Related papers: Quantum Quantile Mechanics: Solving Stochastic Dif…
We propose an approach for learning probability distributions as differentiable quantum circuits (DQC) that enable efficient quantum generative modelling (QGM) and synthetic data generation. Contrary to existing QGM approaches, we perform…
This work studies quantum algorithms to solve high-dimensional stochastic differential equations (SDEs) $\mathrm{d} \mathbf{X}_t = A(t) \mathbf{X}_t \mathrm{d} t + B(t) \mathrm{d} \mathbf{W}_t$. Aiming for a speed-up in the dimension $N$ of…
Stochastic differential equations (SDEs), which models uncertain phenomena as the time evolution of random variables, are exploited in various fields of natural and social sciences such as finance. Since SDEs rarely admit analytical…
Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization.…
Synthetic data generation has proven to be a promising solution for addressing data availability issues in various domains. Even more challenging is the generation of synthetic time series data, where one has to preserve temporal dynamics,…
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 propose several approaches for solving differential equations (DEs) with quantum kernel methods. We compose quantum models as weighted sums of kernel functions, where variables are encoded using feature maps and model derivatives are…
Modeling financial time series by stochastic processes is a challenging task and a central area of research in financial mathematics. As an alternative, we introduce Quant GANs, a data-driven model which is inspired by the recent success of…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…
Quantum computing has recently emerged as a transformative technology. Yet, its promised advantages rely on efficiently translating quantum operations into viable physical realizations. In this work, we use generative machine learning…
Quantum computers are gaining attention for their ability to solve certain problems faster than classical computers, and one example is the quantum expectation estimation algorithm that accelerates the widely-used Monte Carlo method in…
Generative modeling using samples drawn from the probability distribution constitutes a powerful approach for unsupervised machine learning. Quantum mechanical systems can produce probability distributions that exhibit quantum correlations…
We propose a quantum algorithm to solve systems of nonlinear differential equations. Using a quantum feature map encoding, we define functions as expectation values of parametrized quantum circuits. We use automatic differentiation to…
Given a quantum circuit, a quantum computer can sample the output distribution exponentially faster in the number of bits than classical computers. A similar exponential separation has yet to be established in generative models through…
Quantum circuits that generate coherent superpositions of stochastic processes are key to many downstream quantum-accelerated tasks, such as risk analysis, importance sampling, and DNA sequencing. However, traditional methods for designing…
Quantum generative adversarial networks (QGANs) have been investigated as a method for generating synthetic data with the goal of augmenting training data sets for neural networks. This is especially relevant for financial time series,…
Nonlinear stochastic differential equations (NSDEs) are a pillar of mathematical modeling for scientific and engineering applications. Accurate and efficient simulation of large-scale NSDEs is prohibitive on classical computers due to the…
Partial differential equation (PDE) models with multiple temporal/spatial scales are prevalent in several disciplines such as physics, engineering, and many others. These models are of great practical importance but notoriously difficult to…
Quantum algorithms have the potential to outperform their classical counterparts in a variety of tasks. The realization of the advantage often requires the ability to load classical data efficiently into quantum states. However, the best…
Quantum machine learning has recently attracted much attention from the community of quantum computing. In this paper, we explore the ability of generative adversarial networks (GANs) based on quantum computing. More specifically, we…