Study shows classical and quantum resonances match for hyperbolic surfaces.
problem Matching classical and quantum resonances for hyperbolic surfaces.
method Explicit correspondence proven between classical and quantum resonant states.
result Holomorphic sections of line bundles involved at negative integers.
Study of spectral properties of Lorentzian quasi-Fuchsian manifolds.
problem Understanding the spectral properties of Lorentzian quasi-Fuchsian manifolds.
method Analyzing the geodesic flow, Ruelle resonances, and pseudo-Riemannian Laplacian.
result Meromorphic extension of the resolvent of the pseudo-Riemannian Laplacian with poles of finite rank.
We prove an abstract criterion stating resolvent convergence in the case of operators acting in different Hilbert spaces. This result is then applied to the case of Laplacians on a family $X_\eps$ of branched quantum waveguides. Combining it with an exterior complex scaling we show, in particular, that the resonances o…
Quantum resonances for tensors on hyperbolic spaces are studied.
problem Quantum resonances of symmetric tensors on asymptotically hyperbolic spaces.
method Analyzes the Lichnerowicz Laplacian on manifolds with even Riemannian conformally compact Einstein metrics and quotients of hyperbolic space.
result Resolvent of the Lichnerowicz Laplacian has meromorphic continuation to the complex plane, defining quantum resonances.
Procedure maps quantum systems to curved spacetimes with resonant frequencies.
problem Mapping quantum mechanics to curved spacetimes with resonant frequencies.
method Klein-Gordonization procedure, reducing to nonlinear elliptic equation.
result Large family of spacetimes with resonant spectra for massless wave equations.
Classical-quantum correspondence on hyperbolic manifolds established.
problem Classical-quantum spectrum correspondence on hyperbolic manifolds.
method Direct correspondence between geodesic flow and Laplacian spectra.
result Established correspondence for convex cocompact hyperbolic manifolds.
New resonance theory for Anosov flows connects spectral properties to mixing measures.
problem Defining and analyzing Ruelle-Taylor resonances for Anosov actions.
method Combining microlocal methods and J. Taylor's cohomological theory, defining Ruelle-Taylor resonances and proving Fredholm theory.
result Ruelle-Taylor resonances form a discrete subset of Cκ with λ=0 being a leading resonance. We provide two examples of spectral analysis techniques of Schroedinger operators applied to geometric Laplacians. In particular we show how to adapt the method of analytic dilation to Laplacians on complete manifolds with corners of codimension 2 finding the absence of singular continuous spectrum for these operators,…
Resonant machine learning uses electrical network dynamics to optimize learning efficiently.
problem Traditional energy-based learning models are dissipative and inefficient.
method Proposes a new learning framework with two energy components (active and reactive) to ensure active-power dissipation during learning.
result Support vectors in resonant SVMs correspond to self-sustained oscillations in an LC network.
Analyzes how transient conditions affect first-passage times in random walks.
problem Understanding first-passage times in random walks under transient conditions.
method Solves the generalized master equation analytically for a linear chain of states.
result The average first-passage time decreases with a power law dependence on the relaxation rate.
Quantum states can be learned efficiently using gentle measurements.
problem Efficiently learning quantum states with minimal measurements.
method Introducing α-LGM measurements and proving strong quantum DPI.
result The number of states needed for accurate learning is of order 1/(ε^2 α^2).
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.
Neural-Network Quantum States connect to Tensor-Network states, enhancing quantum state representation.
problem Describing complex quantum wave functions efficiently.
method Introducing Neural-Network Quantum States and showing their connections to Tensor-Network states.
result Neural-Network Quantum States and String-Bond States can approximate chiral topological states with better accuracy.
Adversarial learning approximates unknown quantum states on near-term quantum computers.
problem Approximating unknown quantum pure states on near-term quantum computers.
method Two parametrized circuits optimized adversarially, with resilient backpropagation and bipartite entanglement entropy.
result Resilient backpropagation algorithms perform well in optimizing the two circuits.
The paper proves regularity of states on manifolds with unstable dynamics.
problem Propagation of regularity in dynamical systems with unstable manifolds.
method Leafwise semiclassical pseudodifferential calculus adapted to foliated spaces.
result Pollicott-Ruelle resonant states are smooth over entire manifolds if smooth on unstable leaves.
Meta-learning algorithms prepare quantum Gibbs states efficiently for NISQ devices.
problem Efficiently preparing quantum Gibbs states for NISQ devices.
method Meta-Variational Quantum Thermalizer (Meta-VQT) and Neural Network Meta-VQT (NN-Meta VQT) algorithms.
result Meta-learned parameters significantly outperform random initializations in optimization tasks.
Machine learning, specifically LSTM, models quantum experiments efficiently.
problem Modeling complex quantum states with high-dimensional entanglement.
method Used a long short-term memory (LSTM) neural network to predict quantum experiment outcomes.
result LSTM neural networks can accurately predict quantum experiment outcomes without computing the states themselves.
A machine learning framework predicts self-induced stochastic resonance in neurons.
problem Predicting coherent oscillations in slow-fast excitable systems driven by noise.
method Physics-informed machine learning with a Noise-Augmented State Predictor architecture and Kramers' escape theory constraints.
result Trained PINN accurately predicts spike-train coherence on noise intensity, excitability, and timescale separation.
Holomorphic vector bundles on Hopf manifolds admit flat connections.
problem Understanding flat connections on holomorphic vector bundles over Hopf manifolds.
method Defining resonant and non-resonant Mall bundles, proving the existence of flat connections on non-resonant bundles, and applying the Poincare-Dulac theorem.
result Non-resonant Hopf manifolds are linearizable, generalizing Kodaira's result.
Quantum circuits learn to classify non-orthogonal quantum states.
problem Classifying non-orthogonal quantum states is crucial in quantum information.
method Trained quantum circuits using Adam optimization to discover parameters of unknown POVMs.
result Shallow quantum circuits can learn to discriminate among various quantum states with comparable performance to optimal POVMs.
Variational autoencoders improve state representation for hard quantum systems.
problem Simulating and storing quantum states is computationally infeasible.
method Introduced variational autoencoders for quantum state representation.
result Deep networks better represent hard quantum states, suggesting compositional structure.
We study the distribution of resonances for geometrically finite hyperbolic surfaces of infinite area by countting resonances numerically. The resonances are computed as zeros of the Selberg zeta function, using an algorithm for computation of the zeta function for Schottky groups. Our particular focus is on three aspe…
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.
Quantum machine learning classification depends on mutual informations between state and parameter spaces.
problem Generalization in quantum machine learning models.
method Link between quantum machine learning and quantum hypothesis testing, using mutual informations.
result Quantum classifier accuracy and generalization depend on mutual informations between state and parameter spaces.
Novel quantum algorithm for financial market modeling.
problem Accurate quantum state preparation for financial simulation.
method Multi-Split-Steps Quantum Walk (multi-SSQW) with PQC and variational solver.
result Highly accurate modeling of complex financial distributions.
New method for QPT without needing to know or prepare specific input states.
problem Quantum process characterization with unknown input states.
method Blind Quantum Process Tomography (BQPT) with single-preparation methods.
result Ability to characterize quantum processes using arbitrary unknown input states.
Inverse problem solved for rotationally symmetric manifolds using eigenvalues and resonances.
problem Determining the rotation radius of a manifold from its eigenvalues and resonances.
method Unitary equivalence to one-dimensional Schrödinger operators, non-linear real analytic isomorphism between Hilbert spaces.
result The rotation radius is uniquely determined by its eigenvalues and resonances.
Quantum states associated with subsets of product manifolds are separable.
problem Characterizing quantum states associated with subsets of product manifolds.
method Using holomorphic sections of quantum line bundles and restriction maps.
result Quantum states associated with finite unions of products are separable.
Quantum models learn unitary actions on entangled states from product states.
problem Generalization to out-of-distribution data in quantum machine learning.
method Proved out-of-distribution generalization for learning unitary actions.
result Learned unitary actions on entangled states from product states.
Multi-dimensional state-integrals of products of Faddeev's quantum dilogarithms arise frequently in Quantum Topology, quantum Teichmüller theory and complex Chern--Simons theory. Using the quasi-periodicity property of the quantum dilogarithm, we evaluate 1-dimensional state-integrals at rational points and express the…
Resonator Networks solve high-dimensional vector factorization better than optimization methods.
problem High-dimensional vector factorization problem in Vector Symbolic Architectures.
method Recurrent neural network (Resonator Networks) that combines nonlinear dynamics and superposition search.
result Resonator Networks outperform optimization methods in solving high-dimensional vector factorization.
Researchers measure distances between quantum states to speed up machine learning.
problem Calculating distances between quantum states for machine learning is complex.
method Three-step method using many-particle interference to measure Hilbert-Schmidt distance.
result The method reduces complexity in calculating Euclidean distances between quantum states.
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.
Sketch Tomography improves quantum state estimation accuracy.
problem Efficiently estimating quantum states, especially MPS states.
method Hybridizes classical shadow protocol with tensor train ansatz.
result Proven convergence with quadratic sample complexity.
New method uses single quantum state for machine learning tasks, improving accuracy.
problem Challenges in unsupervised learning with quantum data.
method SIngle-Preparation Quantum Information Processing (SIPQIP) concept.
result Significantly more accurate estimation compared to traditional methods.
Quantum statistical models with singularities are studied for state estimation and model selection.
problem Understanding statistical properties of quantum singular models.
method Classical singular learning theory extended to quantum state estimation and model selection using algebraic geometrical methods.
result Asymptotically unbiased estimator (QWAIC) for quantum generalization loss constructed.
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.
Extended quantum state result for gl_n weight systems.
problem Quantum states associated with gl_n weight systems.
method Extended Corfield et al. result to all gl_n weight systems.
result All gl_n weight systems are quantum states.
Quantum reinforcement learning protocol improves state adaptation efficiency.
problem Efficiently adapting quantum states to unknown reference states in dynamic environments.
method Measurement-based adaptation protocol with quantum reinforcement learning.
result Average fidelity of more than 90% achieved with less than 30 iterations.
New method learns quantum states using neural networks, revealing hidden dynamics.
problem High-precision ground state estimation of quantum many-body problems.
method Stochastic reconfiguration method with neural network Ansatz states.
result Learning landscape modes with least entanglement have largest eigenvalues, suggesting correlations are encoded in large flat valleys.
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.
Noise-resilient optimization on noisy quantum computers.
problem Noise's impact on hybrid quantum-classical optimization.
method Iterative quantum circuit with noise consideration, using Quantum Fisher Information bound.
result Algorithm robustness against different noise strengths.
State sums for quantum link invariants from a specific representation.
problem Calculating quantum link invariants from a specific representation of U_q(gl_{N|M}).
method Using state sums and representation theory of U_q(gl_{N|M}).
result Explicit relation with Kashaev invariants for the N-th exterior power of the standard representation.
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 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.
Study reveals a link between Ruelle-Pollicott resonances and cohomology eigenvalues for Anosov diffeomorphisms.
problem Understanding the speed of mixing in Anosov diffeomorphisms.
method Investigates Ruelle-Pollicott resonances on manifolds of any dimension, connecting them to cohomology eigenvalues of a quasi-compact transfer operator.
result Established a cohomological bound for the speed of mixing of Anosov diffeomorphisms.
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.
Quantum algorithms speed up reinforcement learning policies in large state-action spaces.
problem Limitations of quantum access in training reinforcement learning policies.
method Designing quantum algorithms to train reinforcement learning policies.
result Quantum algorithms offer full quadratic speed-ups in sample complexity for well-behaved policies.