Artificial neural networks map quantum phases of disordered topological superconductors.
problem Classifying quantum phases of disordered topological superconductors.
method Supervised artificial neural network trained on ensemble averages of quasiparticle distributions.
result Artificial neural networks can classify quantum phases with high confidence, identifying unknown phases.
Quantum phase diagrams for Chern topological insulators show jumps at critical loci.
problem Understanding phase transitions in Chern topological insulators.
method Mathematical formulation and explicit families of physical systems.
result Synthetic design of arbitrary Chern jumps in topological phases.
Study uses supervised learning to classify quantum phases with limited measurements.
problem Classifying quantum phases of matter with incomplete phase diagrams.
method Combines classical and quantum techniques, including tensor networks, kernel methods, and quantum algorithms.
result Certification of new ground states can be achieved with polynomial measurements.
Fundamental weight systems identified as quantum states.
problem Identifying which weight systems are quantum states.
method Analyzing the Cayley distance kernel on the symmetric group and its positivity.
result All fundamental gl(n)-weight systems are quantum states.
The paper constructs quantum invariants for knotoid diagrams.
problem Quantum invariants for knotoid diagrams in R 2 \mathbb{R}^2 R 2 . method Decompose Morse knotoid diagrams into basic elementary diagrams, each associated with a matrix solving the quantum Yang-Baxter equation. Define quantum state sum models to recover various polynomials.
result Recover and define new polynomials for Morse knotoids.
Phase diagram illustrates key points in Roegenian economics.
problem Understanding the nature of Roegenian economic systems.
method Recalled similarities between Thermodynamics and Roegenian Economics.
result Identified triple and critical points in Roegenian economic system.
An elementary family of local Hamiltonians H , ¸ ℓ , ℓ = 1 , 2 , 3 , l d o t s H_{\c ,\ell}, \ell = 1,2,3, ldots H , ¸ ℓ , ℓ = 1 , 2 , 3 , l d o t s , is described for a 2 − 2- 2 − dimensional quantum mechanical system of spin = 1 / 2 ={1/2} = 1/2 particles. On the torus, the ground state space G ∘ , ℓ G_{\circ,\ell} G ∘ , ℓ is ( log ) (\log) ( log ) extensively degenerate but should collapse under ł ł ł perturbation" to an anyonic syste…
A simple and elegant arrangement of stock components of a portfolio (market index-DJIA) in a recent paper [1], has led to the construction of crossing of stocks diagram. The crossing stocks method revealed hidden remarkable algebraic and geometrical aspects of stock market. The present paper continues to uncover new ma…
Quantum Gaussian processes enable scalable quantum learning.
problem Lack of simple, interpretable, scalable learning frameworks for quantum data.
method Bayesian framework using Gaussian processes with quantum kernels.
result Provable and scalable quantum Gaussian processes for quantum learning.
Diffusion maps help learn complex quantum phase transitions from data.
problem Learning quantum phase transitions from experimental data is challenging.
method Diffusion maps for nonlinear dimensionality reduction and spectral clustering.
result Diffusion maps can learn complex phase transitions unsupervised.
New approach connects quantum phases to VQA trainability, enabling better scaling.
problem Scalability issues in VQAs, especially barren plateaus.
method Analog VQA ansätze composed of quenches of a disordered Ising chain, tuning disorder strength.
result Thermalized and MBL phases reach maximal expressivity at large M M M , but barren plateaus emerge at smaller M M M in the thermalized phase. It is known that every surface-link can be presented by a marked graph diagram, and such a diagram presentation is unique up to moves called Yoshikawa moves. G. Kuperberg introduced a regular isotopy invariant, called the quantum A_2 invariant, for tangled trivalent graph diagrams. In this paper, a polynomial for a mar…
Study of two-layer ReLU neural network phase diagram at infinite-width limit.
problem Characterize the dynamical regimes of two-layer ReLU neural networks.
method Combining experimental and theoretical approaches, including phase diagram analogy.
result Identification of three regimes: linear, critical, and condensed.
Topological quantum computers use hyperbolic knots for computations.
problem The difficulty of calculating quantum invariants of knots.
method Using hyperbolic knots to compute topological quantum computer invariants.
result The hyperbolic geometry of knots is unlikely to be useful for topological quantum computation.
This paper presents a phase diagram for two-layer neural networks under different initialization scales.
problem Understanding the behavior of neural networks under varying scales of initialization.
method Analysis of a phase diagram for two-layer neural networks.
result Condensation of weight vectors on isolated orientations during training.
Minimal sets of moves for rotational Reidemeister diagrams are identified.
problem Understanding the minimal sets of moves for rotational Reidemeister diagrams.
method Detailed description and proof of minimal generating sets for rotational Reidemeister moves.
result Minimal generating sets for oriented, framed links contain 5 moves.
Unified model for knot polynomials using quantum Heegaard diagrams.
problem Categorify knot polynomials using Floer homology.
method Construct quantum Heegaard diagrams, identify gradings, and define a two-variable graded intersection.
result Unified intersection model recovers Alexander and Jones polynomials.
Machine learning classifies phases of spin models using improved correlation configurations.
problem Classifying phases of spin models using machine learning.
method Improved correlation configuration estimator applied to machine learning.
result Classifies Berezinskii-Kosterlitz-Thouless transition in quantum XY model.
Develops Hermitian TQFTs from quantum groups, defining new topological phases.
problem Defining Hermitian non-semisimple TQFTs.
method Categorical context and representation theory of quantum groups.
result New pseudo-Hermitian topological phases from quantum group representations.
Categorifies quantum invariants using cobordism categories and operads.
problem Categorify quantum invariants using cobordism categories and operads.
method Constructs a cobordism category with a colored operad action, categorifies quantum s l n sl_n s l n invariants. result Consistency of the cobordism category and explicit functor to matrix factorizations conjectured.
Unified geometric approach to quantum indeterminacy.
problem Quantum indeterminacy and uncertainty principles.
method Geometric formulation using convex geometry and symplectic topology.
result Robertson-Schrodinger inequalities emerge as geometric principles.
Unified geometric framework for adiabatic quantum mechanics.
problem Understanding geometric phases and exceptional points in quantum mechanics.
method Formal geometric framework for arbitrary non-degenerate Hamiltonians.
result Generalization of geometric phase to non-Hermitian Hamiltonians.
Algorithm computes quantum invariants efficiently using carving-width.
problem Computing quantum invariants of links efficiently.
method Fixed parameter tractable algorithm using carving-width.
result Efficient algorithm for quantum invariants with polynomial dependence on carving-width.
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.
The Reshetikhin-Turaev invariant, Turaev's TQFT, and many related constructions rely on the encoding of certain tangles (n-string links, or ribbon n-handles) as n-forms on the coend of a ribbon category. We introduce the monoidal category of Hopf diagrams, and describe a universal encoding of ribbon string links as Hop…
Quantum invariants of 3-manifolds linked to splice diagrams.
problem Quantum invariants of 3-manifolds and their dependence on splice diagrams.
method Use of normal surface singularities and splice diagrams to study quantum invariants.
result The sum of all quantum invariants Z ^ σ \widehat{Z}_σ Z σ depends only on the splice diagram. Test the robustness of quantum-enhanced phase estimation under various noise conditions.
problem Evaluate the robustness of quantum-enhanced adaptive phase estimation (QEAPE) in noisy conditions.
method Simulated QEAPE under four phase-noise models and compared resource usage of evolutionary and Bayesian control policies.
result Demonstrated the effectiveness of both evolutionary and Bayesian control policies in noisy conditions.
A quantum model classifies financial sentiment by mapping text chunks to quantum circuits.
problem Classifying financial texts with high accuracy and preserving semantic information.
method Chunked diagrams are mapped to quantum circuits, with a Transformer encoder and type embeddings added for context.
result The hybrid model improves sentiment classification over a simple averaging baseline.
Quantum SVM improves financial data classification.
problem Classifying financial data using quantum machine learning.
method Application of quantum kernels to financial data, specifically DSEx Broad Index.
result Empirical quantum advantage demonstrated for financial data classification.
A new geometric approach to quantum mechanics simplifies time-dependent problems.
problem Quantum mechanics ambiguities in time and observer choices.
method Generally covariant phase-spacetime coordinates and geometric flatness condition.
result Quantum mechanics becomes purely geometric and potentially topological.
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.
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.
Machine learning approximates phase transitions using Fisher information.
problem Understanding phase transitions from data using machine learning.
method Information geometry and Fisher information.
result Machine learning indicators approximate the square root of Fisher information.
Theory explains how deep nets learn features from data.
problem Understanding how deep neural networks learn features from data.
method Developed a noise-nonlinearity phase diagram and a mechanical theory.
result Links feature learning across layers to generalization.
We describe a bottom-up framework, based on the identification of appropriate order parameters and determination of phase diagrams, for understanding progressively refined agent-based models and simulations of financial markets. We illustrate this framework by starting with a deterministic toy model, whereby N N N indepe…
Characterizes kernel interpolation in large dimensions, revealing optimal and sub-optimal regions.
problem Understanding the phase diagram of kernel interpolation in large dimensions.
method Characterization of variance and bias under various source conditions.
result Determined the ( s , γ ) (s,γ) ( s , γ ) -phase diagram of large-dimensional kernel interpolation. We adapt the notion of Jacobi diagrams on surfaces (considered by Andersen-Mattes-Reshetikhin), and construct a LMO-like map that we use to compare some functoriality properties of WRT and LMO invariants.
Machine learning improves probing of quantum systems via synchronization.
problem Characterizing the dissipation features of quantum systems.
method Machine learning applied to a probing scheme with quantum synchronization.
result Machine learning significantly improves the inference of dissipation features from probe observables.
M. Khovanov and L. Rozansky gave a categorification of the HOMFLY-PT polynomial. This study is a generalization of the Khovanov-Rozansky homology. We define a homology associated to the quantum ( s l n , ∧ V n ) (sl_n,\land V_n) ( s l n , ∧ V n ) link invariant, where ∧ V n \land V_n ∧ V n is the set of the fundamental representations of the quantum group of $sl…
Program connects quantum computing and topological field theories.
problem Connecting quantum computing and topological field theories.
method Formalizes the connection using cobordisms and parallel transport.
result Realizes quantum circuits as cobordisms in a double category.
In this paper, we reconstruct Kuperberg's G 2 G_2 G 2 web space. We introduce a new web (a trivalent diagram) and new relations between Kuperberg's web diagrams and the new diagram. Using the G 2 G_2 G 2 webs, we define crossing formulas corresponding to R-matrices associated to some G 2 G_2 G 2 irreducible representations and calculate…
We investigate link homology theories for stable equivalence classes of link diagrams on orientable surfaces. We apply (1+1)-dimensional unoriented topological quantum field theories to Bar-Natan's geometric formalism to define new theories for stable equivalence classes.
Quantum groups created from disk configuration space homologies.
problem Creating quantum groups from algebraic structures.
method Reconstructing quantum groups from homologies of configuration spaces of disks.
result New combinatorics and actual submanifolds of configuration spaces.
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.
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.
Quantum algorithm estimates multivariate mean with near-optimal efficiency.
problem Estimating the mean of multivariate random variables efficiently in quantum computing.
method Combines amplitude amplification, quantum singular value transformation, and Bernstein-Vazirani algorithm.
result Quantum estimator outperforms classical estimators outside low-precision regime.
Quantum-assisted Gaussian process speeds up data regression.
problem High computational complexity of Gaussian process regression for large datasets.
method Quantum-assisted sparse Gaussian process regression using random Fourier features.
result Achieves polynomial-order computational speedup compared to classical methods.
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.