Quantum operators limit to morphisms between manifolds.
problem Understanding morphisms between supermanifolds.
method Defined quantum thick morphisms as oscillatory integral operators.
result Quantum thick morphisms are classical limits of thick morphisms.
Quantum neural tangent kernels help understand variational quantum circuits in machine learning.
problem Designing and predicting performance of variational quantum circuits.
method Using quantum neural tangent kernels and dynamical equations for loss functions.
result Analytical solutions for training dynamics in variational quantum circuits.
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.
No chiral field theory for quantum spin chain limits.
problem Chiral conformal field theory limits of quantum spin chains.
method Block spin renormalization, Hamiltonian analysis.
result No continuous limit to chiral field theory.
Novel framework explains generalization in deep neural networks.
problem Understanding and improving generalization in deep neural networks.
method Topological Quantum Neural Networks as the semi-classical limit of Deep Neural Networks.
result Demonstrates that the perceptron, viewed as the semi-classical limit, achieves similar results to standard neural networks without training.
We investigate the behavior of stocks in daily price-limited stock markets by purposing a quantum spatial-periodic harmonic model. The stock price is presumed to oscillate and damp in a quantum spatial-periodic harmonic oscillator potential well. Complicated non-linear relations including inter-band positive correlatio…
VQAs use classical optimization to train quantum circuits, promising quantum advantage.
problem High computational cost of quantum simulations and solving large-scale problems.
method Variational Quantum Algorithms (VQAs) use classical optimizers to train parametrized quantum circuits.
result VQAs are a promising strategy for obtaining quantum advantage.
Quantum machine learning generalizes well from limited data.
problem Generalization in quantum machine learning from few training data.
method Optimizing parameterized quantum circuits on training data sets and analyzing generalization error.
result Generalization error scales at worst as √(T/N) and improves to √(K/N) when only K gates change.
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 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.
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.
Quantum ELMs use a quantum reservoir to learn from data, with limits on expressivity and scalability.
problem Understanding the limits of quantum ELMs for machine learning tasks.
method Decomposed QELM predictions into Fourier series to analyze expressivity and scalability.
result Expressivity of QELMs is limited by the number of Fourier frequencies and observables, and scalability is hindered by hardware noise and entanglement.
Quantum SVMs outperform classical ones on limited data.
problem Classifying and regressing with limited training data.
method Trained SVMs on D-Wave quantum annealer and compared to classical SVMs.
result Quantum SVMs often generalize better to unseen data.
Proposes a new finance model using quantum mechanics.
problem Traditional finance models assume normal distribution of stock prices.
method Used Klein-Gordon equation and conformal transformations.
result Stock prices follow Cauchy distribution in a specific limit.
Quantum machine learning aims to speed up classical algorithms.
problem Speeding up classical machine learning algorithms using quantum computing.
method Review and discussion of quantum machine learning techniques.
result Quantum algorithms offer advantages for certain learning problems.
We study quantum invariant Z(M) for cusped hyperbolic 3-manifold M. We construct this invariant based on oriented ideal triangulation of M by assigning to each tetrahedron the quantum dilogarithm function, which is introduced by Faddeev in studies of the modular double of the quantum group. Following Thurston and Neuma…
Quantum states are not entangled if submanifold is a product.
problem Understanding entanglement in quantum states associated with product submanifolds.
method Analyzing quantum states ρN on submanifolds of product Kähler manifolds in the semiclassical limit. result States are not entangled when submanifold is a product.
Quantum ergodicity and limits for 3D contact sub-Riemannian Laplacians proved.
problem Quantum ergodicity and limits for hypoelliptic operators in sub-Riemannian geometry.
method Microlocal Weyl law, Birkhoff normal form, variance estimate, ergodicity assumption.
result Quantum limits can be decomposed into two mutually singular measures.
Renormalization in neural networks linked to quantum field theory.
problem Implementing renormalization in neural networks.
method Mapping neural networks to quantum field theory, applying renormalization techniques.
result Changing weight standard deviation corresponds to a renormalization flow.
Paper bridges quantum and classical mechanics for open systems.
problem Quantum open systems with bi-Lindblad structure.
method Develops a bridge between bi-Hamiltonian structures and GKSL formalism, introducing contact-compatible Lindblad generators.
result Provides a mathematical mechanism for semiclassical limit of quantum open systems.
Unified framework for learning quantum models from limited measurements.
problem Sample complexity and measurement shots in classical learning of quantum models.
method Unified learning framework considering probabilistic quantum measurements.
result Asymmetrical effects and interplay of sample size and measurement shots on learning performance.
Distributed Quantum Gaussian Processes improve modeling in multi-agent systems.
problem Limited expressivity of classical kernels in complex domains.
method Distributed Quantum Gaussian Process (DQGP) with DR-ADMM algorithm.
result Enhanced modeling capabilities and scalability in multi-agent systems.
Quantum algorithms for multi-armed bandits are explored with limited reward access.
problem Exploring quantum speed-ups in multi-armed bandit problems with limited reward information.
method Introduced new bandit models and showed query complexity equivalence with classical algorithms.
result No quadratic speed-up is possible for multi-armed bandits with limited reward access.
Study explores quantum spaces on toric varieties and their limiting behavior.
problem Understanding quantum spaces on toric varieties and their limiting behavior.
method Established quantum spaces for mixed polarizations and examined one-parameter families of Kähler polarizations.
result Quantum spaces Hk,t converge to Hk as tightarrow∞. Quantum algorithm reduces CVA risk-neutral expectation estimation costs.
problem Reducing Monte Carlo sampling cost for CVA on real quantum hardware.
method Noise-aware quantum workflow combining market calibration, discretisation, and oracle construction.
result CABIQAE achieves lower classical post-processing runtime and more effective error exploitation.
Few quantum measurements limit learning entanglement.
problem Challenges in learning entanglement from limited data.
method Hybrid quantum-classical learning techniques.
result Generalization errors increase with few measurements.
Improved formulation of spinfoam quantum gravity with cosmological constant, ensuring all amplitudes are finite and providing semiclassical asymptotics.
problem Ensuring the finiteness of spinfoam amplitudes and providing semiclassical asymptotics for quantum gravity.
method Using state-integral model of PSL(2, C) Chern-Simons theory and implementing simplicity constraint. result All spinfoam amplitudes are finite and provide semiclassical asymptotics with oscillatory terms related to the Regge action.
Kashaev limits of quantum A-polynomials reveal classical action vanishing and hyperbolic volume deformation.
problem Exploring the Kashaev limits of quantum A-polynomials. method Analyzing the double scaling quasiclassical limit.
result Identifying two phases in the Kashaev limit.
Single T-gate makes distribution learning hard for deep circuits.
problem Learning probability distributions from quantum circuits.
method Characterization of learnability and simulatability of quantum circuit outputs.
result Injection of a single T-gate into depth n^Ω(1) circuits makes distribution learning hard.
In this paper we present some conditions for the (strong) stabilizability of an n-D Quantum MIMO system P(X). It contains two parts. The first part is to introduce the n-D Quantum MIMO systems where the coefficients vary in the algebra of Q-meromorphic functions. Then we introduce some conditions for the stabilizabilit…
Survey of QML applications on near-term quantum devices.
problem Achieving quantum advantage on real-world applications.
method Analysis of supervised and unsupervised techniques, including encoding, ansatz structure, error mitigation, and gradient methods.
result Current QML implementations on quantum hardware face limitations but show potential for real-world applications.
Study shows limitations and possibilities of learning quantum circuit output distributions.
problem Learnability of output distributions of local quantum circuits.
method Investigated within two oracle models: statistical query model and direct sample access model.
result Output distributions of super-logarithmic depth Clifford circuits are not efficiently learnable in the statistical query model.
Study shows mass distribution of random holomorphic sections follows a central limit theorem.
problem Understanding mass distribution of random holomorphic sections.
method Proved a central limit theorem for mass distribution of random holomorphic sections associated with positive line bundles.
result Almost every sequence of random holomorphic sections exhibits quantum ergodicity.
We study possible real structures in the space of solutions to the quantum differential equation. We show that, under mild conditions, a real structure in orbifold quantum cohomology yields a pure and polarized tt^*-geometry near the large radius limit. We compute an example of P^1 which is pure and polarized over the …
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.
Quantum machine learning can't achieve polylogarithmic runtimes, even with quantum data access.
problem Bounding the minimum number of samples required for supervised quantum learning.
method Statistical learning theory and quantum machine learning algorithms.
result Quantum machine learning algorithms for supervised learning have at most polynomial speedups over classical algorithms.
Quantum algorithms for CVaR portfolio optimization face trade-offs between hardware coherence and expressibility.
problem Quantum algorithmic resilience for CVaR portfolio optimization
method WS-QAOA vs. HE-VQNN
result WS-QAOA provides exact theoretical mapping but suffers from hardware decoherence, while HE-VQNN preserves hardware coherence but lacks expressibility.
Study calculates quantum hyperbolic invariants for figure-eight knot complement, finding it either 0 or half the volume.
problem Computing quantum hyperbolic invariants for knot complements.
method Computed the real part of the semi-classical limit of quantum hyperbolic invariants of the figure-eight knot complement.
result The real part is rigid and either 0 or half the hyperbolic volume of the knot complement.
A new hybrid framework reduces quantum runtime and noise effects.
problem Challenges in deploying deep QFMs on real quantum hardware.
method Iterative Quantum Feature Maps (IQFMs) combining shallow QFMs and classical augmentation weights.
result Numerical experiments show IQFMs outperforming quantum convolutional neural networks.
Quantum walk algorithm optimizes quantum state preparation for financial simulations.
problem Efficiently loading classical data into quantum states for quantum computers.
method Split-step quantum walks (SSQW) to design parameterized quantum circuits (PQC).
result SSQW facilitates generating desired probability amplitude distributions for quantum simulations.
This paper proves a conjecture linking quantum modular forms and WRT invariants for specific graphs.
problem Proving a conjecture about quantum modular forms and WRT invariants for unimodular H-graphs.
method Constructed finite sums of rational functions, studied weighted Gauss sums, and combined results to prove the conjecture.
result WRT invariants of H-graphs yield quantum modular forms of depth two and weight one.
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 walks model financial returns with flexibility and asymmetry.
problem Accurate modeling of financial asset price dynamics.
method Discrete-time quantum walks to model asset price evolution.
result Quantum walk models can generate asymmetric return distributions and higher probabilities for extreme events.
Quantum computing aids in optimizing currency reserves for central banks.
problem Optimizing currency composition in foreign exchange reserves.
method Comparison of quantum and classical algorithms for portfolio optimization.
result Quantum algorithms outperform classical methods in currency optimization.
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.
Quantum SVT reduces credit risk analysis costs.
problem Efficiently estimating credit risk metrics using quantum computing.
method Quantum Singular Value Transformation (QSVT) to reduce state preparation costs.
result Significant reduction in implementation costs for quantum credit risk analysis.
Explicit formula found for quantum microformal morphisms of supermanifolds.
problem Finding explicit formulas for quantum microformal morphisms of supermanifolds.
method Provided an explicit formula as a formal differential operator.
result Quantum microformal morphisms act on oscillatory wave functions and reproduce nonlinear pullbacks in the classical limit.
The quantum navigation problem of finding the time-optimal control Hamiltonian that transports a given initial state to a target state through quantum wind, that is, under the influence of external fields or potentials, is analysed. By lifting the problem from the state space to the space of unitary gates realising the…