Related papers: Quantum Algorithms to Matrix Multiplication
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…
Quantum algorithms offer significant speed-ups over their classical counterparts in various applications. In this paper, we develop quantum algorithms for the Kalman filter widely used in classical control engineering using the block…
We present a quantum algorithm for estimating the matrix determinant based on quantum spectral sampling. The algorithm estimates the logarithm of the determinant of an $n \times n$ positive sparse matrix to an accuracy $\epsilon$ in time…
Despite the cloud enormous technical and financial advantages, security and privacy have always been the primary concern for adopting cloud computing facility, especially for government agencies and commercial sectors with high-security…
Understanding the singular value spectrum of a matrix $A \in \mathbb{R}^{n \times n}$ is a fundamental task in countless applications. In matrix multiplication time, it is possible to perform a full SVD and directly compute the singular…
We present a hybrid quantum-classical algorithm to simulate thermal states of a classical Hamiltonians on a quantum computer. Our scheme employs a sequence of locally controlled rotations, building up the desired state by adding qubits one…
MQuantum algorithms of matrix operations are of great significance in many fields in science and technology. In this paper, by leveraging multi-qubit Toffoli gates and basic single-qubit operations, the quantum algorithms of matrix…
Quantum algorithms for simulating large and complex molecular systems are still in their infancy, and surpassing state-of-the-art classical techniques remains an ever-receding goal post. A promising avenue of inquiry in the meanwhile is to…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
We present an algorithmic framework for quantum-inspired classical algorithms on close-to-low-rank matrices, generalizing the series of results started by Tang's breakthrough quantum-inspired algorithm for recommendation systems [STOC'19].…
Quantum computing provides a powerful framework for tackling computational problems that are classically intractable. The goal of this paper is to explore the use of quantum computers for solving relevant problems in systems and control…
Hybrid classical quantum optimization methods have become an important tool for efficiently solving problems in the current generation of NISQ computers. These methods use an optimization algorithm executed in a classical computer, fed with…
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…
Quantum algorithms can enhance machine learning in different aspects. In 2014, Rebentrost $et~al.$ constructed a least squares quantum support vector machine (LS-QSVM), in which the Swap Test plays a crucial role in realizing the…
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…
Quantum machine learning techniques have been proposed as a way to potentially enhance performance in machine learning applications. In this paper, we introduce two new quantum methods for neural networks. The first one is a quantum…
Optimal measurement is required to obtain the quantum and classical correlations of a quantum state, and the crucial difficulty is how to acquire the maximal information about one system by measuring the other part; in other words, getting…
Quantum oracles play key roles in the studies of quantum computation and quantum information. But implementing quantum oracles efficiently with universal quantum gates is a hard work. Motivated by genetic programming, this paper proposes a…
Quantum algorithms are a very promising field. However, creating and manipulating these kind of algorithms is a very complex task, specially for software engineers used to work at higher abstraction levels. The work presented here is part…
Electron-molecule collisions play a central role in both natural processes and modern technological applications, particularly in plasma processing. Conventional computational strategies such as the R-matrix method have been widely adopted…