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Quantum computing and quantum Monte Carlo (QMC) are respectively the state-of-the-art quantum and classical computing methods for understanding many-body quantum systems. Here, we propose a hybrid quantum-classical algorithm that integrates…
Monte Carlo integration using quantum computers has been widely investigated, including applications to concrete problems. It is known that quantum algorithms based on quantum amplitude estimation (QAE) can compute an integral with a…
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…
It is known that quantum computers can speed up Monte Carlo simulation compared to classical counterparts. There are already some proposals of application of the quantum algorithm to practical problems, including quantitative finance. In…
Monte Carlo sampling is a powerful toolbox of algorithmic techniques widely used for a number of applications wherein some noisy quantity, or summary statistic thereof, is sought to be estimated. In this paper, we survey the literature for…
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…
We investigate the feasibility of integrating quantum algorithms as subroutines of simulation-based optimisation problems with relevance to and potential applications in mathematical finance. To this end, we conduct a thorough analysis of…
This paper proposes a method of quantum Monte Carlo integration that retains the full quadratic quantum advantage, without requiring any arithmetic or quantum phase estimation to be performed on the quantum computer. No previous proposal…
We present a quantum algorithm that analyzes risk more efficiently than Monte Carlo simulations traditionally used on classical computers. We employ quantum amplitude estimation to evaluate risk measures such as Value at Risk and…
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…
This Perspective focuses on the several overlaps between quantum algorithms and Monte Carlo methods in the domains of physics and chemistry. We will analyze the challenges and possibilities of integrating established quantum Monte Carlo…
Quantum Monte Carlo and quantum simulation are both important tools for understanding quantum many-body systems. As a classical algorithm, quantum Monte Carlo suffers from the sign problem, preventing its application to most fermion systems…
Quantum computers have a potential for solving quantum chemistry problems with higher accuracy than classical computers. Quantum computing quantum Monte Carlo (QC-QMC) is a QMC with a trial state prepared in quantum circuit, which is…
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…
Quantum algorithms present a quadratically improved complexity over classical ones for certain sampling tasks. For instance, the Quantum Amplitude Estimation (QAE) algorithm promises to speedup the estimation of the mean of certain…
We survey old and new results about optimal algorithms for summation of finite sequences and for integration of functions from Hoelder or Sobolev spaces. First we discuss optimal deterministic and randomized algorithms. Then we add a new…
Quantiles and expected shortfalls are usually used to measure risks of stochastic systems, which are often estimated by Monte Carlo methods. This paper focuses on the use of quasi-Monte Carlo (QMC) method, whose convergence rate is…
The main purpose of this article is to evaluate possible applications of quantum computers in foreign exchange reserves management. The capabilities of quantum computers are demonstrated by means of risk measurement using the quantum Monte…
Quasi-Monte Carlo (qMC) methods are a powerful alternative to classical Monte-Carlo (MC) integration. Under certain conditions, they can approximate the desired integral at a faster rate than the usual Central Limit Theorem, resulting in…
We present the Quantum Monte Carlo Integration (QMCI) engine developed by Quantinuum. It is a quantum computational tool for evaluating multi-dimensional integrals that arise in various fields of science and engineering such as finance.…