Related papers: Solving Differential Equations via Continuous-Vari…
The paper presents a variational quantum algorithm to solve initial-boundary value problems described by second-order partial differential equations. The approach uses hybrid classical/quantum hardware that is well suited for quantum…
While quantum computing provides an exponential advantage in solving linear differential equations, there are relatively few quantum algorithms for solving nonlinear differential equations. In our work, based on the homotopy perturbation…
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…
The role of differential equations (DEs) in science and engineering is of paramount importance, as they provide the mathematical framework for a multitude of natural phenomena. Since quantum computers promise significant advantages over…
We consider the tasks of learning quantum states, measurements and channels generated by continuous-variable (CV) quantum circuits. This family of circuits is suited to describe optical quantum technologies and in particular it includes…
Variational quantum algorithms (VQAs) are a modern family of quantum algorithms designed to solve optimization problems using a quantum computer. Typically VQAs rely on a feedback loop between the quantum device and a classical optimization…
As quantum hardware rapidly advances toward the early fault-tolerant era, a key challenge is to develop quantum algorithms that are not only theoretically sound but also hardware-friendly on near-term devices. In this work, we propose a…
In this work, we present a quantum neighborhood preserving embedding and a quantum local discriminant embedding for dimensionality reduction and classification. We demonstrate that these two algorithms have an exponential speedup over their…
Realizing a large-scale quantum computer requires hardware platforms that can simultaneously achieve universality, scalability, and fault tolerance. As a viable pathway to meeting these requirements, quantum computation based on…
We present a variational quantum algorithm (VQA) to solve the nonlinear one-dimensional Bratu equation. By formulating the boundary value problem within a variational framework and encoding the solution in a parameterized quantum neural…
Quantum computers have the potential to deliver speed-ups for solving certain important problems that are intractable for classical counterparts, making them a promising avenue for advancing modern computation. However, many quantum…
For the solution of partial differential equations (PDEs), we show that the quantum Fourier transform (QFT) can enable the design of quantum circuits that are particularly simple, both conceptually and with regard to hardware requirements.…
Recent work in deep learning focuses on solving physical systems in the Ordinary Differential Equation or Partial Differential Equation. This current work proposed a variant of Convolutional Neural Networks (CNNs) that can learn the hidden…
The variational quantum eigensolver (VQE) is a method that uses a hybrid quantum-classical computational approach to find eigenvalues and eigenvalues of a Hamiltonian. VQE has been proposed as an alternative to fully quantum algorithms such…
We present an efficient quantum algorithm to simulate nonlinear differential equations with polynomial vector fields of arbitrary degree on quantum platforms. Models of physical systems that are governed by ordinary differential equations…
Variational Quantum Circuits (VQCs), or the so-called quantum neural-networks, are predicted to be one of the most important near-term quantum applications, not only because of their similar promises as classical neural-networks, but also…
The development of quantum computational techniques has advanced greatly in recent years, parallel to the advancements in techniques for deep reinforcement learning. This work explores the potential for quantum computing to facilitate…
Discrete-variable (DV) entanglement is crucial for numerous quantum applications, yet its deterministic generation in many bosonic systems remains experimentally challenging. In contrast, continuous-variable (CV) entanglement can be…
This paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs), a.k.a. (Ordinary) Difference Equations. It presents a new framework using these equations as a central tool for computation and…
In the last years, several quantum algorithms that try to address the problem of partial differential equation solving have been devised. On one side, "direct" quantum algorithms that aim at encoding the solution of the PDE by executing one…