Related papers: Analog quantum algorithms for the mixing of Markov…
This paper aims at improving the convergence to equilibrium of finite ergodic Markov chains via permutations and projections. First, we prove that a specific mixture of permuted Markov chains arises naturally as a projection under the KL…
Sampling from a high-dimensional distribution is a fundamental task in statistics, engineering, and the sciences. A canonical approach is the Langevin Algorithm, i.e., the Markov chain for the discretized Langevin Diffusion. This is the…
Mixing properties of discrete-time quantum walks on two-dimensional grids with torus-like boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an…
Motivated by robotic surveillance applications, this paper studies the novel problem of maximizing the return time entropy of a Markov chain, subject to a graph topology with travel times and stationary distribution. The return time entropy…
Since 1997 a considerable effort has been spent to study the mixing time of switch Markov chains on the realizations of graphic degree sequences of simple graphs. Several results were proved on rapidly mixing Markov chains on unconstrained,…
We show that efficient approximate sampling algorithms, combined with a slow exponential time oracle for computing its output distribution, can be combined into constructing efficient perfect samplers, which sample exactly from a target…
We survey recent results concerning the total-variation mixing time of the simple exclusion process on the segment (symmetric and asymmetric) and a continuum analog, the simple random walk on the simplex with an emphasis on cutoff results.…
This article provides the first procedure for computing a fully data-dependent interval that traps the mixing time $t_{\text{mix}}$ of a finite reversible ergodic Markov chain at a prescribed confidence level. The interval is computed from…
We study a simple Markov chain, the switch chain, on the set of all perfect matchings in a bipartite graph. This Markov chain was proposed by Diaconis, Graham and Holmes as a possible approach to a sampling problem arising in Statistics. We…
This work focuses on the quantum mixing time, which is crucial for efficient quantum sampling and algorithm performance. We extend Richter's previous analysis of continuous time quantum walks on the periodic lattice $\mathbb{Z}_{n_1}\times…
Recently, the idea of classical Metropolis sampling through Markov chains has been generalized for quantum Hamiltonians. However, the underlying Markov chain of this algorithm is still classical in nature. Due to Szegedy's method, the…
We compute the stationary distribution of a continuous-time Markov chain which is constructed by gluing together two finite, irreducible Markov chains by identifying a pair of states of one chain with a pair of states of the other and…
Markov chain Monte Carlo (MCMC) methods are widely used in machine learning. One of the major problems with MCMC is the question of how to design chains that mix fast over the whole state space; in particular, how to select the parameters…
To find the number of assignments of zeros and ones satisfying a specific Knapsack Problem is $\#P$ hard, so only approximations are envisageable. A Markov chain allowing uniform sampling of all possible solutions is given by Luby, Randall…
Variational quantum algorithms are poised to have significant impact on high-dimensional optimization, with applications in classical combinatorics, quantum chemistry, and condensed matter. Nevertheless, the optimization landscape of these…
Quantum computers provide an opportunity to efficiently sample from probability distributions that include non-trivial interference effects between amplitudes. Using a simple process wherein all possible state histories can be specified by…
Given random walk on a graph, the corresponding discrete-time quantum walk can be constructed using the method proposed by Szegedy. On the other hand, given a partition of the set of states of a Markov chain, one can study the corresponding…
We consider sampling and enumeration problems for Markov equivalence classes. We create and analyze a Markov chain for uniform random sampling on the DAGs inside a Markov equivalence class. Though the worst case is exponentially slow…
Hitting times provide a fundamental measure of distance in random processes, quantifying the expected number of steps for a random walk starting at node $u$ to reach node $v$. They have broad applications across domains such as network…
Quantum-enhanced Markov chain Monte Carlo, an algorithm in which configurations are proposed through a measured quantum quench and accepted or rejected by a classical algorithm, has been proposed as a possible method for robust quantum…