Related papers: Comparing quantum and classical Monte Carlo algori…
The main idea of this work is that the quantum-classical isomorphism is a suitable framework for a generalization of the notion of detailed balance. The quantum-classical isomorphism is used in order to develop a Monte Carlo simulation with…
Inspired by recent progress in quantum algorithms for ordinary and partial differential equations, we study quantum algorithms for stochastic differential equations (SDEs). Firstly we provide a quantum algorithm that gives a quadratic…
We looked into the algorithm for calculating Betti numbers presented by Lloyd, Garnerone, and Zanardi (LGZ). We present a new algorithm in the same spirit as LGZ with the intent of clarifying quantum algorithms for computing Betti numbers.…
We introduce several new quantum algorithms for estimating homological invariants, specifically Betti numbers and persistent Betti numbers, of a simplicial complex given via a structured classical input. At the core of our algorithm lies…
A hybrid quantum-classical algorithm is a computational scheme in which quantum circuits are used to extract information that is then processed by a classical routine to guide subsequent quantum operations. These algorithms are especially…
Standard quantum amplitude estimation algorithms provide quadratic speedup to Monte-Carlo simulations but require a circuit depth that scales as inverse of the estimation error. In view of the shallow depth in near-term devices, the…
This paper introduces quantum computing methods for Monte Carlo simulations in power systems which are expected to be exponentially faster than their classical computing counterparts. Monte Carlo simulations is a fundamental method, widely…
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 present a new non-local updating scheme for quantum Monte Carlo simulations, which conserves particle number and other symmetries. It allows exact symmetry projection and direct evaluation of the equal-time Green's function and other…
Topological data analysis has emerged as a powerful tool for analyzing large-scale data. An abstract simplicial complex, in principle, can be built from data points, and by using tools from homology, topological features could be…
Contemporary scientific studies often rely on the understanding of complex quantum systems via computer simulation. This paper initiates the statistical study of quantum simulation and proposes a Monte Carlo method for estimating…
Monte Carlo methods play a central role in particle physics, where they are indispensable for simulating scattering processes, modeling detector responses, and performing multi-dimensional integrals. However, traditional Monte Carlo methods…
Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the…
Complex networks contain complete subgraphs such as nodes, edges, triangles, etc., referred to as simplices and cliques of different orders. Notably, cavities consisting of higher-order cliques play an important role in brain functions.…
Quantum neural networks are deemed suitable to replace classical neural networks in their ability to learn and scale up network models using quantum-exclusive phenomena like superposition and entanglement. However, in the noisy intermediate…
Sampling from complicated probability distributions is a hard computational problem arising in many fields, including statistical physics, optimization, and machine learning. Quantum computers have recently been used to sample from…
Quantum computing (QC) has the potential to revolutionise the future of scientific simulations. To harness the capabilities that QC offers, we can integrate it into hybrid quantum-classical simulations, which can boost the capabilities of…
Quantum algorithms for topological data analysis (TDA) seem to provide an exponential advantage over the best classical approach while remaining immune to dequantization procedures and the data-loading problem. In this paper, we give…
We compare the performance of randomized classical and quantum neural networks (NNs) as well as classical and quantum-classical hybrid convolutional neural networks (CNNs) for the task of supervised binary image classification. We keep the…
The classical Langevin Monte Carlo method looks for samples from a target distribution by descending the samples along the gradient of the target distribution. The method enjoys a fast convergence rate. However, the numerical cost is…