相关论文: Pauli Decomposition via the Fast Walsh-Hadamard Tr…

We consider a quantum computation that only extracts one bit of information per $N$-qubit quantum state preparation. This is relevant for error mitigation schemes where the remainder of the system is measured to detect errors. We optimize…

In this paper we show how we can compute in a deterministic way the decomposition of a multivariate rational function with a recombination strategy. The key point of our recombination strategy is the used of Darboux polynomials. We study…

In the paper we analyse the exact solutions to scalar PDEs obtained thanks to summable Taylor series provided by Adomian's decomposition method. We propose the modification of the method which makes the calculations of Taylor coefficients…

Dey and Xin (J.Appl.Comput.Top., 2022, arXiv:1904.03766) describe an algorithm to decompose finitely presented multiparameter persistence modules using a matrix reduction algorithm. Their algorithm only works for modules whose generators…

The Pauli channel acting on 2 x 2 matrices is generalized to an n-level quantum system. When the full matrix algebra M is decomposed into pairwise complementary subalgebras, then trace-preserving linear mappings from M to M are constructed…

Quantum signal processing is a framework for implementing polynomial functions on quantum computers. To implement a given polynomial $P$, one must first construct a corresponding complementary polynomial $Q$. Existing approaches to this…

This paper develops fast and efficient algorithms for computing Tucker decomposition with a given multilinear rank. By combining random projection and the power scheme, we propose two efficient randomized versions for the truncated…

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…

We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning,…

A rapid transformation is derived between spherical harmonic expansions and their analogues in a bivariate Fourier series. The change of basis is described in two steps: firstly, expansions in normalized associated Legendre functions of all…

Variational inference offers scalable and flexible tools to tackle intractable Bayesian inference of modern statistical models like Bayesian neural networks and Gaussian processes. For largely over-parameterized models, however, the…

Algorithms are developed for calculating dealiased linear convolution sums without the expense of conventional zero-padding or phase-shift techniques. For one-dimensional in-place convolutions, the memory requirements are identical with the…

In the paper (math-ph/0504049) Jarlskog gave an interesting simple parametrization to unitary matrices, which was essentially the canonical coordinate of the second kind in the Lie group theory (math-ph/0505047). In this paper we apply the…

Inverse Vandermonde matrix calculation is a long-standing problem to solve nonsingular linear system $Vc=b$ where the rows of a square matrix $V$ are constructed by progression of the power polynomials. It has many applications in…

Invariance transformations of polyadic decompositions of matrix multiplication tensors define an equivalence relation on the set of such decompositions. In this paper, we present an algorithm to efficiently decide whether two polyadic…

We consider a $Q$-polynomial distance-regular graph $\Gamma$ with vertex set $X$ and diameter $D \geq 3$. For $\mu, \nu \in \lbrace \downarrow, \uparrow \rbrace$ we define a direct sum decomposition of the standard module $V=\C X$, called…

Gaussian elimination with full pivoting generates a PLUQ matrix decomposition. Depending on the strategy used in the search for pivots, the permutation matrices can reveal some information about the row or the column rank profiles of the…

In this work, we present a new algorithm for generating quantum circuits that efficiently implement continuous time quantum walks on arbitrary simple sparse graphs. The algorithm, called matching decomposition, works by decomposing a…

This paper provides the spectral decomposition of $(\star,\epsilon)$-palindromic quadratic matrix polynomial $P(\lambda)$ by a standard pair and a parameter matrix. When $J$ is assumed to be a block diagonal matrix, the parameter matrix…

We introduce matrix-valued weight functions of arbitrary size, which are analogues of the weight function for the Gegenbauer or ultraspherical polynomials for the parameter $\nu>0$. The LDU-decomposition of the weight is explicitly given in…