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Quantum simulation, the simulation of quantum processes on quantum computers, suggests a path forward for the efficient simulation of problems in condensed-matter physics, quantum chemistry, and materials science. While the majority of…
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.…
Randomized algorithms for very large matrix problems have received a great deal of attention in recent years. Much of this work was motivated by problems in large-scale data analysis, and this work was performed by individuals from many…
We study the practical performance of quantum-inspired algorithms for recommendation systems and linear systems of equations. These algorithms were shown to have an exponential asymptotic speedup compared to previously known classical…
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…
Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant quantum computers. In this work, we propose variational algorithms for…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
Linear regression is a widely used technique to fit linear models and finds widespread applications across different areas such as machine learning and statistics. In most real-world scenarios, however, linear regression problems are often…
Random quantum circuits have been utilized in the contexts of quantum supremacy demonstrations, variational quantum algorithms for chemistry and machine learning, and blackhole information. The ability of random circuits to approximate any…
Quantum algorithms typically demand prohibitively complicated circuits to solve practical problems. Previous studies have shown that classical randomness can accelerate some specific quantum algorithms. In this work, we introduce the…
Quantum algorithms and complexity have recently been studied not only for discrete, but also for some numerical problems. Most attention has been paid so far to the integration problem, for which a speed-up is shown by quantum computers…
Randomized linear solvers randomly compress and solve a linear system with compelling theoretical convergence rates and computational complexities. However, such solvers suffer a substantial disconnect between their theoretical rates and…
We consider deterministic and {\em randomized} quantum algorithms simulating $e^{-iHt}$ by a product of unitary operators $e^{-iA_jt_j}$, $j=1,...,N$, where $A_j\in\{H_1,...,H_m\}$, $H=\sum_{i=1}^m H_i$ and $t_j > 0$ for every $j$.…
Computational fluid dynamics lies at the heart of many issues in science and engineering, but solving the associated partial differential equations remains computationally demanding. With the rise of quantum computing, new approaches have…
Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing…
We describe an improved version of the quantum simulation method based on the implementation of a truncated Taylor series of the evolution operator. The idea is to add an extra step to the previously known algorithm which implements an…
Randomized iterative algorithms have attracted much attention in recent years because they can approximately solve large-scale linear systems of equations without accessing the entire coefficient matrix. In this paper, we propose two novel…
Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations. Using the "Sender-Receiver" model, we propose quantum algorithms for matrix operations such as matrix-vector product,…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
We introduce the first randomized algorithms for Quantum Singular Value Transformation (QSVT), a unifying framework for many quantum algorithms. Standard implementations of QSVT rely on block encodings of the Hamiltonian, which are costly…