Develops a multi-class classifier using quantum detection theory.
problem Improving multi-class classification models in machine learning.
method Inspired by quantum detection theory, develops a multi-class classifier.
result Demonstrates improved effectiveness of multi-class classification models.
In this article we prove that any unitary, axiomatic topological quantum field theory in four-dimensions can not detect changes in the smooth structure of M, a simply connected, closed (compact without boundary), oriented smooth manifold. However, as Donaldson-Witten theory (a topological quantum field theory but not a…
This paper studies rotational virtual knot theory and its relationship with quantum link invariants. Every quantum link invariant for classical knots and links extends to an invariant of rotational virtual knots and links. The paper sets up the background virtual knot theory, defines rotational virtual knot theory, stu…
Simulated Bifurcation outperforms quantum machines in community detection.
problem Community detection in complex networks
method Quantum-inspired Simulated Bifurcation algorithm for QUBO formulation
result Simulated Bifurcation achieves highest modularity in community detection
GQML uses symmetries from representation theory to improve quantum machine learning.
problem Creating quantum models with symmetries to improve performance.
method Introduction to representation theory for quantum learning, focusing on group actions and symmetries.
result Effective implementation of GQML requires knowledge of group representation theory.
Quantum computing techniques improve graph analysis and community detection.
problem Analyzing large graphs efficiently and accurately.
method Used quantum annealing and quantum gate computers for community detection and regularity checking.
result Demonstrated the effectiveness of quantum computing in solving complex graph problems.
Quantum Support Vector Classifier outperforms other QML models in finance fraud detection.
problem Detecting financial fraud using Quantum Machine Learning.
method Comparative study of four QML models: Quantum Support Vector Classifier, Variational Quantum Classifier, Estimator QNN, and Sampler QNN.
result Quantum Support Vector Classifier achieved the highest F1 scores (0.98) for fraud and non-fraud classes.
Floer theory constructs filtrations on quantum cohomology for symplectic manifolds.
problem Quantum cohomology of symplectic manifolds with C∗-actions. method Floer theory applied to C∗-actions on symplectic manifolds. result Constructs a family of filtrations on quantum cohomology for Conical Symplectic Resolutions.
QFNN-FFD uses quantum computing and FL for secure financial fraud detection.
problem Financial fraud detection in the financial sector.
method Quantum Federated Neural Network (QFNN-FFD) combining QML and FL.
result Achieves precision rates above 95% and robustness against noise.
Improved fraud detection in finance with quantum-enhanced federated learning.
problem Challenges in detecting financial fraud with traditional methods.
method Hybrid quantum-enhanced federated learning framework combining quantum LSTM with privacy-preserving techniques.
result Approximately 5% improvement in performance metrics compared to conventional models.
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.
InQMAD detects anomalies in streaming data using quantum measurements and density matrices.
problem Detecting anomalies in streaming data with challenges like conceptual drift and continuous learning.
method Incremental anomaly detection based on random Fourier features and quantum measurements.
result InQMAD outperforms 12 state-of-the-art methods in a systematic evaluation.
The accurate detection of small deviations in given density matrices is important for quantum information processing. Here we propose a new method based on the concept of data mining. We demonstrate that the proposed method can more accurately detect small erroneous deviations in reconstructed density matrices, which c…
Quantum-enhanced barcode decoding and pattern recognition outperforms classical methods.
problem Improving barcode decoding and pattern recognition using quantum entanglement.
method Quantum hypothesis testing applied to barcode decoding and pattern recognition using entangled quantum sources and measurements.
result Quantum-enhanced methods outperform classical coherent-state strategies for barcode data decoding and classification.
Quantum entropy scoring improves robust mean estimation and outlier detection.
problem Robust mean estimation and outlier detection in high-dimensional data.
method QUE-scoring based on quantum entropy regularization.
result First algorithm with optimal error rates and nearly-linear running time for robust mean estimation.
We consider online detection strategies for identifying a change point in a stream of quantum particles allegedly prepared in identical states. We show that the identification of the change point can be done without error via sequential local measurements while attaining the optimal performance bound set by quantum mec…
Functional integrals explain quantum mechanics and field theory.
problem Explaining quantum mechanics and field theory using functional integrals.
method Describes Feynman's path integral approach to quantum mechanics and field theory.
result Equivalence of path integral formalism to classical mechanics and quantum mechanics.
A novel density-based approach QC detects outliers in data with high precision.
problem Detecting outliers in data with high precision and sensitivity.
method Quantum Clustering (QC) approach based on the density of data points.
result QC effectively finds hidden outliers and subtle outliers with parameter adjustment.
Quantum trace map connects Teichmüller theory and quantum groups.
problem Connecting quantum groups to Teichmüller theory for knots.
method Quantum snakes technology to relate Fock-Goncharov monodromy matrices to quantum SL_n.
result Quantized Fock-Goncharov matrices satisfy quantum SL_n relations.
Quantum theory improves counting overlapping clusters.
problem Counting overlapping clusters in machine learning.
method Applied quantum theory using path integral technique.
result Quantum theory provides a robust statistical method for counting clusters.
Knot theory applied to quantum computing models.
problem Using knot theory for quantum computing models.
method Exploring knot theory applications in quantum computing.
result Knot theory introduces topological concepts to quantum computing.
A consistent theory of quantum gravity (QG) at Planck scale almost sure contains manifestations of Lorentz local symmetry violations (LV) which may be detected at observable scales. This can be effectively described and classified by models with nonlinear dispersions and related Finsler metrics and fundamental geometri…
Quantum computing improves fault diagnosis in industrial processes.
problem Fault detection and diagnosis in industrial process systems.
method Integrates quantum computing and deep learning to extract features and diagnose faults.
result Quantum-assisted deep learning achieves high fault detection rates (79.2% and 99.39%).
Cone structures in quantum field theory linked to information geometry.
problem Understanding geometric structures in quantum field theory.
method Analyzing invariant cones under modular automorphism groups and their relation to Wishart laws.
result Explicit connection between CAH cones and Wishart laws.
Quantum field theory uses Lorentzian bordisms to describe time evolution.
problem Describing the time evolution of quantum field theories.
method Defines a functorial field theory on Lorentzian bordism pseudo-category.
result Lorentzian bordisms naturally arise in algebraic quantum field theory.
Examines quantum mechanics equivalence with Newtonian geometry.
problem Equivalence principle in quantum mechanics.
method Newton--Cartan geometry, non--relativistic twistor theory.
result Discusses equivalence in quantum mechanics.
New method interprets quantum many-body snapshots for phase detection.
problem Classifying phases of matter from quantum simulations.
method Confusion learning with correlation convolutional neural networks.
result Network detects changes in thermodynamic properties of quantum systems.
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.
Holonomy invariants from SL2(C) link complements detect link geometry.
problem Detecting geometric information about links using algebraic quantum invariants.
method Enhanced RT construction with SL2(C) holonomy representations. result Holonomy invariants JN compute Reidemeister torsion for N=2. The operator realizing a Dehn twist in quantum Teichmuller theory is diagonalized and continuous spectrum is obtained. This result is in agreement with the expected spectrum of conformal weights in quantum Liouville theory at c>1. The completeness condition of the eigenvectors includes the integration measure which app…
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.
A general theory of quantum spinor structures on quantum spaces is presented, within the conceptual framework of the formalism of quantum principal bundles. Quantum analogs of all basic objects of the classical theory are constructed and analyzed. This includes Laplace and Dirac operators, quantum versions of Clifford …
Abstract: Topological quantum field theory connects graph evaluations to polynomial identities.
problem Graph evaluations in topological quantum field theory.
method Relates SO(3) topological quantum field theory trace evaluations to topological Tutte polynomial evaluations.
result Generalizes the Tutte golden identity for graphs on the torus.
Quantum field theory connects Riemannian geometry to quantum fluctuations.
problem Generating Riemannian structures from quantum fluctuations.
method QFT approach to Riemannian Geometry, focusing on Ricci curvature.
result Ricci curvature is crucial in generating Riemannian structures.
Quantum Kirwan maps between K-theories of G-varieties and GIT quotients.
problem Constructing maps between K-theories of G-varieties and their GIT quotients.
method Formal construction of maps in quantum K-theory, using equivariant and non-equivariant quantum K-theory.
result Presentation of quantum K-theory for smooth proper toric DM stacks.
Artificial neural networks predict quantum entanglement types.
problem Predicting entanglement types of quantum states.
method Supervised learning and deep neural networks on algebraic varieties.
result Trained neural networks can classify entanglement types for up to 5 binary qubits and 3 qutrits.
This paper applies quantum theory to cost accounting, focusing on WIP valuation.
problem Uncertainties in WIP valuation in cost accounting.
method Quantum theory applied to WIP valuation in cost accounting.
result More nuanced understanding of uncertainties in managerial accounting.
Detecting a change point is a crucial task in statistics that has been recently extended to the quantum realm. A source state generator that emits a series of single photons in a default state suffers an alteration at some point and starts to emit photons in a mutated state. The problem consists in identifying the poin…
Quantum cellular automata form a homology theory.
problem Understanding the topological structure of quantum cellular automata.
method Formal properties of coarse homology theories.
result Quantum cellular automata naturally form the degree-zero part of a coarse homology theory.
Quantum surgery formulas link statistics and topology.
problem Formulate constraints for quantum statistics of entangled systems.
method Geometric-topology surgery theory on spacetime manifolds.
result New quantum surgery formulas and constraints derived.
The study examines how quantum resources enhance the complexity of quantum circuits.
problem Quantum resource enhancement on circuit complexity.
method Utilizing quantum resource theories, the study analyzes statistical complexities of quantum circuits with limited quantum resources.
result Bounds for statistical complexities of quantum circuits are derived and applied to specific cases.
Paper compares algebraic quantum field theories and factorization algebras on Lorentzian manifolds.
problem Relationship between algebraic quantum field theories and factorization algebras on Lorentzian manifolds.
method Developed functorial constructions under natural hypotheses, including local constancy and descent axioms.
result Equivalence theorem between algebraic quantum field theories and prefactorization algebras.
We give a construction of the abelian Chern-Simons gauge theory from the point of view of a 2+1 dimensional topological quantum field theory. The definition of the quantum theory relies on geometric quantization ideas which have been previously explored in connection to the nonabelian Chern-Simons theory [JW,ADW]. We f…
BCIQT model improves ML prediction effectiveness using quantum theory.
problem Improving prediction effectiveness in machine learning models.
method Proposes Binary Classifier Inspired by Quantum Theory (BCIQT) model.
result BCIQT model outperforms state-of-the-art models in recall.
Introduces geometric quantization and Witten's quantum invariants.
problem None explicitly stated; focuses on introduction.
method Expository introduction to geometric quantization and Witten's quantum invariants.
result Introduction to geometric quantization and Witten's quantum invariants.
Study Vassiliev invariants for virtual knots, expanding quantum theory.
problem Understanding Vassiliev invariants for virtual knots.
method Define chord diagrams, weight systems, and Lie algebra weight systems for rotational virtual knots.
result Extended quantum invariants capture more information than standard invariants.
String theory connects lattice models, links, and geometric Langlands.
problem Connecting lattice models, links, and geometric Langlands.
method T-duality and worldvolume theories in string theory.
result Unified understanding of various mathematical concepts.
The relationships between game theory and quantum mechanics let us propose certain quantization relationships through which we could describe and understand not only quantum but also classical, evolutionary and the biological systems that were described before through the replicator dynamics. Quantum mechanics could be…