Related papers: Variational Quantum Linear Solver for Simulating Q…
Superconducting quantum circuits are promising candidate for building scalable quantum computers. Here, we use a four-qubit superconducting quantum processor to solve a two-dimensional system of linear equations based on a quantum algorithm…
Quantum computing holds promise across various fields, particularly with the advent of Noisy Intermediate-Scale Quantum (NISQ) devices, which can outperform classical supercomputers in specific tasks. However, challenges such as noise and…
A kernel-based quantum classifier is the most practical and influential quantum machine learning technique for the hyper-linear classification of complex data. We propose a Variational Quantum Approximate Support Vector Machine (VQASVM)…
We present a scalable algorithm for solving the transport equation in two and three spatial dimensions for variable grid sizes and discrete velocities on a fault-tolerant universal quantum computer. As a proof of concept of our quantum…
We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing mid-circuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of…
Routing problems are a common optimization problem in industrial applications, which occur on a large scale in supply chain planning. Due to classical limitations for solving NP-hard problems, quantum computing hopes to improve upon speed…
Linear systems of equations can be found in various mathematical domains, as well as in the field of machine learning. By employing noisy intermediate-scale quantum devices, variational solvers promise to accelerate finding solutions for…
As the characteristic lengths of advanced electronic devices are approaching the atomic scale, ab initio simulation method, with fully consideration of quantum mechanical effects, becomes essential to study the quantum transport phenomenon…
Extracting eigenvalues and eigenvectors of exponentially large matrices will be an important application of near-term quantum computers. The Variational Quantum Eigensolver (VQE) treats the case when the matrix is a Hamiltonian. Here, we…
We develop a hybrid classical-quantum method for solving the Lorenz system. We use the forward Euler method to discretize the system in time, transforming it into a system of equations. This set of equations is solved using the Variational…
Modeling nanoscale devices quantum mechanically is a computationally challenging problem where new methods to solve the underlying equations are in a dire need. In this paper, we present an approach to calculate the charge density in…
This paper explores the application of tensor networks (TNs) to the simulation of material deformations within the framework of linear elasticity. Material simulations are essential computational tools extensively used in both academic…
Quantum nanosystems involve the coupled dynamics of fermions or bosons across multiple scales in space and time. Examples include quantum dots, superconducting or magnetic nanoparticles, molecular wires, and graphene nanoribbons. The number…
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…
We develop robust and scalable fully implicit nonlinear finite element solvers for the simulations of biological transportation networks driven by the gradient flow minimization of a non-convex energy cost functional. Our approach employs a…
While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…
In recent years, predictive computational modeling has become a cornerstone for the study of fundamental electronic, optical, and thermal properties in complex forms of condensed matter, including Dirac and topological materials. The…
The variational quantum eigensolver (or VQE) uses the variational principle to compute the ground state energy of a Hamiltonian, a problem that is central to quantum chemistry and condensed matter physics. Conventional computing methods are…
Due to the success of the Standard Model~(SM), it is reasonable to anticipate that the signal of new physics~(NP) beyond the SM is small. Consequently, future searches for NP and precision tests of the SM will require high luminosity…
Solving linear systems of equations plays a fundamental role in numerous computational problems from different fields of science. The widespread use of numerical methods to solve these systems motivates investigating the feasibility of…