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.
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 algorithm speeds up Gibbs partition function estimation.
problem Estimating partition functions in sublinear time.
method Sublinear-time quantum algorithm using quantum phase and amplitude estimation.
result First sublinear-time speed-up for partition function estimation.
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.
Geometric approach to quantum thermodynamics models state spaces and processes.
problem Quantum thermodynamics in the regime of non-equilibrium states.
method Contact geometry and principal fiber bundles to model quantum state spaces and processes.
result Geometric formulation reveals the fundamental thermodynamic relations and unattainability of the third law.
Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is essentially a first-order logic template to generate Markov networks. Inference …
New method uses quantum annealing and VAN for better statistical mechanics calculations.
problem Difficulty in computing partition function in statistical mechanics.
method Combines quantum annealing samples with variational autoregressive networks.
result Enhanced accuracy in finite-size Sherrington-Kirkpatrick model.
New MCMC method speeds up quantum physics simulations by a factor of 100.
problem Simulating quantum many-body systems with high computational complexity.
method FFT-accelerated MCMC with coupled particle and auxiliary variables.
result Achieves O ( N log N ) O(N \log N) O ( N log N ) scaling, significantly faster than traditional O ( N 3 ) O(N^3) O ( N 3 ) methods. We introduce two quantum algorithms for solving structured prediction problems. We first show that a stochastic gradient descent that uses the quantum minimum finding algorithm and takes its probabilistic failure into account solves the structured prediction problem with a runtime that scales with the square root of th…
A quantum memory model for Kelly betting with amplified or attenuated outcomes.
problem Optimizing Kelly betting strategies with quantum memory elements.
method Semi-classical model using quantum memory to encode payoff, modeled as random lasing dynamics.
result Best strategy is to invest all capital in coherent state amplitude for optimal performance.
Improved MMWU algorithm achieves instance-optimal regret bound for matrix LEA.
problem Matrix Learning from Expert Advice problem.
method Developed a general potential-based framework for matrix LEA, using a new Jensen's trace inequality.
result Achieved instance-optimal regret bound of O ( T ⋅ S ( X ∣ ∣ d − 1 I d ) ) O(\sqrt{T\cdot S(X||d^{-1}I_d)}) O ( T ⋅ S ( X ∣∣ d − 1 I d ) ) . New method speeds up Gibbs sampling for large graphs.
problem Efficiently sampling from large graphical models.
method Poisson-minibatching Gibbs sampling.
result Theoretical convergence rate guarantees for Poisson-minibatching Gibbs.
Souriau studies Gibbs states for symplectic manifolds with group actions.
problem Understanding Gibbs states for symplectic manifolds with symmetries.
method Adaptation of cross product for pseudo-Euclidean spaces, detailed proofs, examples of Gibbs states.
result Presentation of Gibbs states and associated thermodynamic functions for various symplectic manifolds.
A fundamental task in machine learning and related fields is to perform inference on Bayesian networks. Since exact inference takes exponential time in general, a variety of approximate methods are used. Gibbs sampling is one of the most accurate approaches and provides unbiased samples from the posterior but it has hi…
Improved particle Gibbs sampling by marginalizing parameters.
problem Bayesian inference in high-dimensional state-space models is challenging.
method Marginalized particle Gibbs sampling, combining MCMC and sequential Monte Carlo.
result Marginalization improves performance beyond the Gibbs sampler, scaling linearly.
Study measures rigidity for random walks and flows via generalized u-Gibbs states.
problem Measure rigidity for stationary measures of random walks and flows.
method Factorization method applied to generalized u-Gibbs states.
result Established extra invariance of generalized u-Gibbs states.
In Deep Learning, a well-known approach for training a Deep Neural Network starts by training a generative Deep Belief Network model, typically using Contrastive Divergence (CD), then fine-tuning the weights using backpropagation or other discriminative techniques. However, the generative training can be time-consuming…
Market strategies minimize Fisher information to minimize risk.
problem Applying minimum Fisher information principle to market dynamics.
method Analytical extension to quantum harmonic oscillator eigenstates and Gibbs distribution.
result Minimizing Fisher information reduces information and risk.
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).
DiGS improves sampling from multi-modal distributions.
problem Inadequate mixing in MCMC methods for multi-modal distributions.
method Integrates diffusion models and Gibbs sampling to create an auxiliary noisy distribution.
result DiGS exhibits better mixing for multi-modal distributions than state-of-the-art methods.
With their origin in thermodynamics and symbolic dynamics, Gibbs measures are crucial tools to study the ergodic theory of the geodesic flow on negatively curved manifolds. We develop a framework (through Patterson-Sullivan densities) allowing us to get rid of compactness assumptions on the manifold, and prove many exi…
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.
We analyze the complexity of Gibbs samplers for inference in crossed random effect models used in modern analysis of variance. We demonstrate that for certain designs the plain vanilla Gibbs sampler is not scalable, in the sense that its complexity is worse than proportional to the number of parameters and data. We thu…
Study the Hessian geometry of an ideal gas in a centrifuge.
problem Understanding the Hessian geometry of an ideal gas in a centrifuge.
method Investigate the Hessian geometry associated with an ideal gas in a spherical centrifuge, using the action of the Euclidean rotation group.
result The Hessian geometry of a spherical rigid body is isometric to a hyperbolic space in the high angular velocity limit.
New method transfers instances between domains using Gibbs Sampling and RBM.
problem Transfer Learning between domains with limited target data.
method Gibbs Sampling and RBM for instance transition.
result Significant improvement in target classification.
Gibbs pruning optimizes neural networks by combining physics and regularization.
problem Large neural networks are impractical for many applications.
method Combines statistical physics and stochastic regularization to train and prune networks simultaneously.
result Gibbs pruning achieves state-of-the-art performance on ResNet-56.
Bayesian model learns multiscale interactions in complex systems.
problem Understanding dynamic interplay between processes at different time scales.
method Bayesian learning framework with Particle Gibbs with Ancestor Sampling (PGAS) algorithm.
result Demonstrated the effectiveness of the proposed approach through simulations.
The paper proposes a Gibbs sampler for neural network posterior sampling.
problem Sampling from the posterior of neural networks.
method Adding noise to activations and using a Gibbs sampler.
result The Gibbs sampler achieves similar performance to MCMC methods on real and synthetic data.
Infinite Hidden Markov Models (iHMM's) are an attractive, nonparametric generalization of the classical Hidden Markov Model which can automatically infer the number of hidden states in the system. However, due to the infinite-dimensional nature of transition dynamics performing inference in the iHMM is difficult. In th…
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.
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…
New method reduces Gibbs partition function estimation complexity.
problem Estimating partition functions of Gibbs distributions.
method Doubly-adaptive MCMC with adaptive cooling schedule and mean estimator.
result Outperforms state-of-the-art algorithms in computational complexity and robustness.
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.
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…
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 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…
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.
Improved Gibbs sampler speeds up Bayesian exponential smoothing model.
problem Computational inefficiency of original NUTS sampler.
method Modifications to the original model and a bespoke Gibbs sampler.
result Significant improvement in sampling time by an order of magnitude.
Quantum machine learns faster by reverse annealing on AQCs.
problem Training RBMs on AQCs is hard due to low qubit connectivity.
method Embedding RBM nodes to virtual qubits, semantic quantum search, reverse annealing schedule.
result Reverse annealing accelerates RBM training and improves reconstruction scores.
New PG samplers improve inference in coupled state-space models.
problem Bayesian inference from multiple time series with shared parameters.
method Marginalized Particle Gibbs samplers for coupled state-space models.
result Improved parameter inference through shared information.
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.
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.
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.