Related papers: Quantum Amplitude Estimation for Probabilistic Met…
Classical Monte Carlo methods for pricing catastrophe insurance tail risk converge at order reciprocal root N, requiring large simulation budgets to resolve upper-tail percentiles of the loss distribution. This sample-sparsity problem can…
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…
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…
Software engineers often have to estimate the performance of a software system before having full knowledge of the system parameters, such as workload and operational profile. These uncertain parameters inevitably affect the accuracy of…
Quantum Monte Carlo methods are powerful techniques for studying strongly interacting Fermi systems. However, implementing these methods on computers with finite-precision arithmetic requires careful attention to numerical stability. In the…
Discrete stochastic processes (DSP) are instrumental for modelling the dynamics of probabilistic systems and have a wide spectrum of applications in science and engineering. DSPs are usually analyzed via Monte Carlo methods since the number…
We present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, an algorithm which provides a quadratic speedup compared to classical Monte Carlo methods. The options that we…
We perform a comprehensive analysis of the quantum-enhanced Monte Carlo method [Nature, 619, 282-287 (2023)], aimed at identifying the optimal working point of the algorithm. We observe an optimal mixing Hamiltonian strength and analyze the…
Heavy quark thermalization in the quark-gluon plasma (QGP) is one of the most promising phenomena for understanding the strong interaction, where their energy loss and momentum broadening at low momentum can be well described by a…
In this work, we provide the first QFT-free algorithm for Quantum Amplitude Estimation (QAE) that is asymptotically optimal while maintaining the leading numerical performance. QAE algorithms appear as a subroutine in many applications for…
Multilevel sampling methods, such as multilevel and multifidelity Monte Carlo, multilevel stochastic collocation, or delayed acceptance Markov chain Monte Carlo, have become standard uncertainty quantification (UQ) tools for a wide class of…
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 discuss how quantum computation can be applied to financial problems, providing an overview of current approaches and potential prospects. We review quantum optimization algorithms, and expose how quantum annealers can be used to…
Quantum Monte Carlo (QMC) methods can very accurately compute ground state properties of quantum systems. We applied these methods to a system of boson hard spheres to get exact, infinite system size results for the ground state at several…
A Monte Carlo algorithm for computing quantum mechanical expectation values of coordinate operators in many body problems is presented. The algorithm, that relies on the forward walking method, fits naturally in a Green's Function Monte…
Monte Carlo is a versatile and frequently used tool in statistical physics and beyond. Correspondingly, the number of algorithms and variants reported in the literature is vast, and an overview is not easy to achieve. In this pedagogical…
Random batch algorithms are constructed for quantum Monte Carlo simulations. The main objective is to alleviate the computational cost associated with the calculations of two-body interactions, including the pairwise interactions in the…
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…
Quantum error mitigation (QEM) is a class of promising techniques for reducing the computational error of variational quantum algorithms. In general, the computational error reduction comes at the cost of a sampling overhead due to the…
The maximum likelihood amplitude estimation algorithm (MLAE) is a practical solution to the quantum amplitude estimation problem with Heisenberg limit error convergence. We improve MLAE by using random depths to avoid the so-called critical…