We discuss adiabatic spectra and dynamics of the quantum, i.e. transverse field, Hopfield model with dilute memories (the number of stored patterns $p < log_2 N$, where $N$ is the number of qubits). At some critical transverse field the model undergoes the quantum phase transition from the ordered to the paramagnetic state. The corresponding critical exponents are calculated and used to determine efficiency of quantum annealing protocols. We also discuss implications of these results for the quantum annealing of generic spin glass models.
我们讨论了具有稀释记忆（存储模式的数量 $p
{"title":"Quantum Hopfield Model with Dilute Memories","authors":"Rongfeng Xie, Alex Kamenev","doi":"arxiv-2405.13240","DOIUrl":"https://doi.org/arxiv-2405.13240","url":null,"abstract":"We discuss adiabatic spectra and dynamics of the quantum, i.e. transverse\u0000field, Hopfield model with dilute memories (the number of stored patterns $p <\u0000log_2 N$, where $N$ is the number of qubits). At some critical transverse field\u0000the model undergoes the quantum phase transition from the ordered to the\u0000paramagnetic state. The corresponding critical exponents are calculated and\u0000used to determine efficiency of quantum annealing protocols. We also discuss\u0000implications of these results for the quantum annealing of generic spin glass\u0000models.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141150746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Kirsten Fischer, Javed Lindner, David Dahmen, Zohar Ringel, Michael Krämer, Moritz Helias
A key property of neural networks driving their success is their ability to learn features from data. Understanding feature learning from a theoretical viewpoint is an emerging field with many open questions. In this work we capture finite-width effects with a systematic theory of network kernels in deep non-linear neural networks. We show that the Bayesian prior of the network can be written in closed form as a superposition of Gaussian processes, whose kernels are distributed with a variance that depends inversely on the network width N . A large deviation approach, which is exact in the proportional limit for the number of data points $P = alpha N rightarrow infty$, yields a pair of forward-backward equations for the maximum a posteriori kernels in all layers at once. We study their solutions perturbatively to demonstrate how the backward propagation across layers aligns kernels with the target. An alternative field-theoretic formulation shows that kernel adaptation of the Bayesian posterior at finite-width results from fluctuations in the prior: larger fluctuations correspond to a more flexible network prior and thus enable stronger adaptation to data. We thus find a bridge between the classical edge-of-chaos NNGP theory and feature learning, exposing an intricate interplay between criticality, response functions, and feature scale.
神经网络取得成功的一个关键特性是其从数据中学习特征的能力。从理论角度理解特征学习是一个新兴领域，存在许多未决问题。在这项工作中，我们利用深入非线性神经网络的网络核的系统理论来捕捉有限宽度效应。我们证明，网络的贝叶斯先验可以以封闭形式写成高斯过程的叠加，其内核分布的方差与网络宽度 N 成反比。大偏差方法在数据点数量 $P = alpha N rightarrow infty$ 的比例极限下是精确的，它可以一次性得到所有层中最大后验核的前向后向方程。我们对它们的解进行了扰动研究，以证明跨层的后向传播如何使核与目标保持一致。替代的场论表述表明，贝叶斯后验在有限宽度下的内核适应性来自于先验的波动：较大的波动对应于更灵活的网络先验，从而能够更强地适应数据。因此，我们在经典的边缘混沌 NNGP 理论和特征学习之间找到了一座桥梁，揭示了临界性、响应函数和特征尺度之间错综复杂的相互作用。
{"title":"Critical feature learning in deep neural networks","authors":"Kirsten Fischer, Javed Lindner, David Dahmen, Zohar Ringel, Michael Krämer, Moritz Helias","doi":"arxiv-2405.10761","DOIUrl":"https://doi.org/arxiv-2405.10761","url":null,"abstract":"A key property of neural networks driving their success is their ability to\u0000learn features from data. Understanding feature learning from a theoretical\u0000viewpoint is an emerging field with many open questions. In this work we\u0000capture finite-width effects with a systematic theory of network kernels in\u0000deep non-linear neural networks. We show that the Bayesian prior of the network\u0000can be written in closed form as a superposition of Gaussian processes, whose\u0000kernels are distributed with a variance that depends inversely on the network\u0000width N . A large deviation approach, which is exact in the proportional limit\u0000for the number of data points $P = alpha N rightarrow infty$, yields a pair\u0000of forward-backward equations for the maximum a posteriori kernels in all\u0000layers at once. We study their solutions perturbatively to demonstrate how the\u0000backward propagation across layers aligns kernels with the target. An\u0000alternative field-theoretic formulation shows that kernel adaptation of the\u0000Bayesian posterior at finite-width results from fluctuations in the prior:\u0000larger fluctuations correspond to a more flexible network prior and thus enable\u0000stronger adaptation to data. We thus find a bridge between the classical\u0000edge-of-chaos NNGP theory and feature learning, exposing an intricate interplay\u0000between criticality, response functions, and feature scale.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141150703","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Generative modeling aims at producing new datapoints whose statistical properties resemble the ones in a training dataset. In recent years, there has been a burst of machine learning techniques and settings that can achieve this goal with remarkable performances. In most of these settings, one uses the training dataset in conjunction with noise, which is added as a source of statistical variability and is essential for the generative task. Here, we explore the idea of using internal chaotic dynamics in high-dimensional chaotic systems as a way to generate new datapoints from a training dataset. We show that simple learning rules can achieve this goal within a set of vanilla architectures and characterize the quality of the generated datapoints through standard accuracy measures.
{"title":"Generative modeling through internal high-dimensional chaotic activity","authors":"Samantha J. Fournier, Pierfrancesco Urbani","doi":"arxiv-2405.10822","DOIUrl":"https://doi.org/arxiv-2405.10822","url":null,"abstract":"Generative modeling aims at producing new datapoints whose statistical\u0000properties resemble the ones in a training dataset. In recent years, there has\u0000been a burst of machine learning techniques and settings that can achieve this\u0000goal with remarkable performances. In most of these settings, one uses the\u0000training dataset in conjunction with noise, which is added as a source of\u0000statistical variability and is essential for the generative task. Here, we\u0000explore the idea of using internal chaotic dynamics in high-dimensional chaotic\u0000systems as a way to generate new datapoints from a training dataset. We show\u0000that simple learning rules can achieve this goal within a set of vanilla\u0000architectures and characterize the quality of the generated datapoints through\u0000standard accuracy measures.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141150750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Class imbalance in real-world data poses a common bottleneck for machine learning tasks, since achieving good generalization on under-represented examples is often challenging. Mitigation strategies, such as under or oversampling the data depending on their abundances, are routinely proposed and tested empirically, but how they should adapt to the data statistics remains poorly understood. In this work, we determine exact analytical expressions of the generalization curves in the high-dimensional regime for linear classifiers (Support Vector Machines). We also provide a sharp prediction of the effects of under/oversampling strategies depending on class imbalance, first and second moments of the data, and the metrics of performance considered. We show that mixed strategies involving under and oversampling of data lead to performance improvement. Through numerical experiments, we show the relevance of our theoretical predictions on real datasets, on deeper architectures and with sampling strategies based on unsupervised probabilistic models.
{"title":"Restoring balance: principled under/oversampling of data for optimal classification","authors":"Emanuele Loffredo, Mauro Pastore, Simona Cocco, Rémi Monasson","doi":"arxiv-2405.09535","DOIUrl":"https://doi.org/arxiv-2405.09535","url":null,"abstract":"Class imbalance in real-world data poses a common bottleneck for machine\u0000learning tasks, since achieving good generalization on under-represented\u0000examples is often challenging. Mitigation strategies, such as under or\u0000oversampling the data depending on their abundances, are routinely proposed and\u0000tested empirically, but how they should adapt to the data statistics remains\u0000poorly understood. In this work, we determine exact analytical expressions of\u0000the generalization curves in the high-dimensional regime for linear classifiers\u0000(Support Vector Machines). We also provide a sharp prediction of the effects of\u0000under/oversampling strategies depending on class imbalance, first and second\u0000moments of the data, and the metrics of performance considered. We show that\u0000mixed strategies involving under and oversampling of data lead to performance\u0000improvement. Through numerical experiments, we show the relevance of our\u0000theoretical predictions on real datasets, on deeper architectures and with\u0000sampling strategies based on unsupervised probabilistic models.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141063578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
To improve the storage capacity of the Hopfield model, we develop a version of the dreaming algorithm that perpetually reinforces the patterns to be stored (as in the Hebb rule), and erases the spurious memories (as in dreaming algorithms). For this reason, we called it Daydreaming. Daydreaming is not destructive and it converges asymptotically to stationary retrieval maps. When trained on random uncorrelated examples, the model shows optimal performance in terms of the size of the basins of attraction of stored examples and the quality of reconstruction. We also train the Daydreaming algorithm on correlated data obtained via the random-features model and argue that it spontaneously exploits the correlations thus increasing even further the storage capacity and the size of the basins of attraction. Moreover, the Daydreaming algorithm is also able to stabilize the features hidden in the data. Finally, we test Daydreaming on the MNIST dataset and show that it still works surprisingly well, producing attractors that are close to unseen examples and class prototypes.
{"title":"Daydreaming Hopfield Networks and their surprising effectiveness on correlated data","authors":"Ludovica Serricchio, Dario Bocchi, Claudio Chilin, Raffaele Marino, Matteo Negri, Chiara Cammarota, Federico Ricci-Tersenghi","doi":"arxiv-2405.08777","DOIUrl":"https://doi.org/arxiv-2405.08777","url":null,"abstract":"To improve the storage capacity of the Hopfield model, we develop a version\u0000of the dreaming algorithm that perpetually reinforces the patterns to be stored\u0000(as in the Hebb rule), and erases the spurious memories (as in dreaming\u0000algorithms). For this reason, we called it Daydreaming. Daydreaming is not\u0000destructive and it converges asymptotically to stationary retrieval maps. When\u0000trained on random uncorrelated examples, the model shows optimal performance in\u0000terms of the size of the basins of attraction of stored examples and the\u0000quality of reconstruction. We also train the Daydreaming algorithm on\u0000correlated data obtained via the random-features model and argue that it\u0000spontaneously exploits the correlations thus increasing even further the\u0000storage capacity and the size of the basins of attraction. Moreover, the\u0000Daydreaming algorithm is also able to stabilize the features hidden in the\u0000data. Finally, we test Daydreaming on the MNIST dataset and show that it still\u0000works surprisingly well, producing attractors that are close to unseen examples\u0000and class prototypes.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"192 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Weitao Chen, Olivier Giraud, Jiangbin Gong, Gabriel Lemarié
Due to their analytical tractability, random matrix ensembles serve as robust platforms for exploring exotic phenomena in systems that are computationally demanding. Building on a companion letter [arXiv:2312.17481], this paper investigates two random matrix ensembles tailored to capture the critical behavior of the Anderson transition in infinite dimension, employing both analytical techniques and extensive numerical simulations. Our study unveils two types of critical behaviors: logarithmic multifractality and critical localization. In contrast to conventional multifractality, the novel logarithmic multifractality features eigenstate moments scaling algebraically with the logarithm of the system size. Critical localization, characterized by eigenstate moments of order $q>1/2$ converging to a finite value indicating localization, exhibits characteristic logarithmic finite-size or time effects, consistent with the critical behavior observed in random regular and Erd"os-R'enyi graphs of effective infinite dimensionality. Using perturbative methods, we establish the existence of logarithmic multifractality and critical localization in our models. Furthermore, we explore the emergence of novel scaling behaviors in the time dynamics and spatial correlation functions. Our models provide a valuable framework for studying infinite-dimensional quantum disordered systems, and the universality of our findings enables broad applicability to systems with pronounced finite-size effects and slow dynamics, including the contentious many-body localization transition, akin to the Anderson transition in infinite dimension.
{"title":"Describing the critical behavior of the Anderson transition in infinite dimension by random-matrix ensembles: logarithmic multifractality and critical localization","authors":"Weitao Chen, Olivier Giraud, Jiangbin Gong, Gabriel Lemarié","doi":"arxiv-2405.10975","DOIUrl":"https://doi.org/arxiv-2405.10975","url":null,"abstract":"Due to their analytical tractability, random matrix ensembles serve as robust\u0000platforms for exploring exotic phenomena in systems that are computationally\u0000demanding. Building on a companion letter [arXiv:2312.17481], this paper\u0000investigates two random matrix ensembles tailored to capture the critical\u0000behavior of the Anderson transition in infinite dimension, employing both\u0000analytical techniques and extensive numerical simulations. Our study unveils\u0000two types of critical behaviors: logarithmic multifractality and critical\u0000localization. In contrast to conventional multifractality, the novel\u0000logarithmic multifractality features eigenstate moments scaling algebraically\u0000with the logarithm of the system size. Critical localization, characterized by\u0000eigenstate moments of order $q>1/2$ converging to a finite value indicating\u0000localization, exhibits characteristic logarithmic finite-size or time effects,\u0000consistent with the critical behavior observed in random regular and\u0000Erd\"os-R'enyi graphs of effective infinite dimensionality. Using perturbative\u0000methods, we establish the existence of logarithmic multifractality and critical\u0000localization in our models. Furthermore, we explore the emergence of novel\u0000scaling behaviors in the time dynamics and spatial correlation functions. Our\u0000models provide a valuable framework for studying infinite-dimensional quantum\u0000disordered systems, and the universality of our findings enables broad\u0000applicability to systems with pronounced finite-size effects and slow dynamics,\u0000including the contentious many-body localization transition, akin to the\u0000Anderson transition in infinite dimension.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141150704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The purpose of this manuscript is to review my recent activity on three main research topics. The first concerns the nature of low temperature amorphous solids and their relation with the spin glass transition in a magnetic field. This is the subject of the first chapter where I discuss a new model, the KHGPS model, which allows to make some progress. In the second chapter I review a second research line that concerns the study of the rigidity/jamming transitions in particle system models and their relation to constraint satisfaction and optimization problems in high dimension. Finally in the last chapter I review my activity on the problem of the dynamics of learning algorithms in high-dimensional inference and supervised learning problems.
{"title":"Statistical physics of complex systems: glasses, spin glasses, continuous constraint satisfaction problems, high-dimensional inference and neural networks","authors":"Pierfrancesco Urbani","doi":"arxiv-2405.06384","DOIUrl":"https://doi.org/arxiv-2405.06384","url":null,"abstract":"The purpose of this manuscript is to review my recent activity on three main\u0000research topics. The first concerns the nature of low temperature amorphous\u0000solids and their relation with the spin glass transition in a magnetic field.\u0000This is the subject of the first chapter where I discuss a new model, the KHGPS\u0000model, which allows to make some progress. In the second chapter I review a\u0000second research line that concerns the study of the rigidity/jamming\u0000transitions in particle system models and their relation to constraint\u0000satisfaction and optimization problems in high dimension. Finally in the last\u0000chapter I review my activity on the problem of the dynamics of learning\u0000algorithms in high-dimensional inference and supervised learning problems.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"84 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chuanzhou Zhu, Peter J. Ehlers, Hendra I. Nurdin, Daniel Soh
Quantum Reservoir Computing leverages quantum systems to solve complex computational tasks with unprecedented efficiency and reduced energy consumption. This paper presents a novel QRC framework utilizing a quantum optical reservoir composed of two-level atoms within a single-mode optical cavity. Employing the Jaynes-Cummings and Tavis-Cummings models, we introduce a scalable and practically measurable reservoir that outperforms traditional classical reservoir computing in both memory retention and nonlinear data processing. We evaluate the reservoir's performance through two primary tasks: the prediction of time-series data via the Mackey-Glass task and the classification of sine-square waveforms. Our results demonstrate significant enhancements in performance with increased numbers of atoms, supported by non-destructive, continuous quantum measurements and polynomial regression techniques. This study confirms the potential of QRC to offer a scalable and efficient solution for advanced computational challenges, marking a significant step forward in the integration of quantum physics with machine learning technology.
{"title":"Practical and Scalable Quantum Reservoir Computing","authors":"Chuanzhou Zhu, Peter J. Ehlers, Hendra I. Nurdin, Daniel Soh","doi":"arxiv-2405.04799","DOIUrl":"https://doi.org/arxiv-2405.04799","url":null,"abstract":"Quantum Reservoir Computing leverages quantum systems to solve complex\u0000computational tasks with unprecedented efficiency and reduced energy\u0000consumption. This paper presents a novel QRC framework utilizing a quantum\u0000optical reservoir composed of two-level atoms within a single-mode optical\u0000cavity. Employing the Jaynes-Cummings and Tavis-Cummings models, we introduce a\u0000scalable and practically measurable reservoir that outperforms traditional\u0000classical reservoir computing in both memory retention and nonlinear data\u0000processing. We evaluate the reservoir's performance through two primary tasks:\u0000the prediction of time-series data via the Mackey-Glass task and the\u0000classification of sine-square waveforms. Our results demonstrate significant\u0000enhancements in performance with increased numbers of atoms, supported by\u0000non-destructive, continuous quantum measurements and polynomial regression\u0000techniques. This study confirms the potential of QRC to offer a scalable and\u0000efficient solution for advanced computational challenges, marking a significant\u0000step forward in the integration of quantum physics with machine learning\u0000technology.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140940958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Francesco Ferraro, Christian Grilletta, Amos Maritan, Samir Suweis, Sandro Azaele
We investigate a disordered multi-dimensional linear system in which the interaction parameters vary stochastically in time with defined temporal correlations. We refer to this type of disorder as "annealed", in contrast to quenched disorder in which couplings are fixed in time. We extend Dynamical Mean-Field Theory to accommodate annealed disorder and employ it to find the exact solution of the linear model in the limit of a large number of degrees of freedom. Our analysis yields analytical results for the non-stationary auto-correlation, the stationary variance, the power spectral density, and the phase diagram of the model. Interestingly, some unexpected features emerge upon changing the correlation time of the interactions. The stationary variance of the system and the critical variance of the disorder are generally found to be a non-monotonic function of the correlation time of the interactions. We also find that in some cases a re-entrant phase transition takes place when this correlation time is varied.
{"title":"Exact solution of Dynamical Mean-Field Theory for a linear system with annealed disorder","authors":"Francesco Ferraro, Christian Grilletta, Amos Maritan, Samir Suweis, Sandro Azaele","doi":"arxiv-2405.05183","DOIUrl":"https://doi.org/arxiv-2405.05183","url":null,"abstract":"We investigate a disordered multi-dimensional linear system in which the\u0000interaction parameters vary stochastically in time with defined temporal\u0000correlations. We refer to this type of disorder as \"annealed\", in contrast to\u0000quenched disorder in which couplings are fixed in time. We extend Dynamical\u0000Mean-Field Theory to accommodate annealed disorder and employ it to find the\u0000exact solution of the linear model in the limit of a large number of degrees of\u0000freedom. Our analysis yields analytical results for the non-stationary\u0000auto-correlation, the stationary variance, the power spectral density, and the\u0000phase diagram of the model. Interestingly, some unexpected features emerge upon\u0000changing the correlation time of the interactions. The stationary variance of\u0000the system and the critical variance of the disorder are generally found to be\u0000a non-monotonic function of the correlation time of the interactions. We also\u0000find that in some cases a re-entrant phase transition takes place when this\u0000correlation time is varied.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"72 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140940962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, we explore the information capacity of open quantum systems, focusing on the effective channels formed by the subsystem of random quantum circuits and quantum Hamiltonian evolution. By analyzing the subsystem information capacity, which is closely linked to quantum coherent information of these effective quantum channels, we uncover a diverse range of dynamical and steady behaviors depending on the types of evolution. Therefore, the subsystem information capacity serves as a valuable tool for studying the intrinsic nature of various dynamical phases, such as integrable, localized, thermalized, and topological systems. We also reveal the impact of different initial information encoding schemes on information dynamics including one-to-one, one-to-many, and many-to-many. To support our findings, we provide representative examples for numerical simulations, including random quantum circuits with or without mid-circuit measurements, random Clifford Floquet circuits, free and interacting Aubry-Andr'e models, and Su-Schrieffer-Heeger models. Those numerical results are further quantitatively explained using the effective statistical model mapping and the quasiparticle picture in the cases of random circuits and non-interacting Hamiltonian dynamics, respectively.
{"title":"Subsystem Information Capacity in Random Circuits and Hamiltonian Dynamics","authors":"Yu-Qin Chen, Shuo Liu, Shi-Xin Zhang","doi":"arxiv-2405.05076","DOIUrl":"https://doi.org/arxiv-2405.05076","url":null,"abstract":"In this study, we explore the information capacity of open quantum systems,\u0000focusing on the effective channels formed by the subsystem of random quantum\u0000circuits and quantum Hamiltonian evolution. By analyzing the subsystem\u0000information capacity, which is closely linked to quantum coherent information\u0000of these effective quantum channels, we uncover a diverse range of dynamical\u0000and steady behaviors depending on the types of evolution. Therefore, the\u0000subsystem information capacity serves as a valuable tool for studying the\u0000intrinsic nature of various dynamical phases, such as integrable, localized,\u0000thermalized, and topological systems. We also reveal the impact of different\u0000initial information encoding schemes on information dynamics including\u0000one-to-one, one-to-many, and many-to-many. To support our findings, we provide\u0000representative examples for numerical simulations, including random quantum\u0000circuits with or without mid-circuit measurements, random Clifford Floquet\u0000circuits, free and interacting Aubry-Andr'e models, and Su-Schrieffer-Heeger\u0000models. Those numerical results are further quantitatively explained using the\u0000effective statistical model mapping and the quasiparticle picture in the cases\u0000of random circuits and non-interacting Hamiltonian dynamics, respectively.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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