Related papers: Quasi-optimal quantum Markov chain spectral gap es…
Markov chain Monte Carlo algorithms have important applications in counting problems and in machine learning problems, settings that involve estimating quantities that are difficult to compute exactly. How much can quantum computers speed…
Sampling from the stationary distribution is one of the fundamental tasks of Markov chain-based algorithms and has important applications in machine learning, combinatorial optimization and network science. For the quantum case, qsampling…
In this paper we show how to generalize the quantum approximate counting technique developed by Brassard, H{\o}yer and Tapp [ICALP 1998] to a more general setting: estimating the number of marked states of a Markov chain (a Markov chain can…
We consider the problem of estimating from sample paths the absolute spectral gap $\gamma_*$ of a reversible, irreducible and aperiodic Markov chain $(X_t)_{t \in \mathbb{N}}$ over a finite state space $\Omega$. We propose the ${\tt UCPI}$…
We propose quantum algorithms that provide provable speedups for Markov Chain Monte Carlo (MCMC) methods commonly used for sampling from probability distributions of the form $\pi \propto e^{-f}$, where $f$ is a potential function. Our…
As it has become common to use many computer cores in routine applications, finding good ways to parallelize popular algorithms has become increasingly important. In this paper, we present a parallelization scheme for Markov chain Monte…
The Markov Chain Monte Carlo method is at the heart of efficient approximation schemes for a wide range of problems in combinatorial enumeration and statistical physics. It is therefore very natural and important to determine whether…
Quantum computing offers an alternative paradigm for addressing combinatorial optimization problems compared to classical computing. Despite recent hardware improvements, the execution of empirical quantum optimization experiments at scales…
Markov chain Monte Carlo (MCMC) methods are ubiquitous tools for simulation-based inference in many fields but designing and identifying good MCMC samplers is still an open question. This paper introduces a novel MCMC algorithm, namely,…
The problem of sampling from the stationary distribution of a Markov chain finds widespread applications in a variety of fields. The time required for a Markov chain to converge to its stationary distribution is known as the classical…
Continuous-time measurements are instrumental for a multitude of tasks in quantum engineering and quantum control, including the estimation of dynamical parameters of open quantum systems monitored through the environment. However, such…
Quantum trajectories are Markov processes modeling the evolution of a quantum system subjected to repeated independent measurements. Inspired by the theory of random products of matrices, it has been shown that these Markov processes admit…
We establish non-asymptotic error bounds for the classical Maximal Likelihood Estimation of the transition matrix of a given Markov chain. Meanwhile, in the reversible case, we propose a new reversibility-preserving online Symmetric…
We study the Markov chain Monte Carlo (MCMC) estimator for numerical integration for functions that do not need to be square integrable w.r.t. the invariant distribution. For chains with a spectral gap we show that the absolute mean error…
We show how to exploit symmetries of a graph to efficiently compute the fastest mixing Markov chain on the graph (i.e., find the transition probabilities on the edges to minimize the second-largest eigenvalue modulus of the transition…
We present a novel quantum algorithm for estimating Gibbs partition functions in sublinear time with respect to the logarithm of the size of the state space. This is the first speed-up of this type to be obtained over the seminal…
Randomized block Krylov subspace methods form a powerful class of algorithms for computing the extreme eigenvalues of a symmetric matrix or the extreme singular values of a general matrix. The purpose of this paper is to develop new…
Quantum algorithms can potentially solve a handful of problems more efficiently than their classical counterparts. In that context, it has been discussed that Markov chains problems could be solved significantly faster using quantum…
Probabilistic graphical models play a crucial role in machine learning and have wide applications in various fields. One pivotal subset is undirected graphical models, also known as Markov random fields. In this work, we investigate the…
It has become increasingly easy nowadays to collect approximate posterior samples via fast algorithms such as variational Bayes, but concerns exist about the estimation accuracy. It is tempting to build solutions that exploit approximate…