Kauffman and Lomonaco explored the idea of understanding quantum entanglement (the non-local correlation of certain properties of particles) topologically by viewing unitary entangling operators as braiding operators. In the work of G. Alagic, M. Jarret, and S. Jordan it is shown that entanglement is a necessary condit…
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48 results for “topological entanglement”
Locates entanglement in curves using knot intensity distribution.
problem Finding robust methods for locating entanglement in embedded curves.
method Introducing knot intensity distribution as a local quantifier for entanglement contribution.
result Intensity distributions identify regions in knots accommodating topological changes.
Aggregation and structural phase transitions of semiflexible polymer bundles: a braided circuit topology approachcond-mat.soft
A new approach uses circuit topology to study complex polymer interactions.
problem Understanding structural phase transitions in entangled polymer systems.
method Braided circuit topology framework for multiple-chain systems.
result Circuit topological motif fractions are effective order parameters for structural transitions.
New methods assess topological entanglement in periodic systems.
problem Assessing topological entanglement in systems with periodic boundary conditions.
method Introducing Periodic Jones polynomial and Cell Jones polynomial.
result Periodic Jones polynomial is a recurring factor of Jones polynomial of finite cutoffs.
Any solution to the Yang-Baxter equation yields a family of representations of braid groups. Under certain conditions, identified by Turaev, the appropriately normalized trace of these representations yields a link invariant. Any Yang-Baxter solution can be interpreted as a two-qudit quantum gate. Here we show that if …
Knoto-ID: a tool to study the entanglement of open protein chains using the concept of knotoidsq-bio.BM
The backbone of most proteins forms an open curve. To study their entanglement, a common strategy consists in searching for the presence of knots in their backbones using topological invariants. However, this approach requires to close the curve into a loop, which alters the geometry of curve. Knoto-ID allows evaluatin…
We present atomistic molecular dynamics simulations of two Polyethylene systems where all entanglements are trapped: a perfect network, and a melt with grafted chain ends. We examine microscopically at what level topological constraints can be considered as a collective entanglement effect, as in tube model theories, o…
Develops a braid-theoretic framework to analyze chirality in molecular knots.
problem Analyzing chirality in molecular knots constructed using circuit topology.
method Translated circuit topology approach to knot engineering into braid-theoretic framework, calculating Jones polynomial for binary combinations.
result Jones polynomial provides a powerful tool for analyzing chirality of molecular knots.
We use the conformal invariance and the holographic correspondence to fully specify the dependence of entanglement entropy on the extrinsic geometry of the 2d surface that separates two subsystems of quantum strongly coupled SU(N) superconformal gauge theory. We extend this result and calculate en…
Fibonacci anyons are attractive for use in topological quantum computation because any unitary transformation of their state space can be approximated arbitrarily accurately by braiding. However there is no known braid that entangles two qubits without leaving the space spanned by the two qubits. In other words, there …
New method describes entanglement of straight lines in 3D space.
problem Tackles the geometry and topology of configurations of straight lines.
method Introduces direction matrices and a discrete motion principle.
result Shows n-crosses as links of pairwise connected unknots.
For a given quantum field theory, provided the area of the entangling surface is fixed, what surface maximizes entanglement entropy? We analyze the answer to this question in four and higher dimensions. Surprisingly, in four dimensions the answer is related to a mathematical problem of finding surfaces which minimize t…
Studies of global and local entanglements of individual protein chains using the concept of knotoidsq-bio.BM
We study here global and local entanglements of open protein chains by implementing the concept of knotoids. Knotoids have been introduced in 2012 by Vladimir Turaev as a generalization of knots in 3-dimensional space. More precisely, knotoids are diagrams representing projections of open curves in 3D space, in contras…
New knot models analyze local entanglement for robust curve analysis.
problem Lack of local structural information in classical knot theory.
method Proposed multiscale and persistent Jones polynomials.
result Models are stable to small perturbations, robust for real-world applications.
Parallel algorithm speeds up Jones polynomial computation.
problem Efficient computation of knot complexity measures.
method First parallel algorithm for exact Jones polynomial computation.
result Reduces computational time by an exponential factor.
Polynomial invariants classify molecular chains based on their contact arrangements.
problem No established invariants for molecular chains with both hard and soft contacts.
method Developed polynomial invariants for circuit topology of molecular chains.
result Polynomial invariants efficiently classify chains with various contact types.
Braided vector fields on spatial subdomains homeomorphic to the cylinder play a crucial role in applications such as solar and plasma physics, relativistic astrophysics, fluid and vortex dynamics, elasticity, and bio-elasticity. Often the vector field's topology -- the entanglement of its field lines -- is non-trivial,…
Unified geometric flows improve deep learning efficiency and simplify neural network topologies.
problem Improving deep learning performance and simplifying neural network structures.
method Proposes a thermodynamically coupled Ricci flow that dynamically adapts parameter space geometry to loss landscape topology, enabling automated singularity resolution and providing entanglement entropy bounds.
result Demonstrates 2.1× convergence acceleration and 63% topological simplification while maintaining complexity, outperforming Riemannian baselines by 15.2% in few-shot accuracy.
RNA foldings and Stuck Knotsmath.GT
Study uses knot theory to model RNA foldings, emphasizing both entanglement and intrachain interactions.
problem Modeling RNA foldings considering both entanglement and intrachain interactions.
method Combines knot theory with embedded rigid vertex graphs to emphasize both entanglement and intrachain interactions of RNA foldings.
result Defines and computes a coloring counting invariant for stuck links, providing explicit computations for arc diagrams of RNA foldings.
New method measures entanglement of open and closed curves.
problem Measuring entanglement of curves in 3-space.
method Defining bracket polynomial and Jones polynomial for open and closed curves.
result Jones polynomial applies to both open and closed curves, with continuity properties.
Entanglement and productsmath.DG
Quantum states are not entangled if submanifold is a product.
problem Understanding entanglement in quantum states associated with product submanifolds.
method Analyzing quantum states on submanifolds of product Kähler manifolds in the semiclassical limit.
result States are not entangled when submanifold is a product.
Study on quantum state entanglement using Kaehler manifolds.
problem Quantum state entanglement on Kaehler manifolds.
method Semiclassical asymptotics and pure states on spheres.
result Entropy analysis of quantum states on spheres.
q-CNN learns data features through entangled states.
problem Classifying MNIST and Fashion MNIST datasets.
method Introduces q-CNN model, a tensor network description, and studies entanglement structure.
result q-CNN learns entanglement structure to perform classification tasks accurately.
The paper uncovers the mathematical structure enabling value decomposition in multi-agent systems.
problem Theoretical justification for why value decomposition works effectively in multi-agent systems remains underexplored.
method The paper introduces the concept of Markov entanglement to measure the underlying structure and demonstrates how it can be used to bound the decomposition error.
result The widely-used class of index policies is weakly entangled and enjoys a sublinear scale of decomposition error for -agent systems.
Study uses holography to analyze entanglement entropy in deformed CFTs.
problem Analyzing entanglement entropy in $Tar{T}$-deformed CFTs.
method Holographic methods and direct bulk gravitational action evaluation.
result Agreement with known results for entanglement entropy.
Paper defines untangling number to measure entanglement complexity in 3-periodic networks.
problem Measuring the complexity of entanglement in 3-periodic networks.
method Defining ground states through knot-theoretic crossing diagrams and measuring untangling number.
result Introduced untangling number as a measure of entanglement complexity.
This work introduces 'Artificial Entanglement' to understand LLMs' fine-tuning effectiveness.
problem Understanding the effectiveness of parameter-efficient fine-tuning methods for large language models.
method Adopting a quantum-information-inspired perspective, the study measures 'Artificial Entanglement' in neural networks.
result LoRA and FFT induce distinct internal entanglement signatures but not external ones, suggesting a 'no-hair' property.
When a spacetime has boundaries, the entangling surface does not have to be necessarily compact and it may have boundaries as well. Then there appear a new, boundary, contribution to the entanglement entropy due to the intersection of the entangling surface with the boundary of the spacetime. We study the boundary cont…
Neural-Network Quantum States have been recently introduced as an Ansatz for describing the wave function of quantum many-body systems. We show that there are strong connections between Neural-Network Quantum States in the form of Restricted Boltzmann Machines and some classes of Tensor-Network states in arbitrary dime…
A relation between the conformal anomaly and the logarithmic term in the entanglement entropy is known to exist for CFT's in even dimensions. In odd dimensions the local anomaly and the logarithmic term in the entropy are absent. As was observed recently, there exists a non-trivial integrated anomaly if an odd-dimensio…
We analyze the Ricci flow of a noncompact metric that describes a two-dimensional black hole. We consider entanglement entropy of a 2d black hole which is due to the quantum correlations between two subsystems: one is inside and the other is outside the black hole horizon. It is demonstrated that the entanglement entro…
Paper introduces untangling number to quantify 3-periodic tangle complexity.
problem Quantifying the complexity of 3-periodic tangles in biological, chemical, and physical systems.
method Introduces untangling number, a measure of minimum distance to ground state through diagrammatic operations.
result For infinite open curves, generic ground states are crystallographic rod packings.
We define the local periodic linking number, LK, between two oriented closed or open chains in a system with three-dimensional periodic boundary conditions. The properties of LK indicate that it is an appropriate measure of entanglement between a collection of chains in a periodic system. Using this measure of linking …
New kernels allow learning from non-separable data.
problem Learning from non-separable data.
method Introducing entangled kernels and a two-step algorithm.
result Efficient algorithm for learning entangled kernels.
We connect topological changes that can occur in -space via surgery, with black hole formation, the formation of wormholes and new generalizations of these phenomena, including relationships between quantum entanglement and wormhole formation. By considering the initial manifold as the -dimensional spatial sectio…
Quantum datasets improve QML performance.
problem Benchmarking QML on classical datasets is uncertain.
method Introduced NTangled dataset of quantum states with varying entanglement.
result QML models trained on NTangled dataset outperform classical models.
New method detects and compares folding pathways of knotted proteins.
problem Understanding the function of knots in protein folding.
method Topological analysis of protein knotoid distributions and entanglement.
result Reveals unique folding pathway for shallow knotted Carbonic Anhydrases.
We propose a conceptual design for a quantum blockchain. Our method involves encoding the blockchain into a temporal GHZ (Greenberger-Horne-Zeilinger) state of photons that do not simultaneously coexist. It is shown that the entanglement in time, as opposed to an entanglement in space, provides the crucial quantum adva…
New machine learning method detects quantum separability in large-scale systems.
problem Deciding quantum separability of large-scale bipartite density matrices.
method Frank-Wolfe-based algorithm for finding nearest separable density matrices and classification of density matrices as separable or entangled.
result The method scales up to thousands of density matrices and achieves high quantum entanglement detection accuracy.
A recent proposal by Ryu and Takayanagi for a holographic interpretation of entanglement entropy in conformal field theories dual to supergravity on anti-de Sitter (adS) is generalized to include entanglement entropy of black holes living on the boundary of adS. The generalized proposal is verified in boundary dimensio…
Study tackles causal effects of close contact on MRSA infections from entangled treatment data.
problem Estimating causal effects of close contact on MRSA infections from observational data with entangled treatments.
method NEAT method that models treatment assignment mechanism and mitigates confounding biases.
result NEAT method effectively estimates causal effects from entangled treatment data.
We present the quantum model of Bertrand duopoly and study the entanglement behavior on the profit functions of the firms. Using the concept of optimal response of each firm to the price of the opponent, we found only one Nash equilibirum point for maximally entangled initial state. The very presence of quantum entangl…
New metric for disentangling multivariate representations, accounting for more complex entanglements.
problem Current disentanglement metrics fail to detect entanglements involving more than two variables.
method Partial Information Decomposition framework to analyze information sharing and propose a new disentanglement metric.
result The proposed metric correctly identifies entanglements in high-dimensional spaces.
For a very ample line bundle L on a compact connected complex manifold X, with a real structure, we discuss entanglement properties of certain sequences of vectors in tensor products of spaces of holomorphic sections of powers of L.
Coherent states and entropymath.DG
The study bounds entanglement entropy for coherent states on Kähler manifolds.
problem Bounding entanglement entropy for coherent states on Kähler manifolds.
method Geometric quantization and Hilbert spaces of Kähler manifolds.
result Positive lower bounds for entanglement entropy are provided asymptotically.
Mathematical pipeline identifies structural homology of knotted proteins.
problem Quantification and classification of protein structures, especially knotted proteins, require noise-free and complete data.
method Developed a geometric framework using persistent homology to analyze protein structures.
result Persistent homology accurately represents structural homology of knotted proteins and identifies geometric features of protein entanglement.
A Theory of Complex Adaptive Learning and a Non-Localized Wave Equation in Quantum Mechanicsq-fin.GN
The abstract explores a new wave equation linking quantum mechanics and complex adaptive systems.
problem Understanding the underlying mechanism of distribution formation in complex quantum entanglement.
method Exploring the logical relationship between Schrödinger's wave equation and Shi's trading volume-price wave equation in finance.
result A non-localized wave equation in quantum mechanics reveals the invariance of interaction as a universal law.
Tensor networks improve image classification but require more expressive states.
problem Understanding why tensor networks work in image classification.
method Investigated entanglement properties of tensor network models for supervised image classification.
result Tensor networks can learn states that are robustly entangled, suggesting long-range entanglement is not essential.