Related papers: The Problem with Grover-Rudolph State Preparation …
Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition…
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…
We consider Grover's unstructured search problem in the setting where each oracle call has some small probability of failing. We show that no quantum speed-up is possible in this case.
In this study, we give an extension of Montanaro's arXiv/archive:1504.06987 quantum Monte Carlo method, tailored for computing expected values of random variables that exhibit infinite variance. This addresses a challenge in analyzing…
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…
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…
Despite intensive research, the physical origin of the speed-up offered by quantum algorithms remains mysterious. No general physical quantity, like, for instance, entanglement, can be singled out as the essential useful resource. Here we…
Quantum states can in a sense be thought of as generalizations of classical probability distributions, but are more powerful than probability distributions when used for computation or communication. Quantum speedup therefore requires some…
Quantum Monte Carlo data are often afflicted with distributions that resemble lognormal probability distributions and consequently their statistical analysis can not be based on simple Gaussian assumptions. To this extent a method is…
Sparse quantum state preparation is a common subroutine in quantum algorithms, where classical data with few nonzero entries must be loaded into a quantum state. In this work, we consider the Grover-Rudolph algorithm, which has recently…
The mean of a random variable can be understood as a linear functional on the space of probability distributions. Quantum computing is known to provide a quadratic speedup over classical Monte Carlo methods for mean estimation. In this…
Experimental attempts to implement quantum speedup of computations over the past 30 years have yielded a negative result, despite the absence of physical laws prohibiting such speedup. The article formulates the limitation of quantum…
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.…
This tutorial paper introduces quantum approaches to Monte Carlo computation with applications in computational finance. We outline the basics of quantum computing using Grover's algorithm for unstructured search to build intuition. We then…
We develop Monte Carlo methods for sampling random states and corresponding bit strings in qubit systems. To this end, we derive exact probability density functions that yield the Porter-Thomas distribution in the limit of large systems. We…
A quantum Monte Carlo method with non-local update scheme is presented. The method is based on a path-integral decomposition and a worm operator which is local in imaginary time. It generates states with a fixed number of particles and…
High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local…
We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known…
We investigate the issue of speed-up and the necessity of entanglement in Grover's quantum search algorithm. We find that in a pure state implementation of Grover's algorithm entanglement is present even though the initial and target states…
Quantum Monte Carlo methods are first-principle approaches that approximately solve the Schr\"odinger equation stochastically. As compared to traditional quantum chemistry methods, they offer important advantages such as the ability to…