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.
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).
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.
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.
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.
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.
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.
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.
Neural-Network Quantum States have been recently introduced as an Ansatz for describing the wave function of quantum many-body systems. We show that there are strong connections between Neural-Network Quantum States in the form of Restricted Boltzmann Machines and some classes of Tensor-Network states in arbitrary dime…
We demonstrate how machine learning is able to model experiments in quantum physics. Quantum entanglement is a cornerstone for upcoming quantum technologies such as quantum computation and quantum cryptography. Of particular interest are complex quantum states with more than two particles and a large number of entangle…
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.
Characterizes optimal-speed quantum state evolution Hamiltonians.
problem Optimal-speed unitary time evolution of pure and quasi-pure quantum states.
method Construction of the manifold of pure states and isometry with flag manifold, characterization of equigeodesic vectors.
result Hamiltonians generating optimal-speed time evolution are fully characterized by equigeodesic vectors of the flag manifold.
Quantum traces embed into quantum tori for surface skein algebras.
problem Embedding stated skein algebras into quantum tori.
method Two different embeddings using quantum trace maps and lambda length coordinates.
result Quantum cluster algebra of Muller equals reduced stated skein algebra.
Quantum computing for option pricing using MPS states.
problem Efficiently generating time series for path-dependent options on quantum computers.
method Proposes a Matrix Product State (MPS) model for time series generation and trains it for the Heston model.
result Demonstrates the MPS model's capability to generate paths in the Heston model for path-dependent option pricing.
Studying general quantum many-body systems is one of the major challenges in modern physics because it requires an amount of computational resources that scales exponentially with the size of the system.Simulating the evolution of a state, or even storing its description, rapidly becomes intractable for exact classical…
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 mechanics fundamentally forbids deterministic discrimination of quantum states and processes. However, the ability to optimally distinguish various classes of quantum data is an important primitive in quantum information science. In this work, we train near-term quantum circuits to classify data represented by …
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.
Quantum models generalize well with little data, challenging traditional generalization theories.
problem Quantum machine learning models generalize well with few data, contradicting traditional theories.
method Systematic randomization experiments and theoretical constructions.
result Quantum neural networks can fit random states and labels, defying current generalization measures.
Study noncommutative Sobolev inequalities using quantum state metrics.
problem Establishing Sobolev inequalities in noncommutative settings.
method Generalizing monotone metrics in quantum states.
result Developed new matrix-valued Beckner inequalities.
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.
Quantum Process Tomography (QPT) methods aim at identifying, i.e. estimating, a given quantum process. QPT is a major quantum information processing tool, since it especially allows one to characterize the actual behavior of quantum gates, which are the building blocks of quantum computers. However, usual QPT procedure…
Quantum method generates unbiased samples from discrete graphical models.
problem Sampling from discrete graphical models is challenging and intractable in high dimensions.
method Embedding graphical models into unitary operators and using quantum circuits.
result Provably generates unbiased and independent samples from general discrete factor models.
SSDMs generate quantum states directly, outperforming classical methods.
problem Generating pure-state quantum representations efficiently.
method Score-based generative model on complex projective manifold.
result SSDMs match target pure-state ensembles by orders of magnitude.
Adversarial learning is one of the most successful approaches to modelling high-dimensional probability distributions from data. The quantum computing community has recently begun to generalize this idea and to look for potential applications. In this work, we derive an adversarial algorithm for the problem of approxim…
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.
This work proposes efficient classical training protocols for IQP circuits to train quantum generative models.
problem Training quantum generative models on industrially relevant probability distributions is challenging due to high computational cost.
method Developed protocols for classical training of IQP circuits, which are hard to sample but have efficient gradient computation.
result Classically trained IQP circuits can efficiently sample from target probability distributions, demonstrating practical quantum advantage.
Quantum models are rephrased as kernel methods, improving performance.
problem Improving quantum machine learning models by encoding data into quantum states.
method Rephrasing quantum models as kernel methods and using support vector machines.
result Kernel-based training finds better quantum models than variational circuit training.
Quantum neural networks generalize better due to flatter parameter space.
problem Generalization in quantum neural networks.
method Mapped feature data to a quantum state, applied unitary evolution, and measured for classification.
result Quantum neural networks have better generalization than classical networks.
New methods optimize training VQAs without barren plateaus, improving efficiency and applicability.
problem Barren plateaus in training variational quantum algorithms.
method Derive adaptive learning rates and use Gaussian kernels to optimize movement in parameter space.
result Optimized training methods outperform other routines and can train VQAs free of barren plateaus.
New quantum states capture more information, enabling advanced processing tasks.
problem Quantum information processing challenges with limited statistical information.
method Introducing Random-Coefficient Pure States (RCPS) and exploiting their higher-order statistics.
result RCPS provide richer information than density operators, enabling new quantum tasks.
Global EQG sums boundary states over manifold diffeomorphism classes.
problem Summing boundary states over manifold diffeomorphism classes.
method Formulated as classical statistical physics, weights determined by general principles.
result Hartle-Hawking state as a probability measure.
Quantum ML predicts data with improved speed and accuracy.
problem Predicting data using maximum likelihood in a quantum setting.
method Quantum states embedding and minimization of quantum relative entropy.
result Unified framework for classical and quantum LLMs with performance guarantees.
It is a fundamental, but still elusive question whether the schemes based on quantum mechanics, in particular on quantum entanglement, can be used for classical information processing and machine learning. Even partial answer to this question would bring important insights to both fields of machine learning and quantum…
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.
Paper generalizes VB-FTRL for online learning of quantum states with logarithmic loss.
problem Online learning of quantum states with logarithmic loss.
method Generalizes VB-FTRL algorithm for LL-OLQS with polynomial-time implementation.
result Achieves a regret rate of O(d2log(d+T)) for LL-OLQS. 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.
We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits new generalizations in different directions. In it a pure state of some quantum s…
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…
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.
The paper constructs quantum invariants for knotoid diagrams.
problem Quantum invariants for knotoid diagrams in R2. 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.
Study online learning of quantum processes, showing feasibility for certain types.
problem Learning quantum processes adaptively, especially for bounded gate complexity and Pauli channels.
method Online learning, mistake-bounded model, multiplicative weights update algorithm, Bell sampling.
result Online learning feasible for quantum channels of bounded gate complexity and Pauli channels.
The paper introduces a quantum state system to count perfect matchings in graphs.
problem Counting perfect matchings in graphs using quantum state systems.
method Topological quantum field theory (TQFT) and spectral sequences.
result The filtered n-color vertex homology for n=2 is generated by perfect matchings. 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.
In this paper, we give a precise and workable definition of a quantum knot system, the states of which are called quantum knots. This definition can be viewed as a blueprint for the construction of an actual physical quantum system. Moreover, this definition of a quantum knot system is intended to represent the "quantu…
New algorithm improves efficiency of quantum system modeling.
problem Intractable complexities in quantum Hamiltonian learning and Gibbs sampling.
method Generalized quantum natural gradient descent and Quantum-Probabilistic Mirror Descent.
result Data sample efficiency proven using information geometry and quantum metrology.
Quantum machine learning has received significant attention in recent years, and promising progress has been made in the development of quantum algorithms to speed up traditional machine learning tasks. In this work, however, we focus on investigating the information-theoretic upper bounds of sample complexity - how ma…
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.