Related papers: Speed-up via Quantum Sampling
A new Markov Chain Monte Carlo method for simulating the dynamics of molecular systems characterized by hard-core interactions is introduced. In contrast to traditional Kinetic Monte Carlo approaches, where the state of the system is…
Markov Chain Monte Carlo (MCMC) algorithms are essential tools in computational statistics for sampling from unnormalised probability distributions, but can be fragile when targeting high-dimensional, multimodal, or complex target…
Quantum computing was so far mainly concerned with discrete problems. Recently, E. Novak and the author studied quantum algorithms for high dimensional integration and dealt with the question, which advantages quantum computing can bring…
Quantum computation provides exponential speedup for solving certain mathematical problems against classical computers. Motivated by current rapid experimental progress on quantum computing devices, various models of quantum computation…
We present a Hamiltonian Monte Carlo algorithm to sample from multivariate Gaussian distributions in which the target space is constrained by linear and quadratic inequalities or products thereof. The Hamiltonian equations of motion can be…
The famous least squares Monte Carlo (LSM) algorithm combines linear least square regression with Monte Carlo simulation to approximately solve problems in stochastic optimal stopping theory. In this work, we propose a quantum LSM based on…
It has been shown that the Metropolis algorithm can be implemented on quantum computers in a way that avoids the sign problem. However, flat histogram techniques are often preferred as they don't suffer from the same limitations that…
Markov chain Monte Carlo methods have become standard tools in statistics to sample from complex probability measures. Many available techniques rely on discrete-time reversible Markov chains whose transition kernels build up over the…
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…
Preparing ground states and thermal states is essential for simulating quantum systems on quantum computers. Despite the hope for practical quantum advantage in quantum simulation, popular state preparation approaches have been challenged.…
Quantum speedup for mixing a Markov chain can be achieved based on the construction of slowly-varying $r$ Markov chains where the initial chain can be easily prepared and the spectral gaps have uniform lower bound. The overall complexity is…
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…
State-space models are commonly used to describe different forms of ecological data. We consider the case of count data with observation errors. For such data the system process is typically multi-dimensional consisting of coupled Markov…
Quantum computers have been widely speculated to offer significant advantages in obtaining the ground state of difficult Hamiltonian in chemistry and physics. In this work, we first propose a Lyapunov control-inspired strategy to accelerate…
We propose an efficient Markov Chain Monte Carlo method for sampling equilibrium distributions for stochastic lattice models, capable of handling correctly long and short-range particle interactions. The proposed method is a Metropolis-type…
Stochastic processes play a fundamental role in physics, mathematics, engineering and finance. One potential application of quantum computation is to better approximate properties of stochastic processes. For example, quantum algorithms for…
We propose a new Markov chain Monte Carlo method in which trial configurations are generated by evolving a state, sampled from a prior distribution, using a Markov transition matrix. We present two prototypical algorithms and derive their…
Markov chain Monte Carlo methods have become popular in statistics as versatile techniques to sample from complicated probability distributions. In this work, we propose a method to parameterize and train transition kernels of Markov chains…
Computational methods both open the frontiers of economic analysis and serve as a bottleneck in what can be achieved. We are the first to study whether Quantum Monte Carlo (QMC) algorithm can improve the runtime of economic applications and…
As industrial models and designs grow increasingly complex, the demand for optimal control of large-scale dynamical systems has significantly increased. However, traditional methods for optimal control incur significant overhead as problem…