Related papers: Efficient quantum algorithms for solving quantum l…
Solving linear systems of equations is a fundamental problem with a wide variety of applications across many fields of science, and there is increasing effort to develop quantum linear solver algorithms. [Suba\c{s}i et al., Phys. Rev. Lett.…
We present an efficient, nearly optimal quantum algorithm for solving linear matrix differential equations, with applications to the simulation of open quantum systems and beyond. For unitary or dissipative dynamics, the algorithm computes…
We demonstrate that with an optimally tuned scheduling function, adiabatic quantum computing (AQC) can readily solve a quantum linear system problem (QLSP) with $\mathcal{O}(\kappa~\text{poly}(\log(\kappa/\epsilon)))$ runtime, where…
Recently, several approaches to solving linear systems on a quantum computer have been formulated in terms of the quantum adiabatic theorem for a continuously varying Hamiltonian. Such approaches enabled near-linear scaling in the condition…
Harrow, Hassidim, and Lloyd showed that for a suitably specified $N \times N$ matrix $A$ and $N$-dimensional vector $\vec{b}$, there is a quantum algorithm that outputs a quantum state proportional to the solution of the linear system of…
Linear equations play a pivotal role in many areas of science and engineering, making efficient solutions to linear systems highly desirable. The development of quantum algorithms for solving linear systems has been a significant…
Quantum machine learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure…
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,…
We address the problem of solving a system of linear equations via the Quantum Singular Value Transformation (QSVT). One drawback of the QSVT algorithm is that it requires huge quantum resources if we want to achieve an acceptable accuracy.…
Quantum algorithms for solving the Quantum Linear System (QLS) problem are among the most investigated quantum algorithms of recent times, with potential applications including the solution of computationally intractable differential…
We establish an improved classical algorithm for solving linear systems in a model analogous to the QRAM that is used by quantum linear solvers. Precisely, for the linear system $A\x = \b$, we show that there is a classical algorithm that…
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
Finding a good approximation of the top eigenvector of a given $d\times d$ matrix $A$ is a basic and important computational problem, with many applications. We give two different quantum algorithms that, given query access to the entries…
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…
Solving systems of linear equations is a fundamental problem, but it can be computationally intensive for classical algorithms in high dimensions. Existing quantum algorithms can achieve exponential speedups for the quantum linear system…
We present a variational algorithm for fault tolerant quantum computing to solve a system of linear equations which directly maximises the parameters of the target fidelity. This so-called measurement test algorithm can be applied to any…
This work presents a quantum algorithm for solving linear systems of equations of the form $\mathbf{A}{\frac{\mathbf{\partial f}}{\mathbf{\partial x}}} = \mathbf{B}\mathbf{f}$, based on the Quantum Singular Value Transformation (QSVT). The…
Solving the Toeplitz systems, which is to find the vector $x$ such that $T_nx = b$ given an $n\times n$ Toeplitz matrix $T_n$ and a vector $b$, has a variety of applications in mathematics and engineering. In this paper, we present a…
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…