Related papers: Quantum-inspired sublinear classical algorithms fo…
Low rank approximation of matrices has been well studied in literature. Singular value decomposition, QR decomposition with column pivoting, rank revealing QR factorization (RRQR), Interpolative decomposition etc are classical deterministic…
This paper presents a complete algorithmic study of the decision Boolean Satisfiability Problem under the classical computation and quantum computation theories. The paper depicts deterministic and probabilistic algorithms, propositions of…
We present classical and quantum algorithms based on spectral methods for a problem in tensor principal component analysis. The quantum algorithm achieves a quartic speedup while using exponentially smaller space than the fastest classical…
The Fokker-Planck equation models rare events across sciences, but its high-dimensional nature challenges classical computers. Quantum algorithms for such non-unitary dynamics often suffer from exponential {decay in} success probability. We…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
We introduce a new quantum optimization algorithm for dense Linear Programming problems, which can be seen as the quantization of the Interior Point Predictor-Corrector algorithm \cite{Predictor-Corrector} using a Quantum Linear System…
Recent studies on quantum computing algorithms focus on excavating features of quantum computers which have potential for contributing to computational model enhancements. Among various approaches, quantum annealing methods effectively…
It has recently been shown that starting with a classical query algorithm (decision tree) and a guessing algorithm that tries to predict the query answers, we can design a quantum algorithm with query complexity $O(\sqrt{GT})$ where $T$ is…
Time-dependent linear differential equations are a common type of problem that needs to be solved in classical physics. Here we provide a quantum algorithm for solving time-dependent linear differential equations with logarithmic dependence…
We propose a new approach to utilize quantum computers for binary linear programming (BLP), which can be extended to general integer linear programs (ILP). Quantum optimization algorithms, hybrid or quantum-only, are currently general…
In this paper, we present two tensor network quantum-inspired algorithms to solve the knapsack and the shortest path problems, and enables to solve some of its variations. These methods provide an exact equation which returns the optimal…
This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as…
A hybrid quantum-classical algorithm is a computational scheme in which quantum circuits are used to extract information that is then processed by a classical routine to guide subsequent quantum operations. These algorithms are especially…
Binary Neural Networks are a promising technique for implementing efficient deep models with reduced storage and computational requirements. The training of these is however, still a compute-intensive problem that grows drastically with the…
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 $\textbf{\emph{x}}(0)$,…
We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of…
This paper presents a weakly intrusive strategy for computing a low-rank approximation of the solution of a system of nonlinear parameter-dependent equations. The proposed strategy relies on a Newton-like iterative solver which only…
The solution of linear systems of equations is a very frequent operation and thus important in many fields. The complexity using classical methods increases linearly with the size of equations. The HHL algorithm proposed by Harrow et al.…
CUR matrix decomposition is a randomized algorithm that can efficiently compute the low rank approximation for a given rectangle matrix. One limitation with the existing CUR algorithms is that they require an access to the full matrix A for…
Solving linear systems is of great importance in numerous fields. Proposed quantum algorithms for preparing solutions for linear systems include the HHL algorithm with subsequent refinements and variational methods. Circulant linear systems…