Related papers: Quantum Quantile Mechanics: Solving Stochastic Dif…
Partial differential equations (PDEs) play a crucial role in financial mathematics, particularly in portfolio optimization, and solving them using classical numerical or neural network methods has always posed significant challenges. Here,…
Parameterized quantum circuits (PQCs), as one of the most promising schemes to realize quantum machine learning algorithms on near-term quantum computers, have been designed to solve machine earning tasks with quantum advantages. In this…
This paper introduces a new approach to generating sample paths of unknown Markovian stochastic differential equations (SDEs) using diffusion models, a class of generative AI methods commonly employed in image and video applications. Unlike…
Quantum neural networks are expected to be a promising application in near-term quantum computing, but face challenges such as vanishing gradients during optimization and limited expressibility by a limited number of qubits and shallow…
Diffusion processes with branching play an important role in statistical dynamics. They are a common approach to the computing of quantum mechanical groundstates, and serve as models for population dynamics and as physical pictures for…
This study examines the potential for fault-tolerant quantum computers to provide utility in fluid dynamics simulations, with a focus on drag force calculations for ship hull design. We assess whether quantum algorithms can surpass…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…
In the quantum Monte Carlo (QMC) method, the Pseudo-Random Number Generator (PRNG) plays a crucial role in determining the computation time. However, the hidden structure of the PRNG may lead to serious issues such as the breakdown of the…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
State-of-the-art computer codes for simulating real physical systems are often characterized by a vast number of input parameters. Performing uncertainty quantification (UQ) tasks with Monte Carlo (MC) methods is almost always infeasible…
Quantum data loading plays a central role in quantum algorithms and quantum information processing. Many quantum algorithms hinge on the ability to prepare arbitrary superposition states as a subroutine, with claims of exponential speedups…
A dynamical quantum model assigns an eigenstate to a specified observable even when no measurement is made, and gives a stochastic evolution rule for that eigenstate. Such a model yields a distribution over classical histories of a quantum…
Demonstrating quantum advantage using conventional quantum algorithms remains challenging on current noisy gate-based quantum computers. Automated quantum circuit synthesis via quantum machine learning has emerged as a promising solution,…
Linear dissipative differential equation is a fundamental model for a large number of physical systems, such as quantum dynamics with non-Hermitian Hamiltonian, open quantum system dynamics, diffusion process and damped system. In this…
The intensive computation and memory requirements of generative adversarial neural networks (GANs) hinder its real-world deployment on edge devices such as smartphones. Despite the success in model reduction of CNNs, neural network…
Quantum Diffusion Models (QDMs) are an emerging paradigm in Generative AI that aims to use quantum properties to improve the performances of their classical counterparts. However, existing algorithms are not easily scalable due to the…
Recent research has shown that wavefunction evolution in real- and imaginary-time can generate quantum subspaces with significant utility for obtaining accurate ground state energies. Inspired by these methods, we propose combining quantum…
Recent breakthroughs in generative machine learning, powered by massive computational resources, have demonstrated unprecedented human-like capabilities. While beyond-classical quantum experiments can generate samples from classically…
Solving a quadratic nonlinear system of equations (QNSE) is a fundamental, but important, task in nonlinear science. We propose an efficient quantum algorithm for solving $n$-dimensional QNSE. Our algorithm embeds QNSE into a…
Quantile regression is an effective technique to quantify uncertainty, fit challenging underlying distributions, and often provide full probabilistic predictions through joint learnings over multiple quantile levels. A common drawback of…