Related papers: A square-root speedup for finding the smallest eig…
This work presents a novel approach to compute the eigenvalues of non-Hermitian matrices using an enhanced shifted QR algorithm. The existing QR algorithms fail to converge early in the case of non-hermitian matrices, and our approach shows…
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 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 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…
This work concerns the global minimization of a prescribed eigenvalue or a weighted sum of prescribed eigenvalues of a Hermitian matrix-valued function depending on its parameters analytically in a box. We describe how the analytical…
Gradient descent is one of the most basic algorithms for solving continuous optimization problems. In [Jordan, PRL, 95(5):050501, 2005], Jordan proposed the first quantum algorithm for estimating gradients of functions close to linear, with…
A framework is presented for the design and analysis of quantum mechanical algorithms, the sqrt(N) step quantum search algorithm is an immediate consequence of this framework. It leads to several other search-type applications - several…
Vector set orthogonal normalization and matrix QR decomposition are fundamental problems in matrix analysis with important applications in many fields. We know that Gram-Schmidt process is a widely used method to solve these two problems.…
The eigenvalue density of a matrix plays an important role in various types of scientific computing such as electronic-structure calculations. In this paper, we propose a quantum algorithm for computing the eigenvalue density in a given…
Finding a Hadamard matrix of a specific order using a quantum computer can lead to a demonstration of practical quantum advantage. Earlier efforts using a quantum annealer were impeded by the limitations of the present quantum resource and…
We consider the problem of estimating the expected outcomes of Monte Carlo processes whose outputs are described by multidimensional random variables. We tightly characterize the quantum query complexity of this problem for various choices…
We propose and study an algorithm for computing a nearest passive system to a given non-passive linear time-invariant system (with much freedom in the choice of the metric defining `nearest', which may be restricted to structured…
Quantum phase estimation algorithm has been successfully adapted as a sub frame of many other algorithms applied to a wide variety of applications in different fields. However, the requirement of a good approximate eigenvector given as an…
We present quantum algorithms, for Hamiltonians of linear combinations of local unitary operators, for Hamiltonian matrix-vector products and for preconditioning with the inverse of shifted reduced Hamiltonian operator that contributes to…
Hamiltonian simulation is a domain where quantum computers have the potential to outperform their classical counterparts. One of the main challenges of such quantum algorithms is increasing the system size, which is necessary to achieve…
We present a fast Jacobi-like algorithm for computing the eigenvalues, and optionally the eigenvectors, of a real normal matrix. The method gains a computational advantage by using Paardekooper's method for skew-symmetric matrices The…
We present the NMR implementation of a recently proposed quantum algorithm to find the parity of a permutation. In the usual qubit model of quantum computation, speedup requires the presence of entanglement and thus cannot be achieved by a…
We propose a novel parallel numerical algorithm for calculating the smallest eigenvalues of highly ill-conditioned matrices. It is based on the {\it LDLT} decomposition and involves finding a $k \times k$ sub-matrix of the inverse of the…
This paper presents a hybrid variational quantum algorithm that finds a random eigenvector of a unitary matrix with a known quantum circuit. The algorithm is based on the SWAP test on trial states generated by a parametrized quantum…
We propose quantum algorithms, purely quantum in nature, for calculating the determinant and inverse of an $(N-1)\times (N-1)$ matrix (depth is $O(N^2\log N)$) which is a simple modification of the algorithm for calculating the determinant…