Related papers: Solving nonlinear PDEs with Quantum Neural Network…
The prosperous development of both hardware and algorithms for quantum computing (QC) potentially prompts a paradigm shift in scientific computing in various fields. As an increasingly active topic in QC, the variational quantum algorithm…
Quantum algorithms to integrate nonlinear PDEs governing flow problems are challenging to discover but critical to enhancing the practical usefulness of quantum computing. We present here a near-optimal, robust, and end-to-end quantum…
We propose a quantum machine learning framework for approximating solutions to high-dimensional parabolic partial differential equations (PDEs) that can be reformulated as backward stochastic differential equations (BSDEs). In contrast to…
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…
A recently proposed variational quantum algorithm has expanded the horizon of variational quantum computing to nonlinear physics and fluid dynamics. In this work, we probe the ability of such approaches to capture the ground state of the…
Variational Quantum Algorithms (VQAs) provide a promising framework for tackling complex optimization problems on near-term quantum hardware. Here, we demonstrate that hybrid qubit--qumode quantum devices offer an efficient route to solving…
Applying low-depth quantum neural networks (QNNs), variational quantum algorithms (VQAs) are both promising and challenging in the noisy intermediate-scale quantum (NISQ) era: Despite its remarkable progress, criticisms on the efficiency…
Variational Quantum Algorithms (VQAs) are a promising approach to leverage Noisy Intermediate-Scale Quantum (NISQ) computers. However, choosing optimal quantum circuits that efficiently solve a given VQA problem is a non-trivial task.…
Variational quantum algorithms (VQAs) incorporate hybrid quantum-classical computation aimed at harnessing the power of noisy intermediate-scale quantum (NISQ) computers to solve challenging computational problems. In this thesis, three…
In this paper, we propose and study neural network based methods for solutions of high-dimensional quadratic porous medium equation (QPME). Three variational formulations of this nonlinear PDE are presented: a strong formulation and two…
We propose a neural-network variational quantum algorithm to simulate the time evolution of quantum many-body systems. Based on a modified restricted Boltzmann machine (RBM) wavefunction ansatz, the proposed algorithm can be efficiently…
We present a novel variational quantum framework for linear partial differential equation (PDE) constrained optimization problems. Such problems arise in many scientific and engineering domains. For instance, in aerodynamics, the PDE…
In the present noisy intermediate scale quantum computing era, there is a critical need to devise methods for the efficient implementation of gate-based variational quantum circuits. This ensures that a range of proposed applications can be…
The Variational Quantum Algorithms (VQAs) are hybrid quantum-classical algorithms and they can be used in the Nosiy Intermadiate Scale Quantum (NISQ) devises. The Variational Quantum Eigensolver (VQE) was suggested as a first VQA. VQE is…
Quadratic Unconstrained Binary Optimization (QUBO) is a broad class of optimization problems with many practical applications. To solve its hard instances in an exact way, known classical algorithms require exponential time and several…
Solving combinatorial optimization problems on near-term quantum devices has gained a lot of attraction in recent years. Currently, most works have focused on single-objective problems, whereas many real-world applications need to consider…
This paper presents methodological improvements to variational quantum algorithms (VQAs) for solving multicriteria optimization problems. We introduce two key contributions. First, we reformulate the parameter optimization task of VQAs as a…
We propose a method combining boundary integral equations and neural networks (BINet) to solve partial differential equations (PDEs) in both bounded and unbounded domains. Unlike existing solutions that directly operate over original PDEs,…
Quantum annealers can solve QUBO problems efficiently but struggle with continuous optimization tasks like regression due to their discrete nature. We introduce Quadratic Continuous Quantum Optimization (QCQO), an anytime algorithm that…
Quantum computers promise a great computational advantage over classical computers, yet currently available quantum devices have only a limited amount of qubits and a high level of noise, limiting the size of problems that can be solved…