Article
Mathematics
Xue Liu
Summary: In this paper, the statistical properties of Anosov systems on a surface driven by an external force are studied. Using the Birkhoff cone method, it is shown that if the systems on the surface satisfy the Anosov and topological mixing on fibers property, the quenched random correlation for Holder observables with respect to the unique random SRB measures decays exponentially.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2024)
Article
Mathematics, Applied
Armen Shirikyan
Summary: This paper explores the relationship between controllability and mixing properties of random dynamical systems, showing that approximate controllability and local stabilisation properties are key factors in achieving the uniqueness of a stationary measure and exponential mixing in specific systems. The results are then applied to the boundary-driven Navier-Stokes system, leading to local exponential stabilisation through regular boundary control.
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
(2021)
Article
Robotics
Peinan Yan, Jiang Zou, Jianglong Guo, Jinsong Leng, Guoying Gu
Summary: Electroadhesion often suffers from slow de-electroadhesion due to residual charges, limiting its application in handling lightweight objects. In this study, we propose an electrical solution using programmable exponential decay alternative voltage to achieve rapid de-electroadhesion. We investigate the influence of voltage parameters on de-electroadhesion time and demonstrate the effectiveness of our method in achieving fast release of electroadhesion.
IEEE ROBOTICS AND AUTOMATION LETTERS
(2023)
Article
Mathematics, Applied
Salman Siddiqi
Summary: This paper establishes exponential decay of correlations of all orders for locally G-accessible isometric extensions of transitive Anosov flows under the assumption that the strong stable and strong unstable distributions of the base Anosov flow are C-1. This is achieved by translating the accessibility properties of the extension into local non-integrability estimates measured by infinitesimal transitivity groups, which allows us to obtain contraction properties for a class of 'twisted' symbolic transfer operators.
ERGODIC THEORY AND DYNAMICAL SYSTEMS
(2023)
Article
Physics, Mathematical
Ramis Movassagh, Jeffrey Schenker
Summary: This research represents discrete quantum processes using quantum channels and discovers that under specific conditions, the state under such processes converges rapidly to an ergodic sequence independent of the initial state. The research also applies to the thermodynamic limit of ergodic matrix product states and proves that the 2-point correlations of local observables in such states decay exponentially with their distance.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2022)
Article
Mathematics, Applied
Draifia Alaeddine
Summary: This work addresses decay rates for energy in a system of nonlinear singular viscoelastic equations with a nonlocal boundary condition. The study proves decay rates for the energy of a singular one-dimensional viscoelastic system with a nonlinear source term and nonlocal boundary condition.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Statistics & Probability
Benjamin Lees, Lorenzo Taggi
Summary: The study demonstrates the exponential decay of transverse correlations in the Spin O(N) model for all N > 1, with a novel result when N > 3. It serves as an alternative to the Lee-Yang theorem for N = 2, 3 and extends to a wide class of multi-component spin systems with continuous symmetry.
PROBABILITY THEORY AND RELATED FIELDS
(2021)
Article
Geosciences, Multidisciplinary
L. M. Phillipson, R. Toumi
Summary: Research indicates that the decay rate of landfalling tropical cyclones is gradually slowing, resulting in an increase in wind speed within 24 hours after landfall. The trend may be driven by an initial increase in wind speed or a slowing of the decay rate.
GEOPHYSICAL RESEARCH LETTERS
(2021)
Article
Statistics & Probability
Guus Regts
Summary: In this paper, we demonstrate that the partition function of the hard-core model on bounded degree graphs without complex zeros implies strong spatial mixing of the associated hard-core measure. As a result, we establish that the hard-core measure on bounded degree claw-free graphs exhibits strong spatial mixing regardless of the fugacity parameter. Additionally, we establish the strong spatial mixing of graph homomorphism measures based on the absence of zeros in the graph homomorphism partition function.
PROBABILITY THEORY AND RELATED FIELDS
(2023)
Article
Computer Science, Theory & Methods
Zongchen Chen, Kuikui Liu, Eric Vigoda
Summary: The FPTAS method can be used to estimate the partition function for general antiferromagnetic 2-spin systems on graphs with maximum degree Δ. In the tree nonuniqueness region, it is proven that there is no FPRAS to estimate the partition function unless NP = RP. This work connects three disparate algorithmic approaches and shows that contraction of tree recursions with a suitable potential function establishes rapid mixing of the Glauber dynamics.
SIAM JOURNAL ON COMPUTING
(2023)
Article
Physics, Mathematical
A. J. A. Ramos, D. S. Almeida Junior, M. M. Freitas, A. S. Noe, M. J. Dos Santos
Summary: This article examines the swelling problem in porous elastic soils with fluid saturation, studies the well-posedness of the problem based on semigroup theory, proves the dissipative nature of the energy associated with the system, and establishes the exponential stability of the system. To ensure stability, both viscous damping and a time delay term on the first equation of the system are considered.
JOURNAL OF MATHEMATICAL PHYSICS
(2021)
Article
Astronomy & Astrophysics
Gui-Jun Ding, Jun-Nan Lu, Jose W. F. Valle
Summary: The proposed flavor theory of leptons incorporates an A(4) family symmetry and allows for the derivation of trimaximal neutrino mixing from first principles, leading to straightforward and testable predictions for neutrino mixing and CP violation. This theory posits that dark matter mediates neutrino mass generation, similar to the simplest scotogenic model.
Article
Physics, Mathematical
Ling Zhou, Chun-Lei Tang
Summary: In this paper, we address the global well-posedness of strong solutions to nonhomogeneous Navier-Stokes equations with density-dependent viscosity and vacuum. Using the energy method, we prove the existence and uniqueness of strong solutions globally, provided the initial mass is sufficiently small. Notably, the initial velocity can be arbitrarily large. This work builds upon the previous research by He, Li, and Lu (Arch. Ration. Mech. Anal. 239, 1809-1835, 2021) and extends the results of Liu (Discrete Contin. Dyn. Syst. B 26, 1291-1303, 2021) to allow for large oscillations of the solutions.
JOURNAL OF MATHEMATICAL PHYSICS
(2023)
Article
Mathematics, Applied
Djamel Ouchenane, Abdelbaki Choucha, Mohamed Abdalla, Salah Mahmoud Boulaaras, Bahri Belkacem Cherif
Summary: The paper discusses the stability of a one-dimensional porous-elastic system with thermoelasticity of type III and distributed delay term, analyzing both cases of equal and nonequal speeds of wave propagation. It establishes the well-posedness of the system and uses energy methods combined with Lyapunov functions for the analysis.
JOURNAL OF FUNCTION SPACES
(2021)
Article
Astronomy & Astrophysics
E. Klempt, A. Sarantsev
Summary: The mixing angles between scalar isoscalar resonances and a scalar glueball are determined from their decays into two pseudoscalar mesons. Results show that a small glueball component is admitted by some scalar isoscalar resonances, while significant glueball fractions are required for other resonances. The summation of all observed glueball fractions yields approximately 78%.
Article
Allergy
Sascha Hein, Marie-Luise Herrlein, Ines Mhedhbi, Daniela Bender, Vanessa Haberger, Nuka Benz, Jonathan Eisert, Julia Stingl, Michael Dreher, Doris Oberle, Jessica Schulze, Christin Mache, Matthias Budt, Christoph Hildt, Thorsten Wolff, Eberhard Hildt
Summary: The study revealed differences in titer, neutralizing capacity, and affinity of antibodies between sera elicited by BNT162b2 and CVnCoV vaccines, which could potentially contribute to the observed differences in vaccine efficacy. BNT162b2-elicited sera and convalescent sera showed higher levels of spike-RBD-specific antibodies and neutralizing antibodies compared to CVnCoV-elicited sera, with a reduction in binding and neutralizing antibodies for the B.1.351 variant of concern.
Article
Multidisciplinary Sciences
Abhinav Deshpande, Arthur Mehta, Trevor Vincent, Nicolas Quesada, Marcel Hinsche, Marios Ioannou, Lars Madsen, Jonathan Lavoie, Haoyu Qi, Jens Eisert, Dominik Hangleiter, Bill Fefferman, Ish Dhand
Summary: This research work makes progress in improving both the theoretical evidence and experimental prospects for demonstrating a quantum computational advantage in photonics. They propose a programmable QCA architecture called high-dimensional GBS and show that high-dimensional GBS experiments outperform particular algorithms for simulating GBS.
Article
Physics, Mathematical
J. Haferkamp, F. Montealegre-Mora, M. Heinrich, J. Eisert, D. Gross, I Roth
Summary: Many quantum information protocols require the use of random unitaries, and unitary t-designs are often used as an alternative to Haar-random unitaries. In this work, we explore the non-Clifford resources needed to break the limitation of only being able to implement up to 3-designs with Clifford operations. We find that injecting a certain number of non-Clifford gates into a random Clifford circuit can produce an epsilon-approximate t-design, regardless of the system size. We also derive new bounds on the convergence time of random Clifford circuits to the t-th moment of the uniform distribution on the Clifford group.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2023)
Article
Physics, Multidisciplinary
M. Hinsche, M. Ioannou, A. Nietner, J. Haferkamp, Y. Quek, D. Hangleiter, J. -P. Seifert, J. Eisert, R. Sweke
Summary: The task of learning a probability distribution from samples is common in the natural sciences. This study extensively characterizes the learnability of output distributions from local quantum circuits. The results show that Clifford circuit output distributions are efficiently learnable, but the injection of a single T gate makes density modeling task difficult. Additionally, generative modeling of universal quantum circuits is hard for any learning algorithm, classical or quantum, indicating no quantum advantage for probabilistic modeling tasks.
PHYSICAL REVIEW LETTERS
(2023)
Article
Multidisciplinary Sciences
Mohammadamin Tajik, Marek Gluza, Nicolas Sebe, Philipp Schuettelkopf, Federica Cataldini, Joao Sabino, Frederik Moller, Si-Cong Ji, Sebastian Erne, Giacomo Guarnieri, Spyros Sotiriadis, Jens Eisert, Jorg Schmiedmayer
Summary: We investigate signal propagation in a quantum field simulator of the Klein-Gordon model using two strongly coupled parallel one-dimensional quasi-condensates. We observe the propagation of correlations along sharp light-cone fronts by measuring local phononic fields after a quench. The curved propagation fronts and reflection at sharp edges are observed when the local atomic density is inhomogeneous. By comparing the data with theoretical predictions, we find agreement with curved geodesics of an inhomogeneous metric.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2023)
Article
Quantum Science & Technology
Johannes Jakob Meyer, Marian Mularski, Elies Gil-Fuster, Antonio Anna Mele, Francesco Arzani, Alissa Wilms, Jens Eisert
Summary: Variational quantum machine learning is a widely studied application of near-term quantum computers. This work explores how symmetries of the learning problem can be used to construct quantum learning models with symmetrical outcomes. By utilizing tools from representation theory, a standard gateset can be transformed into an equivariant gateset that respects the symmetries of the problem. The proposed methods are benchmarked on toy problems and show a substantial increase in generalization performance.
Review
Physics, Multidisciplinary
Dominik Hangleiter, Jens Eisert
Summary: Quantum random sampling is the main proposal to demonstrate the computational advantage of quantum computers over classical computers. Recent large-scale implementations of quantum random sampling have possibly surpassed the capabilities of existing classical hardware for simulation. This review comprehensively discusses the theoretical basis and practical implementation of quantum random sampling, as well as its classical simulation, and explores open questions and potential applications in the field.
REVIEWS OF MODERN PHYSICS
(2023)
Article
Multidisciplinary Sciences
J. Helsen, M. Ioannou, J. Kitzinger, E. Onorati, A. H. Werner, J. Eisert, I. Roth
Summary: With quantum computing devices becoming more complex, there is a need for tools that can provide precise diagnostic information about quantum operations. The authors propose a new approach that uses random gate sequences and native measurements followed by classical post-processing to estimate various gate set properties. They also discuss applications for optimizing quantum gates and diagnosing cross-talk. This research is important for the development and improvement of quantum computing devices.
NATURE COMMUNICATIONS
(2023)
Article
Multidisciplinary Sciences
F. H. B. Somhorst, R. van der Meer, M. Correa Anguita, R. Schadow, H. J. Snijders, M. de Goede, B. Kassenberg, P. Venderbosch, C. Taballione, J. P. Epping, H. H. van den Vlekkert, J. Timmerhuis, J. F. F. Bulmer, J. Lugani, I. A. Walmsley, P. W. H. Pinkse, J. Eisert, N. Walk, J. J. Renema
Summary: This study demonstrates that in a unitarily evolving system, single-mode measurements can converge to a thermal state using photons in an integrated optical interferometer. The resolution to the paradox between unitary evolution and the second law of thermodynamics is the recognition that the global unitary evolution of a multi-partite quantum state causes local subsystems to evolve towards maximum-entropy states. The experiment utilizes a programmable integrated quantum photonic processor to manipulate quantum states and shows the potential of photonic devices for simulating non-Gaussian states.
NATURE COMMUNICATIONS
(2023)
Article
Quantum Science & Technology
Ingo Roth, Jadwiga Wilkens, Dominik Hangleiter, Jens Eisert
Summary: Extracting tomographic information about quantum states is crucial in developing high-precision quantum devices. This study shows that by exploiting the low-rank structure of quantum states, a scalable 'blind' tomography scheme can be achieved with a computationally efficient post-processing algorithm. The efficiency of the scheme is further improved by utilizing the sparse structure of the calibrations.
Article
Optics
Niklas Pirnay, Ryan Sweke, Jens Eisert, Jean-Pierre Seifert
Summary: Density modeling is the task of learning an unknown probability density function from samples, and it is a central problem in unsupervised machine learning. This research demonstrates that fault-tolerant quantum computers can offer a superpolynomial advantage over classical learning algorithms in a specific density modeling problem, assuming standard cryptographic assumptions. The results also provide insights for future distribution learning separations between quantum and classical learning algorithms, including the relationship between hardness results in supervised learning and distribution learning.
Article
Materials Science, Multidisciplinary
Philipp Schmoll, Augustine Kshetrimayum, Jan Naumann, Jens Eisert, Yasir Iqbal
Summary: We investigate the ground state of the spin S = 1/2 Heisenberg antiferromagnet on the shuriken lattice, and found that a valence bond crystal with resonances over length six loops emerges as the ground state, yielding the lowest reported estimate of the ground state energy for this model. We also study the model in the presence of an external magnetic field and find the emergence of 0, 1/3, and 2/3 magnetization plateaus, with the 1/3 and 2/3 plateau states respecting translation and point group symmetries and featuring loop-four plaquette resonances.
Article
Quantum Science & Technology
Konstantin Tiurev, Peter-Jan H. S. Derks, Joschka Roffe, Jens Eisert, Jan-Michael Reiner
Summary: This study develops topological surface codes adapted to known noise structures and investigates their performance with specific decoders. Experimental results show that this approach significantly improves error thresholds and reduces failure rates. Furthermore, the study reveals the importance of tailored surface codes in correcting local noise.
Article
Quantum Science & Technology
Jarn de Jong, Frederik Hahn, Jens Eisert, Nathan Walk, Anna Pappa
Summary: Sharing multi-partite quantum entanglement allows for diverse secure communication tasks. In this work, an anonymous CKA protocol for three parties is proposed, implemented in a highly practical network setting using a linear cluster state among quantum nodes. The protocol protects the identities of the participants and contributes to identifying feasible quantum communication tasks for network architectures beyond point-to-point.
Article
Quantum Science & Technology
Jonathan Conrad, Jens Eisert, Francesco Arzani
Summary: The study examines the application of general Gottesman-Kitaev-Preskill (GKP) codes in continuous-variable quantum error correction using lattice theory. It proposes new methods to obtain GKP codes and identifies potential resource savings. The general findings are illustrated through examples from different classes of codes.