Article
Physics, Multidisciplinary
Archak Purkayastha, Madhumita Saha, Bijay Kumar Agarwalla
Summary: This study reveals that a one-dimensional ordered fermionic lattice system connected to two baths with different chemical potentials at zero temperature exhibits two phases of subdiffusive conductance scaling with system size, unlike the perfectly ballistic transport in the isolated system. Interestingly, there are two chemical-potential-driven subdiffusive to ballistic phase transitions at zero temperature in the open system scenario.
PHYSICAL REVIEW LETTERS
(2021)
Article
Materials Science, Multidisciplinary
Alan Morningstar, Nicholas O'Dea, Jonas Richter
Summary: In systems with conserved density, the additional conservation of the center of mass has been found to slow down hydrodynamics. However, long-range interactions generally result in faster transport and information propagation. In this study, we investigate the competition between these two effects and develop a hydrodynamic theory for long-range center-of-mass-conserving systems, showing a rich dynamical phase diagram with varying dynamical exponents.
Article
Multidisciplinary Sciences
Nicolo Defenu
Summary: In systems with power-law decaying couplings, the spectrum remains discrete up to the thermodynamic limit, unlike traditional results on the chaotic nature of spectra in many-body quantum systems. The existence of QSSs may be related to the finiteness of Poincare recurrence times, extending known results on anomalous magnetization dynamics in the quantum Ising model with power-law decaying couplings. The comparison between the discrete spectrum of long-range systems and more conventional examples of pure point spectra in the disordered case is also discussed.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2021)
Article
Materials Science, Multidisciplinary
I. Lukin, A. G. Sotnikov
Summary: We introduce the continuous matrix-product states approach for describing inhomogeneous one-dimensional quantum systems with long-range interactions. The method is applied to the solvable Calogero-Moser model, demonstrating its high accuracy in reproducing the ground-state properties of many-body systems. We also discuss potential errors arising from approximating nonlocal interaction potentials with singularities.
Article
Materials Science, Multidisciplinary
Karol Kawa, Pawel Machnikowski
Summary: In this study, we investigate the spread of correlations in a one-dimensional lattice system with high on-site energy disorder and long-range couplings. We find that the increase in correlation between two nodes exhibits three phases and we also obtain an approximate solution of the model valid in the limit of strong disorder.
Article
Multidisciplinary Sciences
Andrea Pizzi, Johannes Knolle, Andreas Nunnenkamp
Summary: Researchers have found that in the presence of long-range interactions and transverse fields, a clean spin-1/2 system can support a variety of different 'higher-order' discrete time crystals with integer and even fractional values of n. These phases, characterized as arguably prethermal non-equilibrium states, are stable in models with continuous driving and time-independent interactions, making them suitable for experimental implementations using ultracold atoms or trapped ions.
NATURE COMMUNICATIONS
(2021)
Article
Physics, Multidisciplinary
Chufan Lyu, Xiaoyu Tang, Junning Li, Xusheng Xu, Man-Hong Yung, Abolfazl Bayat
Summary: Current quantum simulators face limitations in coherence time, operations quality, readout accuracy, and qubit connectivity. Variational quantum algorithms are the most promising approach for near-term practical quantum advantage. This study explores variational quantum algorithms with different qubit connectivity levels for digital simulation of long-range interacting systems and generation of spin squeezed states. The results show that longer-range interactions decrease the efficiency and fidelity of the algorithms, requiring more optimization iterations. Increasing qubit connectivity improves results with fewer resources. Mixing circuit layers with different connectivity levels can significantly enhance performance. The same circuit design can also be used for variational spin squeezed state generation for quantum metrology.
NEW JOURNAL OF PHYSICS
(2023)
Article
Physics, Multidisciplinary
Tomotaka Kuwahara, Keiji Saito
Summary: This study disproves fast scrambling in generic long-range interacting systems with alpha > D, where the OTOC shows a polynomial growth over time as long as alpha > D and the necessary scrambling time over a distance R is larger than t greater than or similar to R[(2 alpha-2D)/(2 alpha-D+1)].
PHYSICAL REVIEW LETTERS
(2021)
Article
Physics, Multidisciplinary
Luhang Yang, Adrian Feiguin
Summary: In this study, the nature of excitations in an antiferromagnetic Heisenberg chain with staggered long range interactions was investigated using numerical methods and a multi-spinon approximation. It was found that the emergence of Neel order can be explained by the behavior of the spin dynamic structure factor. The chain undergoes true symmetry breaking and develops long range order, transitioning to a gapped ordered antiferromagnetic phase.
Article
Materials Science, Multidisciplinary
Tianci Zhou, Andrew Guo, Shenglong Xu, Xiao Chen, Brian Swingle
Summary: The FKPP equation provides a mean-field theory for out-of-time ordered commutators in quantum chaotic systems. The fractional-derivative FKPP equation offers a mean-field theory for systems with power-law interactions. However, the fractional FKPP description is subject to strong quantum fluctuation effects, and its effectiveness for generic chaotic systems with power-law interactions is unclear. This study investigates this problem using a model of coupled quantum dots and demonstrates that the parameters of the effective theory can be chosen to reproduce the previously found butterfly light cone scalings.
Article
Materials Science, Multidisciplinary
Devendra Singh Bhakuni, Lea F. Santos, Yevgeny Bar Lev
Summary: A mechanism to suppress heating in periodically driven many-body quantum systems is proposed, utilizing long-range interactions and relevant initial conditions. Decreasing the driving frequency can reduce heating and entanglement buildup in these systems. This mechanism is robust to local perturbations and can be generalized to higher dimensions.
Article
Physics, Multidisciplinary
Pierre-Henri Chavanis
Summary: This study develops the kinetic theory of collisionless relaxation for systems with long-range interactions, specifically in relation to Lynden-Bell's statistical theory. The authors discuss the multi-level case and establish the connection between the kinetic equation derived from the quasilinear theory of the Vlasov equation and the relaxation equation obtained from a maximum entropy production principle. They propose a method to close the infinite hierarchy of kinetic equations and obtain a generalized Landau, Lenard-Balescu, or Kramers equation for the coarse-grained distribution function. The authors also explore the analogies with two-dimensional turbulence and potential applications to fermionic and bosonic dark matter halos.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2022)
Article
Automation & Control Systems
Xiaoling Wang, Zhen Fan, Yingjiang Zhou, Youhong Wan
Summary: This paper focuses on the distributed observer design problem of a discrete-time complex dynamical system with long-rang interactions. A group of agents communicate through a directed graph to measure the system's outputs, where each agent can access only a part of the outputs. The paper presents a simple full-order distributed observer and a reduced-order distributed observer to reduce the number of integrators. Numerical simulations are provided to verify the theoretical results.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2023)
Article
Physics, Fluids & Plasmas
Jie Ren, Zhao Wang, Weixia Chen, Wen-Long You
Summary: In this study, we investigate quantum phase transitions in Heisenberg antiferromagnetic chains with staggered power-law decaying long-range interactions. By using the density-matrix renormalization group (DMRG) algorithm and the fidelity susceptibility as the criticality measure, we obtain more accurate values of quantum critical points compared to previous studies. Furthermore, we explore the effects of anisotropic long-range interactions and symmetry breaking, which result in the emergence of various quantum phases.
Article
Mathematics, Applied
J. -B. Bru, W. de Siqueira Pedra
Summary: The study focuses on the quantum part of the macroscopic dynamics with long-range interactions in fermion and quantum-spin systems, revealing a complex combination of classical and short-range quantum dynamics. The development of a suitable mathematical framework is necessary to go beyond previous results. The entanglement between classical and quantum worlds is attributed to the highly non local character of long-range interactions.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Physics, Multidisciplinary
Alex Gnech, Corey Adams, Nicholas Brawand, Giuseppe Carleo, Alessandro Lovato, Noemi Rocco
Summary: The groundbreaking works of Weinberg have paved the way for calculating atomic nuclei using systematically improvable Hamiltonians, with the help of artificial neural networks.
Article
Physics, Multidisciplinary
Tong Liu, Xu Xia, Stefano Longhi, Laurent Sanchez-Palencia
Summary: This study reveals a new class of mobility edges, called anomalous mobility edges, which separate localized states from critical states in diagonal and off-diagonal quasiperiodic models. The existence of anomalous mobility edges is analytically demonstrated in a solvable diagonal model, and numerical evidence is shown in an off-diagonal model. The results shed light on the localization and critical properties of low-dimensional systems with aperiodic order.
Article
Physics, Multidisciplinary
Damian Hofmann, Giammarco Fabiani, Johan H. Mentink, Giuseppe Carleo, Michael A. Sentef
Summary: This article focuses on the time evolution of the two-leg Heisenberg ladder in a non-equilibrium state and finds that the nonlinear equations of motion amplify noise, leading to numerical instabilities. Stability can be greatly improved by appropriate choice of regularization, without additional computational cost.
Article
Multidisciplinary Sciences
Javier Robledo Moreno, Giuseppe Carleo, Antoine Georges, James Stokes
Summary: We introduce a new family of variational wave functions for simulating strongly correlated fermionic systems. By incorporating hidden additional degrees of freedom and optimizing the constraint and single-particle orbitals using a neural network parameterization, our construction overcomes limitations of hidden-particle representations and is proven to be universal. Applied to the ground-state properties of the Hubbard model, our approach achieves competitive levels of accuracy with state-of-the-art variational methods.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2022)
Article
Physics, Multidisciplinary
Kevin Zhang, Samuel Lederer, Kenny Choo, Titus Neupert, Giuseppe Carleo, Eun-Ah Kim
Summary: This article introduces the use of neural networks to approximately solve quantum many-body problems, and proposes a new method to evaluate the quality of neural network wavefunctions. Through Hamiltonian reconstruction, the characteristics of reconstructed Hamiltonians in certain situations and the importance of wavefunction symmetry are discovered.
Article
Multidisciplinary Sciences
Giacomo Torlai, Christopher J. Wood, Atithi Acharya, Giuseppe Carleo, Juan Carrasquilla, Leandro Aolita
Summary: The impressive advance of quantum technology requires robust and scalable techniques for characterizing and validating quantum hardware. A technique for quantum process tomography is proposed, combining a tensor network representation with data-driven optimization inspired by unsupervised machine learning. Through synthetic data, the technique achieves process fidelities above 0.99 using significantly fewer measurement shots than traditional tomographic techniques, providing a practical and timely tool for benchmarking quantum circuits in current and near-term quantum computers.
NATURE COMMUNICATIONS
(2023)
Article
Computer Science, Artificial Intelligence
James Stokes, Saibal De, Shravan Veerapaneni, Giuseppe Carleo
Summary: We introduce the exploration of neural network quantum state algorithms for analyzing continuous-variable quantum systems. A simple family of continuous-variable trial wavefunctions is proposed, which generalizes the restricted Boltzmann machine (RBM) wavefunction for analyzing quantum spin systems. The same variational Monte Carlo training algorithms for spin systems have natural analogues in the continuum. We demonstrate the feasibility for ground state determination of a stoquastic quantum rotor Hamiltonian and compare the results with PDE-based scalable eigensolvers. This study provides a benchmark for future investigation of continuous-variable neural quantum states and highlights the need for deep network architectures and more sophisticated training algorithms.
QUANTUM MACHINE INTELLIGENCE
(2023)
Article
Quantum Science & Technology
Jannes Nys, Giuseppe Carleo
Summary: Local Hamiltonians of fermionic systems on a lattice can be mapped onto qubit Hamiltonians with auxiliary degrees of freedom to maintain locality. This work introduces quantum circuits that exactly satisfy the constraints of the fermionic degrees of freedom, allowing for Trotterized time-evolution with constant circuit depth per time step. The construction is advantageous for simulating fermionic systems in dimensions greater than one and can be used as variational quantum states.
Article
Materials Science, Multidisciplinary
Or Sharir, Amnon Shashua, Giuseppe Carleo
Summary: We establish a direct connection between general tensor networks and deep feed-forward artificial neural networks, allowing efficient tensor contractions and use of nonlinear activation functions. The resulting deep networks closely match the contraction complexity of the tensor networks to be approximated. Specifically in the context of many-body quantum states, our results show that neural-network states have strictly the same or higher expressive power than variational tensor networks. We also demonstrate that all matrix product states can be efficiently expressed as neural-network states with polynomial number of edges and logarithmic depth.
Article
Physics, Multidisciplinary
Alessandro Lovato, Corey Adams, Giuseppe Carleo, Noemi Rocco
Summary: We generalize the hidden-fermion family of neural network quantum states to solve the nuclear many-body Schrodinger equation, achieving accuracy comparable to other exact methods in light nuclei and 16O. This method enhances the expressivity of the neural network architecture and opens the way to highly-accurate quantum Monte Carlo studies of medium-mass nuclei.
PHYSICAL REVIEW RESEARCH
(2022)
Article
Physics, Multidisciplinary
Stefano Barison, Filippo Vicentini, Ignacio Cirac, Giuseppe Carleo
Summary: In this study, we propose a variational quantum algorithm to study the real-time dynamics of quantum systems. Through numerical experiments, we demonstrate its robustness and feasibility.
PHYSICAL REVIEW RESEARCH
(2022)
Article
Materials Science, Multidisciplinary
Guglielmo Lami, Giuseppe Carleo, Mario Collura
Summary: By introducing backflow transformation and tensor network Ansatz, this study extends the matrix product state representation of a quantum many-body wave function and provides enough resources to ensure that states in dimensions larger than or equal to one follow the area law for entanglement. The optimization scheme that combines tensor network and variational Monte Carlo algorithms efficiently addresses the ground-state search problem and demonstrates high accuracy and precision in spin models.
Article
Materials Science, Multidisciplinary
J. T. Schneider, S. J. Thomson, L. Sanchez-Palencia
Summary: Entanglement is a central feature in many-body quantum systems, especially in quantum phase transitions. In this study, we investigate the entanglement spectrum of the long-range XXZ model and find remarkable self-similarity within the critical phase. Our results confirm the predictions of renormalization group theory and provide insights into the quantum phase diagram of the model.
Article
Physics, Multidisciplinary
Gabriel Pescia, Jiequn Han, Alessandro Lovato, Jianfeng Lu, Giuseppe Carleo
Summary: Researchers introduce a family of neural quantum states for simulating strongly interacting systems with spatial periodicity. Their variational state is parametrized by a Deep Sets neural network architecture and includes a permutationally invariant part. By transforming the input coordinates and directly describing periodic bosonic systems, they achieve accurate estimations of ground-state energies and radial distribution functions for one-dimensional systems, as well as comparable results for two-dimensional systems.
PHYSICAL REVIEW RESEARCH
(2022)
Article
Computer Science, Artificial Intelligence
Tianchen Zhao, Giuseppe Carleo, James Stokes, Shravan Veerapaneni
Summary: The concept of quantum natural evolution strategies is introduced, which combines known quantum/classical algorithms for classical black-box optimization. The work by Gomes et al (2019 arXiv:1910.10675) highlights the connection between neural quantum states and natural evolution strategies (NES) in heuristic combinatorial optimization, showing a systematic strategy for improving approximation ratios. It is found that NES can achieve competitive approximation ratios for Max-Cut with commonly used heuristic algorithms, albeit with increased computation time.
MACHINE LEARNING-SCIENCE AND TECHNOLOGY
(2021)
