Related papers: Quantum Algorithm for Solving a Quadratic Nonlinea…
Solving linear systems of equations is a frequently encountered problem in machine learning and optimisation. Given a matrix $A$ and a vector $\mathbf b$ the task is to find the vector $\mathbf x$ such that $A \mathbf x = \mathbf b$. We…
We propose a novel quantum algorithm for solving linear optimization problems by quantum-mechanical simulation of the central path. While interior point methods follow the central path with an iterative algorithm that works with successive…
In contexts where relevant problems can easily attain configuration spaces of enormous sizes, solving Linear Differential Equations (LDEs) can become a hard achievement for classical computers; on the other hand, the rise of quantum…
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…
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.…
Quantum adiabatic algorithm is of vital importance in quantum computation field. It offers us an alternative approach to manipulate the system instead of quantum gate model. Recently, an interesting work arXiv:1805.10549 indicated that we…
To approximate solutions of complex nonlinear partial differential equations remains a computational challenge, especially for sets of equations relevant in industry, such as Euler or Navier-Stokes equations. Even the most sophisticated…
Quantum computers are known to provide an exponential advantage over classical computers for the solution of linear differential equations in high-dimensional spaces. Here, we present a quantum algorithm for the solution of nonlinear…
Quantum linear system algorithms (QLSAs) for gate-based quantum computing can provide exponential speedups for solving linear systems but face challenges when applied to finite element problems due to the growth of the condition number with…
We present a quantum algorithm to solve systems of linear equations of the form $A\mathbf{x}=\mathbf{b}$, where $A$ is a tridiagonal Toeplitz matrix and $\mathbf{b}$ results from discretizing an analytic function, with a circuit complexity…
Systems of linear equations are used to model a wide array of problems in all fields of science and engineering. Recently, it has been shown that quantum computers could solve linear systems exponentially faster than classical computers,…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a $d$-dimensional system…
We present a quantum algorithm that analyzes time series data simulated by a quantum differential equation solver. The proposed algorithm is a quantum version of the dynamic mode decomposition algorithm used in diverse fields such as fluid…
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…
We transform the problem of solving linear system of equations $A\mathbf{x}=\mathbf{b}$ to a problem of finding the right singular vector with singular value zero of an augmented matrix $C$, and present two quantum algorithms for solving…
We present and experimentally realize a quantum algorithm for efficiently solving the following problem: given an $N\times N$ matrix $\mathcal{M}$, an $N$-dimensional vector $\textbf{\emph{b}}$, and an initial vector $\textbf{\emph{x}}(0)$,…
Nonlinear differential equations model diverse phenomena but are notoriously difficult to solve. While there has been extensive previous work on efficient quantum algorithms for linear differential equations, the linearity of quantum…
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 computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for…