Related papers: A Quantum-Quantum Metropolis Algorithm
Monte Carlo (MC) sampling methods are widely applied in Bayesian inference, system simulation and optimization problems. The Markov Chain Monte Carlo (MCMC) algorithms are a well-known class of MC methods which generate a Markov chain with…
I generalize the well-known classical Metropolis-Hastings algorithm into a quantum algorithm that can equilibrate, measure, and mix a quantum thermal state on a quantum computer. It performs non-symmetric transitions on labels of state…
The Metropolis algorithm is a Markov chain Monte Carlo (MCMC) algorithm used to simulate from parameter distributions of interest, such as generalized linear model parameters. The "Metropolis step" is a keystone concept that underlies…
Szegedy developed a generic method for quantizing classical algorithms based on random walks [Proceedings of FOCS, 2004, pp. 32-41]. A major contribution of his work was the construction of a walk unitary for any reversible random walk.…
We introduce a Metropolis-Hastings Markov chain for Boltzmann distributions of classical spin systems. It relies on approximate tensor network contractions to propose correlated collective updates at each step of the evolution. We present…
A coinless quantisation procedure of general reversible Markov chains on graphs is presented. A quantum Hamiltonian H is obtained by a similarity transformation of the fundamental transition probability matrix K in terms of the square root…
Sampling tasks are a natural class of problems for quantum computers due to the probabilistic nature of the Born rule. Sampling from useful distributions on noisy quantum hardware remains a challenging problem. A recent paper [Layden, D. et…
Quantum walks are promising tools based on classical random walks, with plenty of applications such as many variants of optimization. Here we introduce the semiclassical walks in discrete time, which are algorithms that combines classical…
A majority of numerical scientific computation relies heavily on handling and manipulating matrices, such as solving linear equations, finding eigenvalues and eigenvectors, and so on. Many quantum algorithms have been developed to advance…
Consider the problem of approximating a given probability distribution on the cube $[0,1]^n$ via the use of a square lattice discretization with mesh-size $1/N$ and the Metropolis algorithm. Here the dimension $n$ is fixed and we focus for…
Quantum walks provide a powerful framework for achieving algorithmic speedup in quantum computing. This paper presents a quantum search algorithm for 2-tessellable graphs, a generalization of bipartite graphs, achieving a quadratic speedup…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian…
Szegedy's quantum walk is an algorithm for quantizing a general Markov chain. It has plenty of applications such as many variants of optimizations. In order to check its properties in an error-free environment, it is important to have a…
A Kernel Adaptive Metropolis-Hastings algorithm is introduced, for the purpose of sampling from a target distribution with strongly nonlinear support. The algorithm embeds the trajectory of the Markov chain into a reproducing kernel Hilbert…
We present an improved Metropolis algorithm for arbitrary hard core systems in any dimensions. In the new updating scheme the conventional Metropolis step of a single particle is replaced by a collective step of a chain of particles. For…
The Metropolis-Hastings algorithm is a fundamental Markov chain Monte Carlo (MCMC) method for sampling and inference. With the advent of Big Data, distributed and parallel variants of MCMC methods are attracting increased attention. In this…
We introduce a new tool for quantum algorithms called quantum fast-forwarding (QFF). The tool uses quantum walks as a means to quadratically fast-forward a reversible Markov chain. More specifically, with $P$ the Markov chain transition…
After the first detection of a gravitational wave in 2015, the number of successes achieved by this innovative way of looking through the universe has not stopped growing. However, the current techniques for analyzing this type of events…
Classical algorithms are often not effective for solving nonconvex optimization problems where local minima are separated by high barriers. In this paper, we explore possible quantum speedups for nonconvex optimization by leveraging the…