Quantum physics model uses knot theory for fragile topology.
problem Modeling quantum physics' fragile topology.
method Knot theoretic algorithm.
result Quantum physics' fragile topology modeled.
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48 results for “Quantum physics”
Quantum cohomology connects quantum physics with classical math.
problem Quantum cohomology's relevance in modern mathematics.
method Informal review and discussion of connections.
result Quantum cohomology still has significant relevance in mathematics.
We analyze the relationships between game theory and quantum mechanics and the extensions to statistical physics and information theory. We use certain quantization relationships to assign quantum states to the strategies of a player. These quantum states are contained in a density operator which describes the new quan…
A quantum state generation method that respects physical constraints.
problem Generating quantum states with complex-valued Hermitian, positive semi-definite, and trace one properties.
method Mirror diffusion model with von Neumann entropy to enforce structural constraints.
result Demonstrated effective generation of quantum states with conditional guidance.
Study symmetry breaking in quantum mechanics to understand many-body physics.
problem Understanding many-body physics from quantum mechanics.
method Analyzing potentials with unstable critical points and local minima.
result Emergence of many-body physics from spontaneous symmetry breaking.
Observing how deep neural networks understand physics through the energy spectrum of one-dimensional quantum mechanicsphysics.comp-ph
NNs accurately predict energy eigenvalues and other physical phenomena in 1D quantum mechanics.
problem Understanding how neural networks interpret physics.
method Training NNs to predict energy eigenvalues from potentials and testing their ability to generalize.
result NNs can predict physical phenomena not learned during training, indicating a new way of understanding physics.
New trends explore quantum machine learning to speed up computations and analyze data.
problem Speeding up machine learning computations and analyzing large quantum data.
method Interplay between quantum physics and machine learning, including new algorithms and hardware.
result Breakthroughs in quantum machine learning can provide advantages over classical methods.
De la structure des espaces fibrés aux équations fondamentales de la physique. Une introductionphysics.class-ph
This text explains how fiber bundle structure is fundamental for classical physics.
problem None explicitly stated, but implied as understanding fiber bundles is crucial for physics.
method Explains the fiber bundle structure and its universality for physics laws.
result Fiber bundle structure is fundamental for classical physics laws.
Quantum hybrid vision transformers improve event classification in high energy physics.
problem Excessive computational resources for training and deploying vision transformer models.
method Constructed quantum hybrid vision transformers for high energy physics event classification.
result Quantum hybrid models achieve comparable performance to classical models with fewer parameters.
Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistryquant-ph
Derives symmetric and antisymmetric kernels for quantum physics and chemistry applications.
problem Efficiently handling symmetries and antisymmetries in machine learning for quantum physics and chemistry.
method Symmetrizing and antisymmetrizing conventional kernels, analyzing feature space dimensions, proving kernel properties, proposing Slater determinant representation.
result Efficient evaluation of antisymmetric Gaussian kernels even in high-dimensional state spaces, significant reduction in training data size.
This document contains a description of physics entirely based on a geometric presentation: all of the theory is described giving only a pseudo-riemannian manifold (M, g) of dimension n > 5 for which the g tensor is, in studied domains, almost everywhere of signature (-, -, +, ..., +). No object is added to this space-…
Counting the number of clusters, when these clusters overlap significantly is a challenging problem in machine learning. We argue that a purely mathematical quantum theory, formulated using the path integral technique, when applied to non-physics modeling leads to non-physics quantum theories that are statistical in na…
Quantum character varietiesmath.QA
Quantum character varieties unify four construction methods.
problem No specific problem stated; unification of approaches.
method Four different approaches to construction.
result Unified understanding of quantum character varieties.
Physicists use quantum models to describe the behavior of physical systems. Quantum models owe their success to their interpretability, to their relation to probabilistic models (quantization of classical models) and to their high predictive power. Beyond physics, these properties are valuable in general data science. …
Quantum Curriculum Learningquant-ph
Q-CurL optimizes quantum learning with a curriculum design.
problem Efficiently training quantum models with limited resources.
method Quantum curriculum learning framework.
result Q-CurL enhances training convergence and generalization.
We analyze complexity of financial (and general economic) processes by comparing classical and quantum-like models for randomness. Our analysis implies that it might be that a quantum-like probabilistic description is more natural for financial market than the classical one. A part of our analysis is devoted to study t…
Defines a map connecting 3d-index and skein module.
problem Connecting mathematical physics predictions with topological quantum field theory.
method Defines a map from skein module to Laurent series ring.
result The map fulfills a supersymmetry prediction and is part of a conjectural topological quantum field theory.
Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering, the most abstract reaches of theoretical physics has spawned topological models ha…
Analyzes the concept of fields in classical and quantum physics.
problem Challenges in defining fields in classical and quantum physics.
method Uses groupoid description of quantum mechanics and categorical language.
result Fields as functors among groupoids of test particles and intrinsic system nature.
We show how to train a quantum network of pairwise interacting qubits such that its evolution implements a target quantum algorithm into a given network subset. Our strategy is inspired by supervised learning and is designed to help the physical construction of a quantum computer which operates with minimal external cl…
A graphical calculus for microformal morphisms simplifies complex operations in classical and quantum physics.
problem Simplifying operations in classical and quantum microformal morphisms.
method Developed a graphical calculus inspired by Cattaneo-Dherin-Felder's work on formal symplectic groupoids, extended to quantum thick morphisms.
result Infinite series can be written as sums over bipartite trees for both classical and quantum thick morphisms.
Over the past three decades, black holes have played an important role in quantum gravity, mathematical physics, numerical relativity and gravitational wave phenomenology. However, conceptual settings and mathematical models used to discuss them have varied considerably from one area to another. Over the last five year…
Quantum ML promises faster data analysis but faces trainability challenges.
problem Challenges in training quantum machine learning models.
method Review of current methods and applications of quantum neural networks and quantum deep learning.
result Opportunities for quantum advantage in quantum machine learning.
By analyzing the relationships between a socioeconomical system modeled through evolutionary game theory and a physical system modeled through quantum mechanics we show how although both systems are described through two theories apparently different both are analogous and thus exactly equivalents. The extensions of qu…
Quantum theory of curved tetrahedrons yields quantum group intertwiners.
problem Quantum geometry of curved tetrahedrons and their intertwiners.
method Combinatorial quantization of tetrahedron phase space, relating to SU(2) flat connections.
result Physical Hilbert space coincides with Uq(su(2)) intertwiners, consistent with LQG area spectrum.
Learning phases with Quantum Monte Carlo simulation cellcond-mat.str-el
Spin-opstrings from QMC simulations enable ML of quantum phases.
problem Capturing and predicting quantum phase transitions using ML.
method Spin-opstrings derived from QMC simulations used as ML input.
result Spin-opstrings accurately predict quantum phase transitions.
Quantum Inception Scorequant-ph
Proposes qIS for quantum generative models, extending classical inception score.
problem Develop a metric to evaluate quantum generative models.
method Introduces qIS, relating quality to Holevo information of quantum channel.
result qIS enhances the quality of quantum generative models, showing physical limitations.
Quantum memory limits set by relativity theory.
problem Quantum memory efficiency and relativity constraints.
method Relativistic quantum field theory and Lieb-Robinson bounds.
result Quantum memory capacity is limited by fundamental physics.
Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machinesphysics.data-an
We compare and contrast the statistical physics and quantum physics inspired approaches for unsupervised generative modeling of classical data. The two approaches represent probabilities of observed data using energy-based models and quantum states respectively.Classical and quantum information patterns of the target d…
Some simple examples from quantum physics and control theory are used to illustrate the application of the theory of Lie systems. We will show, in particular, that for certain physical models both of the corresponding classical and quantum problems can be treated in a similar way, may be up to the replacement of the in…
Quantum Field Theory and Differential Geometryphysics.pop-ph
We introduce the historical development and physical idea behind topological Yang-Mills theory and explain how a physical framework describing subatomic physics can be used as a tool to study differential geometry. Further, we emphasize that this phenomenon demonstrates that the interrelation between physics and mathem…
Quantum models face barren plateaus, but specific losses can be trainable.
problem Barren plateaus and loss concentration in quantum generative models.
method Investigated explicit and implicit losses, and their interplay.
result Explicit losses lead to new barren plateaus, while implicit losses can be trainable.
The resemblance between the methods used in quantum-many body physics and in machine learning has drawn considerable attention. In particular, tensor networks (TNs) and deep learning architectures bear striking similarities to the extent that TNs can be used for machine learning. Previous results used one-dimensional T…
Bank deposits are analyzed as having dual characteristics, akin to quantum physics.
problem Understanding the dual nature of bank deposits.
method Application of quantum physics concepts to bank deposits.
result Bank deposits have a hybrid nature, combining debt and equity features.
Perelman's Ricci flow emerges in quantum gravity, linking math and physics.
problem Understanding Perelman's Ricci flow equations in quantum gravity.
method Mapping Perelman's Ricci flow equations to localization equations in topological quantum gravity.
result Perelman's dilaton and fixed volume condition emerge dynamically.
Global EQG sums boundary states over manifold diffeomorphism classes.
problem Summing boundary states over manifold diffeomorphism classes.
method Formulated as classical statistical physics, weights determined by general principles.
result Hartle-Hawking state as a probability measure.
Physics: Similar long-distance properties can mask vastly different short-distance metrics.
problem Classifying homogeneous metrics on group manifolds by long-distance properties.
method Apply universality concept to geometry, focusing on metrics on Lie groups.
result Many metrics on low-dimensional Lie groups have similar long-distance properties despite differing short-distance properties.
FFT-Accelerated Auxiliary Variable MCMC for Fermionic Lattice Models: A Determinant-Free Approach with Complexitycond-mat.str-el
New MCMC method speeds up quantum physics simulations by a factor of 100.
problem Simulating quantum many-body systems with high computational complexity.
method FFT-accelerated MCMC with coupled particle and auxiliary variables.
result Achieves scaling, significantly faster than traditional methods.
Quantum Knots and Mosaicsquant-ph
In this paper, we give a precise and workable definition of a quantum knot system, the states of which are called quantum knots. This definition can be viewed as a blueprint for the construction of an actual physical quantum system. Moreover, this definition of a quantum knot system is intended to represent the "quantu…
Geometry and the Quantumhep-th
We give a survey of our joint ongoing work with Ali Chamseddine, Slava Mukhanov and Walter van Suijlekom. We show how a problem purely motivated by "how geometry emerges from the quantum formalism" gives rise to a slightly noncommutative structure and a spectral model of gravity coupled with matter which fits with expe…
We propose a quantum machine learning algorithm for efficiently solving a class of problems encoded in quantum controlled unitary operations. The central physical mechanism of the protocol is the iteration of a quantum time-delayed equation that introduces feedback in the dynamics and eliminates the necessity of interm…
Integral Transforms in a Physics-Informed (Quantum) Neural Network setting: Applications & Use-Casesquant-ph
This work integrates differentiation and integration in Physics-Informed Neural Networks.
problem Solving integro-differential equations and computing integral transforms.
method Augmenting Physics-Informed Neural Networks with automatic integration.
result Solving complex integral transforms and integro-differential equations.
Introduces noncommutative geometry for modeling quantum spacetime.
problem Modeling quantum spacetime.
method Operator algebras, K-theory, spectral geometry, quantum groups, and deformation quantization.
result Framework for quantum spacetime.
RILA learns HQMMs robustly against adversarial corruption.
problem Robustness of HQMM learning algorithms under adversarial perturbations.
method Adversarially Corrupted HQMM (AC-HQMM) and Robust Iterative Learning Algorithm (RILA).
result RILA outperforms existing algorithms in convergence stability, corruption resilience, and physical validity.
This work explores using deep NNs to learn quantum systems from probability distributions.
problem Learning quantum systems from limited probability distribution data.
method Using deep neural networks to reconstruct quantum Hamiltonian from probability distributions.
result Deep neural networks can learn quantum Hamiltonians from probability distributions.
Commuting Line Defects At hep-th
Explains a property of algebras related to quantum field theories.
problem Explains a property of algebras encoding line defects in quantum field theories.
method Physical explanation of a property of quantized algebras using dualities and field theories.
result Physical explanation of a large center in quantized algebras when the deformation parameter is a root of unity.
Abstract reviews symmetry and reduction in dynamical systems.
problem Understanding symmetries and reductions in dynamical systems.
method Algebraic formulation for dynamics of physical systems.
result Describes a reduction procedure for classical and quantum evolutions.
We elaborate a detailed study of certain aspects of (a version of) the AdS/CFT correspondence, conjectured by Maldacena and Witten, between quantum field theories in a gravitational background given by an asymptotically anti-de Sitter (AAdS) spacetime, and conformally covariant quantum field theories in the latter's co…