Related papers: Quantum Gibbs Sampling in Infinite Dimensions: Gen…
Mainstream machine-learning techniques such as deep learning and probabilistic programming rely heavily on sampling from generally intractable probability distributions. There is increasing interest in the potential advantages of using…
In this paper we propose a continuous-time, dissipative Markov dynamics that asymptotically drives a network of n-dimensional quantum systems to the set of states that are invariant under the action of the subsystem permutation group. The…
We characterise the convergence of the Gibbs sampler which samples from the joint posterior distribution of parameters and missing data in hierarchical linear models with arbitrary symmetric error distributions. We show that the convergence…
Sampling from the full posterior distribution of high-dimensional non-linear, non-Gaussian latent dynamical models presents significant computational challenges. While Particle Gibbs (also known as conditional sequential Monte Carlo) is…
Gibbs states (i.e., thermal states) can be used for several applications such as quantum simulation, quantum machine learning, quantum optimization, and the study of open quantum systems. Moreover, semi-definite programming, combinatorial…
Preparing thermal (Gibbs) states is a common task in physics and computer science. Recent algorithms mimic cooling via system-bath coupling, where the cost is determined by mixing time, akin to classical Metropolis-like algorithms. However,…
On noisy intermediate-scale quantum (NISQ) devices, expectation values of many observables are obtained through sampling-based approximations to trace-like quantities. A central limitation of this approach is destructive cancellation under…
Recently, there have been several advancements in quantum algorithms for Gibbs sampling. These algorithms simulate the dynamics generated by an artificial Lindbladian, which is meticulously constructed to obey a detailed-balance condition…
Synthetic data generation has proven to be a promising solution for addressing data availability issues in various domains. Even more challenging is the generation of synthetic time series data, where one has to preserve temporal dynamics,…
Quantum state processing is one of the main tools of quantum technologies. While real systems are complicated and/or may be driven by non-ideal control they may nevertheless exhibit simple dynamics approximately confined to a low-energy…
The inadequate mixing of conventional Markov Chain Monte Carlo (MCMC) methods for multi-modal distributions presents a significant challenge in practical applications such as Bayesian inference and molecular dynamics. Addressing this, we…
We prove two statements about the long time dynamics of integrable Hamiltonian systems. In classical mechanics, we prove the microcanonical version of the Generalized Gibbs Ensemble (GGE) by mapping it to a known theorem and then extend it…
Gibbs sampling is a Markov chain Monte Carlo method that is often used for learning and inference on graphical models. Minibatching, in which a small random subset of the graph is used at each iteration, can help make Gibbs sampling scale…
Given a quantum circuit, a quantum computer can sample the output distribution exponentially faster in the number of bits than classical computers. A similar exponential separation has yet to be established in generative models through…
Quantum annealers are emerging as programmable, dynamical experimental platforms for probing strongly correlated spin systems. Yet key thermal assumptions, chiefly a Gibbs-distributed output ensemble, remain unverified in the large-scale…
We reconstruct all (2+1)D quantum double models of finite groups from their boundary symmetries through the repeated application of a gauging procedure, extending the existing construction for abelian groups. We employ the recently proposed…
We study in general the time-evolution of correlation functions in a extended quantum system after the quench of a parameter in the hamiltonian. We show that correlation functions in d dimensions can be extracted using methods of boundary…
Local samplers are algorithms that generate random samples based on local queries to high-dimensional distributions, ensuring the samples follow the correct induced distributions while maintaining time complexity that scales locally with…
We study general coordinate-wise MCMC schemes (such as Metropolis-within-Gibbs samplers), which are commonly used to fit Bayesian non-conjugate hierarchical models. We relate their convergence properties to the ones of the corresponding…
We develop a framework for approximating collapsed Gibbs sampling in generative latent variable cluster models. Collapsed Gibbs is a popular MCMC method, which integrates out variables in the posterior to improve mixing. Unfortunately for…