carlo---which are known to experience an exponential slowdown when simulating certain quantum systems. To overcome this slowdown while still leveraging machine learning, we propose a variational quantum algorithm which merges quantum simulation and quantum machine learning to classify phases of matter. Our classifier is directly fed labeled states recovered by the variational quantum eigensolver algorithm, thereby avoiding the data-reading slowdown experienced in many applications of quantum enhanced machine learning. We propose families of variational ansatz states that are inspired directly by tensor networks. This allows us to use tools from tensor network theory to explain properties of the phase diagrams the presented quantum algorithm recovers. Finally, we propose a majority vote quantum classifier built from a nearest-neighbor (checkerboard) quantum neural network. This classifier is successfully trained to recognize phases of matter with 99% accuracy for the transverse field Ising model and 94% accuracy for the $XXZ$ model. These findings suggest that a merger between quantum simulation and quantum enhanced machine learning offers a fertile ground to develop computational insights into quantum systems.

DOI
10.1103/physreva.102.012415

Related papers

An Application of Quantum Machine Learning on Quantum Correlated Systems: Quantum Convolutional Neural Network as a Classifier for Many-Body Wavefunctions from the Quantum Variational Eigensolver

Nathaniel Wrobel, Anshumitra Baul, Juana Moreno +1 more

Machine learning has been applied on a wide variety of models, from classical statistical mechanics to quantum strongly correlated systems for the identification of phase transitions. The recently proposed quantum convolutional neural network (QCNN) provides a new framework for using quantum circuits instead of classical neural networks as the backbone of classification methods. We present here the results from training the QCNN by the wavefunctions of the variational quantum eigensolver for the one-dimensional transverse field Ising model (TFIM). We demonstrate that the QCNN identifies wavefunctions which correspond to the paramagnetic phase and the ferromagnetic phase of the TFIM with good accuracy. The QCNN can be trained to predict the corresponding phase of wavefunctions around the putative quantum critical point, even though it is trained by wavefunctions far away from it. This provides a basis for exploiting the QCNN to identify the quantum critical point.

arXiv:2111.05076•Nov 9, 2021•0 citations

Quantum Phase Recognition using Quantum Tensor Networks

Shweta Sahoo, Utkarsh Azad, Singh, Harjinder

Machine learning (ML) has recently facilitated many advances in solving problems related to many-body physical systems. Given the intrinsic quantum nature of these problems, it is natural to speculate that quantum-enhanced machine learning will enable us to unveil even greater details than we currently have. With this motivation, this paper examines a quantum machine learning approach based on shallow variational ansatz inspired by tensor networks for supervised learning tasks. In particular, we first look at the standard image classification tasks using the Fashion-MNIST dataset and study the effect of repeating tensor network layers on ansatz's expressibility and performance. Finally, we use this strategy to tackle the problem of quantum phase recognition for the transverse-field Ising and Heisenberg spin models in one and two dimensions, where we were able to reach $\geq 98\%$ test-set accuracies with both multi-scale entanglement renormalization ansatz (MERA) and tree tensor network (TTN) inspired parametrized quantum circuits.

arXiv:2212.06207•Dec 12, 2022•0 citations

Quantum neural network quantum state

Xin Pang, Yanan Li, Zhimin Wang

Quantum many-body computation is a central challenge across multiple domains of scientific research, and Monte Carlo method has emerged as one of the most effective numerical techniques for investigating large-scale many-body systems. In recent years, the integration of Monte Carlo methods with machine learning has led to the development of neural quantum state approach. Quantum neural networks (QNNs) offer superior expressiveness compared to classical neural networks. In this paper, we propose a novel Quantum Neural Network Quantum State (QNNQS) method, based on the variational Monte Carlo framework. This approach leverages a quantum neural network to represent the many-body quantum state, and optimizes it iteratively through gradient descent to determine the ground-state energy. To assess the performance of this method, we conduct simulations of the one-dimensional transverse-field Ising model, investigating the influence of quantum circuit architecture on circuit expressibility, entangling capability, and computational accuracy. The results demonstrate that the QNNQS method achieves comparable simulation accuracy while utilizing significantly fewer parameters and requiring less training resources than classical network quantum state methods.

International Conference on Algorithms, Network, and Communication Technology (ICANCT)•Mar 3, 2025•2 citations

Quantum phase transition detection via quantum support vector machine

Youle Wang, Linyun Cao

Abstract Unveiling quantum phase transitions (QPTs) is important for characterising physical systems at low temperatures. However, the detection of these transitions is encumbered by significant challenges, especially in the face of the exponential growth in ground state complexity with system scale. The emergence of quantum machine learning has lately gained traction as a promising method for elucidating the properties of many-body systems, providing a different avenue to study QPT. In this paper, we propose a novel and efficient quantum algorithm for identifying QPT synthesising quantum feature with quantum machine learning. Our approach is anchored in the utilisation of quantum computers to directly encode the kernel matrix into Hilbert spaces, realised by the parallel implementation of the quantum feature map. Specifically, we generate a quantum state encoding the information of ground states of the given quantum systems by employing the parallel quantum feature map. The resultant state preparation circuit is then used to implement a block-encoding of the kernel matrix. Equipped with the associated labels and this encoding, we devise a new quantum support vector machine (QSVM) algorithm, forming the main ingredient of the classifier. The presented method refines the efficiency of the prevailing QSVM algorithm for processing quantum and classical data. We demonstrate the effectiveness of our quantum classifier in predicting QPT within the transverse-field Ising model. The findings affirm the efficacy of quantum machine learning in recognising QPT in many-body systems and offer insights into the design of quantum machine learning algorithms.

Quantum Science and Technology•Nov 28, 2024•10 citations

Quantum kernels to learn the phases of quantum matter

Teresa Sancho-Lorente, Juan Román-Roche, David Zueco

Classical machine learning has succeeded in the prediction of both classical and quantum phases of matter. Notably, kernel methods stand out for their ability to provide interpretable results, relating the learning process with the physical order parameter explicitly. Here we exploit quantum kernels instead. They are naturally related to the fidelity, and thus it is possible to interpret the learning process with the help of quantum information tools. In particular, we use a support vector machine (with a quantum kernel) to predict and characterize second-order quantum phase transitions. We explain and understand the process of learning when the fidelity per site (rather than the fidelity) is used. The general theory is tested in the Ising chain in transverse field. We show that for small-sized systems, the algorithm gives accurate results, even when trained away from criticality. Besides, for larger sizes we confirm the success of the technique by extracting the correct critical exponent $\ensuremath{\nu}$. Finally, we present two algorithms, one based on fidelity and one based on the fidelity per site, to classify the phases of matter in a quantum processor.

arXiv:2109.02686•Physical Review A•Apr 25, 2022•24 citations

Detecting Quantum Critical Points of Correlated Systems by Quantum Convolutional Neural Network Using Data from Variational Quantum Eigensolver

Nathaniel Wrobel, Anshumitra Baul, Ka-Ming Tam +1 more

Machine learning has been applied to a wide variety of models, from classical statistical mechanics to quantum strongly correlated systems, for classifying phase transitions. The recently proposed quantum convolutional neural network (QCNN) provides a new framework for using quantum circuits instead of classical neural networks as the backbone of classification methods. We present the results from training the QCNN by the wavefunctions of the variational quantum eigensolver for the one-dimensional transverse field Ising model (TFIM). We demonstrate that the QCNN identifies wavefunctions corresponding to the paramagnetic and ferromagnetic phases of the TFIM with reasonable accuracy. The QCNN can be trained to predict the corresponding ‘phase’ of wavefunctions around the putative quantum critical point even though it is trained by wavefunctions far away. The paper provides a basis for exploiting the QCNN to identify the quantum critical point.

Quantum Reports•Dec 8, 2022•3 citations
Machine learning has emerged as a promising approach to unveil properties of many-body systems. Recently proposed as a tool to classify phases of matter, the approach relies on classical simulation methods---such as Monte Carlo---which are known to experience an exponential slowdown when simulating certain quantum systems. To overcome this slowdown while still leveraging machine learning, we propose a variational quantum algorithm which merges quantum simulation and quantum machine learning to classify phases of matter. Our classifier is directly fed labeled states recovered by the variational quantum eigensolver algorithm, thereby avoiding the data-reading slowdown experienced in many applications of quantum enhanced machine learning. We propose families of variational ansatz states that are inspired directly by tensor networks. This allows us to use tools from tensor network theory to explain properties of the phase diagrams the presented quantum algorithm recovers. Finally, we propose a majority vote quantum classifier built from a nearest-neighbor (checkerboard) quantum neural network. This classifier is successfully trained to recognize phases of matter with 99% accuracy for the transverse field Ising model and 94% accuracy for the XXZXXZXXZ model. These findings suggest that a merger between quantum simulation and quantum enhanced machine learning offers a fertile ground to develop computational insights into quantum systems.
Machine learning has been applied on a wide variety of models, from classical statistical mechanics to quantum strongly correlated systems for the identification of phase transitions. The recently proposed quantum convolutional neural network (QCNN) provides a new framework for using quantum circuits instead of classical neural networks as the backbone of classification methods. We present here the results from training the QCNN by the wavefunctions of the variational quantum eigensolver for the one-dimensional transverse field Ising model (TFIM). We demonstrate that the QCNN identifies wavefunctions which correspond to the paramagnetic phase and the ferromagnetic phase of the TFIM with good accuracy. The QCNN can be trained to predict the corresponding phase of wavefunctions around the putative quantum critical point, even though it is trained by wavefunctions far away from it. This provides a basis for exploiting the QCNN to identify the quantum critical point.
Machine learning (ML) has recently facilitated many advances in solving problems related to many-body physical systems. Given the intrinsic quantum nature of these problems, it is natural to speculate that quantum-enhanced machine learning will enable us to unveil even greater details than we currently have. With this motivation, this paper examines a quantum machine learning approach based on shallow variational ansatz inspired by tensor networks for supervised learning tasks. In particular, we first look at the standard image classification tasks using the Fashion-MNIST dataset and study the effect of repeating tensor network layers on ansatz's expressibility and performance. Finally, we use this strategy to tackle the problem of quantum phase recognition for the transverse-field Ising and Heisenberg spin models in one and two dimensions, where we were able to reach ≥98%\geq 98\%≥98% test-set accuracies with both multi-scale entanglement renormalization ansatz (MERA) and tree tensor network (TTN) inspired parametrized quantum circuits.
Quantum many-body computation is a central challenge across multiple domains of scientific research, and Monte Carlo method has emerged as one of the most effective numerical techniques for investigating large-scale many-body systems. In recent years, the integration of Monte Carlo methods with machine learning has led to the development of neural quantum state approach. Quantum neural networks (QNNs) offer superior expressiveness compared to classical neural networks. In this paper, we propose a novel Quantum Neural Network Quantum State (QNNQS) method, based on the variational Monte Carlo framework. This approach leverages a quantum neural network to represent the many-body quantum state, and optimizes it iteratively through gradient descent to determine the ground-state energy. To assess the performance of this method, we conduct simulations of the one-dimensional transverse-field Ising model, investigating the influence of quantum circuit architecture on circuit expressibility, entangling capability, and computational accuracy. The results demonstrate that the QNNQS method achieves comparable simulation accuracy while utilizing significantly fewer parameters and requiring less training resources than classical network quantum state methods.
Abstract Unveiling quantum phase transitions (QPTs) is important for characterising physical systems at low temperatures. However, the detection of these transitions is encumbered by significant challenges, especially in the face of the exponential growth in ground state complexity with system scale. The emergence of quantum machine learning has lately gained traction as a promising method for elucidating the properties of many-body systems, providing a different avenue to study QPT. In this paper, we propose a novel and efficient quantum algorithm for identifying QPT synthesising quantum feature with quantum machine learning. Our approach is anchored in the utilisation of quantum computers to directly encode the kernel matrix into Hilbert spaces, realised by the parallel implementation of the quantum feature map. Specifically, we generate a quantum state encoding the information of ground states of the given quantum systems by employing the parallel quantum feature map. The resultant state preparation circuit is then used to implement a block-encoding of the kernel matrix. Equipped with the associated labels and this encoding, we devise a new quantum support vector machine (QSVM) algorithm, forming the main ingredient of the classifier. The presented method refines the efficiency of the prevailing QSVM algorithm for processing quantum and classical data. We demonstrate the effectiveness of our quantum classifier in predicting QPT within the transverse-field Ising model. The findings affirm the efficacy of quantum machine learning in recognising QPT in many-body systems and offer insights into the design of quantum machine learning algorithms.
Classical machine learning has succeeded in the prediction of both classical and quantum phases of matter. Notably, kernel methods stand out for their ability to provide interpretable results, relating the learning process with the physical order parameter explicitly. Here we exploit quantum kernels instead. They are naturally related to the fidelity, and thus it is possible to interpret the learning process with the help of quantum information tools. In particular, we use a support vector machine (with a quantum kernel) to predict and characterize second-order quantum phase transitions. We explain and understand the process of learning when the fidelity per site (rather than the fidelity) is used. The general theory is tested in the Ising chain in transverse field. We show that for small-sized systems, the algorithm gives accurate results, even when trained away from criticality. Besides, for larger sizes we confirm the success of the technique by extracting the correct critical exponent $\ensuremath{\nu}$. Finally, we present two algorithms, one based on fidelity and one based on the fidelity per site, to classify the phases of matter in a quantum processor.
Machine learning has been applied to a wide variety of models, from classical statistical mechanics to quantum strongly correlated systems, for classifying phase transitions. The recently proposed quantum convolutional neural network (QCNN) provides a new framework for using quantum circuits instead of classical neural networks as the backbone of classification methods. We present the results from training the QCNN by the wavefunctions of the variational quantum eigensolver for the one-dimensional transverse field Ising model (TFIM). We demonstrate that the QCNN identifies wavefunctions corresponding to the paramagnetic and ferromagnetic phases of the TFIM with reasonable accuracy. The QCNN can be trained to predict the corresponding ‘phase’ of wavefunctions around the putative quantum critical point even though it is trained by wavefunctions far away. The paper provides a basis for exploiting the QCNN to identify the quantum critical point.