Related papers: Tensor-Programmable Quantum Circuits for Solving D…
This article proposes a Variational Quantum Algorithm to solve linear and nonlinear thermofluid dynamic transport equations. The hybrid classical-quantum framework is applied to problems governed by the heat, wave, and Burgers' equation in…
Quantum computing, leveraging principles of quantum mechanics, represents a transformative approach in computational methodologies, offering significant enhancements over traditional classical systems. This study tackles the complex and…
Quantum computing uses the physical principles of very small systems to develop computing platforms which can solve problems that are intractable on conventional supercomputers. There are challenges not only in building the required…
Fault-tolerant quantum computing is a promising technology to solve linear partial differential equations that are classically demanding to integrate. It is still challenging to solve non-linear equations in fluid dynamics, such as the…
The article provides a framework to solve linear differential equations based on partial commutativity which is introduced by means of the Fedorov theorem. The framework is applied to specific types of three-level and four-level quantum…
Efficient quantum circuit optimization schemes are central to quantum simulation of strongly interacting quantum many body systems. Here, we present an optimization algorithm which combines machine learning techniques and tensor network…
In recent times, Variational Quantum Circuits (VQC) have been widely adopted to different tasks in machine learning such as Combinatorial Optimization and Supervised Learning. With the growing interest, it is pertinent to study the…
Quantum computation offers a promising alternative to classical computing methods in many areas of numerical science, with algorithms that make use of the unique way in which quantum computers store and manipulate data often achieving…
Variational Quantum algorithms, especially Quantum Approximate Optimization and Variational Quantum Eigensolver (VQE) have established their potential to provide computational advantage in the realm of combinatorial optimization. However,…
The variational principle serves as a fundamental framework for describing equilibrium states of physical systems via the minimization or extremization of an energy-like functional. While quantum algorithms have demonstrated promising…
A hybrid algorithm based on machine learning and quantum ensemble learning is proposed that is capable of finding a solution to a partial differential equation with good precision and favorable scaling in the required number of qubits. The…
We introduce a hybrid quantum-classical framework for efficiently implementing approximate unitary dilations of non-unitary operators with enhanced noise resilience. The method embeds a target non-unitary operator into a subblock of a…
The solution for non-linear, complex partial differential Equations (PDEs) is achieved through numerical approximations, which yield a linear system of equations. This approach is prevalent in Computational Fluid Dynamics (CFD), but it…
Time-dependent linear differential equations are a common type of problem that needs to be solved in classical physics. Here we provide a quantum algorithm for solving time-dependent linear differential equations with logarithmic dependence…
The accurate computation of ground and excited states of many-fermion quantum systems is one of the most consequential, contemporary challenges in the physical and computational sciences whose solution stands to benefit significantly from…
Most modern classical processors support so-called von Neumann architecture with program and data registers. In present work is revisited similar approach to models of quantum processors. Deterministic programmable quantum gate arrays are…
Recently J. M. Arrazola et al. [Phys. Rev. A 100, 032306 (2019)] proposed a quantum algorithm for solving nonhomogeneous linear partial differential equations of the form $A\psi(\textbf{r})=f(\textbf{r})$. Its nonhomogeneous solution is…
Constructing general programmable circuits to be able to run any given unitary operator efficiently on a quantum processor is of fundamental importance. We present a new quantum circuit design technique resulting two general programmable…
Partial differential equations (PDEs) are crucial for modeling various physical phenomena such as heat transfer, fluid flow, and electromagnetic waves. In computer-aided engineering (CAE), the ability to handle fine resolutions and large…
Gaussian processes are widely known for their ability to provide probabilistic predictions in supervised machine learning models. Their non-parametric nature and flexibility make them particularly effective for regression tasks. However,…