Introduces Quantum Data Center for quantum era benefits.
problem No specific problem stated; focuses on future potential.
method Combines QRAM and quantum networks.
result QDC offers efficiency, security, and precision.
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48 results for “Quantum Data Center”
Center identified in stated skein algebra for quantum traces.
problem Understanding the center of the stated skein algebra.
method Analyzing the algebra as a generalization of Kauffman bracket skein algebra, focusing on the case when the quantum parameter is a root of unity.
result Simple description and dimension calculation of the center over the center module.
Study centers of quantum tori and skein algebras for even roots of unity.
problem Understanding the center of quantum tori and skein algebras for even roots of unity.
method Analyzing quantum tori and skein algebras, computing PI-degree, and decomposing matrices.
result PI-degrees of quantum tori and skein algebras are the same.
The paper studies properties of stated SL(n)-skein algebras and their centers.
problem Properties of stated SL(n)-skein algebras and their centers.
method Quantum trace maps and embeddings into quantum tori.
result Finitely generation and PI-degrees of centers of stated SL(n)-skein algebras.
We provide a method to prepare covariance matrices for quantum datasets.
problem No concrete protocol for preparing covariance matrices for quantum datasets.
method Amplitude encoding of data, exploiting global phase symmetry to center the dataset.
result Covariance matrix can be prepared for arbitrary quantum datasets or centered classical datasets.
Equivariant representations for molecular Hamiltonians and N-center atomic-scale propertiesphysics.chem-ph
New features for quantum calculations learn N-center Hamiltonian matrix elements.
problem Quantum calculations need features for N-center Hamiltonians, not just atom-centered ones.
method Developed fully equivariant N-center features for machine learning.
result Learned matrix elements of N-center Hamiltonians efficiently.
We build extensions of the arc rings, relate their centers to the cohomology rings of the Springer varieties, and categorify all level two representations of quantum sl(N).
This paper introduces quantum invariants for 3-alterfolds and proves their consistency with topological moves.
problem Quantum invariants for 3-alterfolds and their consistency with topological moves.
method Introduction of 3-alterfolds with embedded separating surfaces and spherical fusion categories.
result Quantum invariants of 3-alterfolds are consistent with topological moves and generalize invariants of 3-manifolds containing framed links.
Survey of stated skein modules/algebras of 3-manifolds/surfaces.
problem Understanding stated skein modules/algebras of 3-manifolds/surfaces.
method Discussion of splitting homomorphism, general structures, Frobenius homomorphism, center, dimension, representation theory.
result Skein algebra of non-closed marked surface at any root of 1 is a maximal order.
Study centers of generalized skein algebras, showing almost Azumaya properties.
problem Understanding the center of generalized skein algebras.
method Generalized skein algebra generated by loops and arcs, computed center, discussed implications.
result Center of Muller-Roger-Yang skein algebra is almost Azumaya.
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.
We define invariants for a framed link equipped with a SL2 local system in its complement and additional combinatorial data based on the theory of representations of stated skein algebras at roots of unity of punctured bigons and the geometric interpretation of their centers. The gauge invariance of the link invariant …
We define a family of the braid group representations via the action of the -matrix (of the quasitriangular extension) of the restricted quantum on a tensor power of a simple projective module. This family is an extension of the Lawrence representation specialized at roots of unity. Although the c…
Let p an integer. We define a family of idempotents (and nilpotents) in the Temperley - Lieb algebras at 4p-th roots of unity which generalize the usual Jones-Wenzl idempotents. These new idempotents correspond to finite dimentional simple and projective indecomposable representations of the restricted quantum group Uq…
Let G be a discrete group and C be an additive spherical G-fusion category. We prove that the state sum 3-dimensional HQFT derived from C is isomorphic to the surgery 3-dimensional HQFT derived from the G-center of C.
Quantum groups give lower genus bounds for links.
problem Finding lower bounds for Seifert genus of links.
method Using unrolled restricted quantum groups at roots of unity and their invariants.
result ADO link polynomials from quantum groups give genus bounds.
Generalizes positivity conjecture to Roger--Yang skein algebras using polynomials.
problem Positivity conjecture for Roger--Yang skein algebras.
method Used explicit polynomials like Chebyshev polynomials of the first kind to give candidates of positive bases.
result Polynomials form a lower bound in the sense of [Lê18] and [LTY21].
For a group G, the notion of a ribbon G-category was introduced by the second author in a previous work with a view towards constructing 3-dimensional homotopy quantum field theories (HQFT's) with target K(G,1). We discuss here how to derive ribbon G-categories from a simple complex Lie algebra g where G is the center …
Lomonaco and Kauffman introduced knot mosaic system to give a definition of quantum knot system. This definition is intended to represent an actual physical quantum system. A knot -mosaic is an matrix of mosaic tiles which are through depicted as below, representing a knot or a link b…
Let be a finite type surface and a complex root of unity. The Kauffman bracket skein algebra is an important object in both classical and quantum topology as it has relations to the character variety, the Teichmüller space, the Jones polynomial, and the Witten-Reshetikhin-Turaev Topological Quantum Fie…
In Levin-Wen (LW) models, a wide class of exactly solvable discrete models, for two dimensional topological phases, it is relatively easy to describe only single fluxon excitations, but not the charge and dyonic as well as many-fluxon excitations. To incorporate charged and dyonic excitations in (doubled) topological p…
The HKR (Hennings-Kauffman-Radford) framework is used to construct invariants of 4-thickenings of 2-dimensional CW complexes under 2-deformations (1- and 2- handle slides and creations and cancellations of 1-2 handle pairs). The input of the invariant is a finite dimensional unimodular ribbon Hopf algebra A and an elem…
In this work, we give a formula for the logarithmic invariant of knots in terms of certain derivatives of the colored Jones invariant. This invariant is related to the logarithmic conformal field theory, and was defined by using the centers in the radical of the restricted quantum group at root of unity. A relation bet…
Exponential families are a particular class of statistical manifolds which are particularly important in statistical inference, and which appear very frequently in statistics. For example, the set of normal distributions, with mean μ and deviation σ, form a 2-dimensional exponential family. In this paper, we show that …
New basis for quantum gl_N invariants derived from Macdonald polynomials.
problem Constructing new bases for quantum gl_N invariants.
method Using interpolation Macdonald polynomials and Okounkov's results.
result Cyclotomic expansions for gl_N invariants and knot invariants.
We will announce some results on the values of quantum sl_2 invariants of knots and integral homology spheres. Lawrence's universal sl_2 invariant of knots takes values in a fairly small subalgebra of the center of the h-adic version of the quantized enveloping algebra of sl_2. This implies an integrality result on the…
New MBQC algorithm uses randomness for generative modeling.
problem Designing efficient quantum algorithms for generative modeling.
method Proposes a variational MBQC algorithm that treats randomness as a resource.
result Randomness in MBQC can lead to significant gains in generative modeling performance.
Path probability of stochastic motion: A functional approachcond-mat.stat-mech
The path probability of a particle undergoing stochastic motion is studied by the use of functional technique, and the general formula is derived for the path probability distribution functional. The probability of finding paths inside a tube/band, the center of which is stipulated by a given path, is analytically eval…
A given set of data-points in some feature space may be associated with a Schrodinger equation whose potential is determined by the data. This is known to lead to good clustering solutions. Here we extend this approach into a full-fledged dynamical scheme using a time-dependent Schrodinger equation. Moreover, we approx…
Refines geometric center of mass analysis for Einstein field equations.
problem Analyzing the geometric center of mass of Willmore surfaces in initial data for Einstein field equations.
method Refined Lyapunov-Schmidt analysis to study geometric center of mass of area-constrained Willmore surfaces.
result The geometric center of mass agrees with the Hamiltonian center of mass under specific conditions.
FSPA bypasses eigenvalue estimation for quantum PCA, achieving optimal complexity and robustness.
problem Quantum PCA eigenvalue estimation is computationally expensive and prone to errors.
method Filtered Spectral Projection Algorithm (FSPA) that projects onto the dominant spectral subspace directly.
result FSPA achieves optimal complexity and robustness, outperforming classical methods.
For Machine Learning (ML) classification problem, where a vector of --observations (values of attributes) is mapped to a single value (class label), a generalized Radon--Nikodym type of solution is proposed. Quantum--mechanics --like probability states are considered and "Cluster Cente…
The paper generalizes Kuperberg invariants using twisted Drinfeld doubles.
problem Quantum invariants of knots with additional structure.
method Using twisted Drinfeld doubles and Reshetikhin-Turaev invariants.
result Reidemeister torsion of knot complements as a quantum invariant.
On Kauffman bracket skein modules of marked 3-manifolds and the Chebyshev-Frobenius homomorphismmath.GT
In this paper we study the skein algebras of marked surfaces and the skein modules of marked 3-manifolds. Muller showed that skein algebras of totally marked surfaces may be embedded in easy to study algebras known as quantum tori. We first extend Muller's result to permit marked surfaces with unmarked boundary compone…
The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first consider the similarity of elements in the data as the connectivity of nodes in an…
The Jones-Witten theory gives rise to representations of the (extended) mapping class group of any closed surface Y indexed by a semi-simple Lie group G and a level k. In the case G=SU(2) these representations (denoted V_A(Y)) have a particularly simple description in terms of the Kauffman skein modules with parameter …
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.
Many pattern recognition methods rely on statistical information from centered data, with the eigenanalysis of an empirical central moment, such as the covariance matrix in principal component analysis (PCA), as well as partial least squares regression, canonical-correlation analysis and Fisher discriminant analysis. R…
QCML uses quantum geometry to represent data.
problem Data representation and the curse of dimensionality.
method QCML encodes data as Hermitian matrices in Hilbert space.
result Data geometry reveals intrinsic dimension and topological properties.
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.
Quantum Earth Mover's distance improves stability and efficiency in quantum learning.
problem Quantum learning's loss landscapes often lead to poor local minima and gradients.
method Introduced the quantum Earth Mover's (EM) distance and proposed a quantum Wasserstein generative adversarial network (qWGAN).
result The quantum EM distance makes quantum learning more stable and efficient.
This paper examines the impact of centering in PCA and SVD.
problem The influence of centering in PCA and SVD.
method Detailed exploration of centering in PCA and SVD.
result Two PCA embeddings derived from SVD with and without centering can be aligned under certain conditions.
QGAA learns latent quantum states, reducing errors in quantum data generation.
problem Learning latent representations for quantum data generation.
method Quantum Generative Adversarial Autoencoder (QGAA) combining QAE and QGAN.
result Average errors in energies for H2 and LiH are 0.02 Ha and 0.06 Ha respectively, demonstrating QGAA's potential.
New method uses quantum computing to process classical data efficiently.
problem Inefficient quantum machine learning due to data loading and trainability issues.
method Linear Hamiltonian-based machine learning with ground state problems for k-local Hamiltonians.
result Demonstrated the effectiveness and scalability of the method on up to 50 qubits.
This work analyzes centered binary Restricted Boltzmann Machines (RBMs) and binary Deep Boltzmann Machines (DBMs), where centering is done by subtracting offset values from visible and hidden variables. We show analytically that (i) centering results in a different but equivalent parameterization for artificial neural …
Quantum learning complexity reviewed using information theory.
problem Learning properties of quantum systems or processing data via quantum computing.
method Information-theoretic techniques focusing on data, copy, and model complexity.
result Copy complexity due to irreversible quantum measurements limits information extraction.
MPE framework proves universal approximation for quantum data distribution.
problem Challenges in generating quantum data from underlying distributions.
method Many-body Projected Ensemble (MPE) framework for quantum state design.
result MPE can approximate any quantum distribution within 1-Wasserstein distance error.
D-Wave quantum annealing fails to improve sampling quality from RBMs compared to Gibbs sampling.
problem Improving sampling quality from RBMs using D-Wave quantum annealing.
method Comparison of D-Wave quantum annealing and Gibbs sampling for RBM sampling.
result D-Wave sampling does not significantly improve the number of local valleys compared to Gibbs sampling.