Related papers: Fast quantum subroutines for the simplex method
We develop an efficient quantum implementation of an important signal processing algorithm for line spectral estimation: the matrix pencil method, which determines the frequencies and damping factors of signals consisting of finite sums of…
We study matrix multiplication in the low-bandwidth model: There are $n$ computers, and we need to compute the product of two $n \times n$ matrices. Initially computer $i$ knows row $i$ of each input matrix. In one communication round each…
We develop several efficient algorithms for the classical \emph{Matrix Scaling} problem, which is used in many diverse areas, from preconditioning linear systems to approximation of the permanent. On an input $n\times n$ matrix $A$, this…
Quantum computers promise to perform certain computations exponentially faster than any classical device. Precise control over their physical implementation and proper shielding from unwanted interactions with the environment become more…
We propose fast and practical quantum-inspired classical algorithms for solving linear systems. Specifically, given sampling and query access to a matrix $A\in\mathbb{R}^{m\times n}$ and a vector $b\in\mathbb{R}^m$, we propose classical…
Control of quantum operations is a crucial yet expensive construct for quantum computation. Efficient implementations of controlled operations often avoid applying control to certain subcircuits, which can significantly reduce the number of…
Matrix powering is a fundamental computational primitive in linear algebra. It has widespread applications in scientific computing and engineering, and underlies the solution of time-homogeneous linear ordinary differential equations,…
We provide new high-accuracy randomized algorithms for solving linear systems and regression problems that are well-conditioned except for $k$ large singular values. For solving such $d \times d$ positive definite system our algorithms…
In this paper, we give quantum algorithms for two fundamental computation problems: solving polynomial systems over finite fields and optimization where the arguments of the objective function and constraints take values from a finite field…
Circuit-augmentation algorithms are generalizations of the Simplex method, where in each step one is allowed to move along a fixed set of directions, called circuits, that is a superset of the edges of a polytope. We show that in the…
We present a novel quantum high-dimensional linear regression algorithm with an $\ell_1$-penalty based on the classical LARS (Least Angle Regression) pathwise algorithm. Similarly to available classical algorithms for Lasso, our quantum…
We propose a quantum data fitting algorithm for non-sparse matrices, which is based on the Quantum Singular Value Estimation (QSVE) subroutine and a novel efficient method for recovering the signs of eigenvalues. Our algorithm generalizes…
We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the…
We present an efficient quantum algorithm for simulating the evolution of a sparse Hamiltonian H for a given time t in terms of a procedure for computing the matrix entries of H. In particular, when H acts on n qubits, has at most a…
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…
We analyze the performance of a variant of Newton method with quadratic regularization for solving composite convex minimization problems. At each step of our method, we choose regularization parameter proportional to a certain power of the…
In this paper, a double-pivot simplex method is proposed. Two upper bounds of iteration numbers are derived. Applying one of the bounds to some special linear programming (LP) problems, such as LP with a totally unimodular matrix and Markov…
In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…
Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…
We provide an explicit recursive divide and conquer approach for simulating quantum dynamics and derive a discrete first quantized non-relativistic QED Hamiltonian based on the many-particle Pauli Fierz Hamiltonian. We apply this recursive…