Related papers: Comparison of Multi-quark Matrix Inversion Algorit…
The quantum permutation algorithm provides computational speed-up over classical algorithms in determining the parity of a given cyclic permutation. For its $n$-qubit implementations, the number of required quantum gates scales…
An efficient error reconciliation scheme is important for post-processing of quantum key distribution (QKD). Recently, a multi-matrix low-density parity-check codes based reconciliation algorithm which can provide remarkable perspectives…
In this paper, we study quantum algorithms of matrix multiplication from the viewpoint of inputting quantum/classical data to outputting quantum/classical data. The main target is trying to overcome the input and output problem, which are…
Matrix multiplication consumes a large fraction of the time taken in many machine-learning algorithms. Thus, accelerator chips that perform matrix multiplication faster than conventional processors or even GPU's are of increasing interest.…
In this paper we present computational experiments with the Markov Chain Monte Carlo Matrix Inversion ($(\text{MC})^2\text{MI}$) on several accelerator architectures and investigate their impact on performance and scalability of the method.…
The efficient preparation of input distributions is an important problem in obtaining quantum advantage in a wide range of domains. We propose a novel quantum algorithm for the efficient preparation of arbitrary normal distributions in…
We call matrix algorithms superfast if they use much fewer flops and memory cells than the input matrix has entries. Using such algorithms is indispensable for Big Data Mining and Analysis, where the input matrices are so immense that one…
We evaluate the accuracy of the quantum inverse (Q-Inv) algorithm in which the multiplication of $\hat{H}^{-k}$ to the reference wavefunction is replaced by the Fourier Transformed multiplication of $e^{-i\lambda \hat{H}}$, as a function of…
In this paper we focus on the solution of shifted quasiseparable systems and of more general parameter dependent matrix equations with quasiseparable representations. We propose an efficient algorithm exploiting the invariance of the…
We investigate effects of ordering in blocked matrix--matrix multiplication. We find that submatrices do not have to be stored contiguously in memory to achieve near optimal performance. Instead it is the choice of execution order of the…
In this paper we derive and analyze an algorithm for inverting quaternion matrices. The algorithm is an analogue of the Frobenius algorithm for the complex matrix inversion. On the theory side, we prove that our algorithm is more efficient…
$k$-diagonal circulant matrices and cyclic banded matrices are widely used in numerical simulations and signal processing of circular linear systems. Algorithms that directly involve or specify linear or quadratic complexity for the…
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…
Non-negative Matrix Factorization(NMF) algorithm can only be used to find low rank approximation of original non-negative data while Concept Factorization(CF) algorithm extends matrix factorization to single non-linear kernel space,…
Quantum-dot cellular automata (QCA) shows promise as a post silicon CMOS, low power computational technology. Nevertheless, to generalize QCA for next-generation digital devices, the ability to implement conventional programmable circuits…
Matrix multiplication is fundamental in the backpropagation algorithm used to train deep neural network models. Libraries like Intel's MKL or NVIDIA's cuBLAS implemented new and optimized matrix multiplication techniques that increase…
This article presents matrix backpropagation algorithms for the QR decomposition of matrices $A_{m, n}$, that are either square (m = n), wide (m < n), or deep (m > n), with rank $k = min(m, n)$. Furthermore, we derive novel matrix…
Results on the computational efficiency of 2-flavor staggered Wilson fermions compared to usual Wilson fermions in a quenched lattice QCD simulation on $16^3\times32$ lattice at $\beta=6$ are reported. We compare the cost of inverting the…
The number of parameters in deep neural networks (DNNs) is rapidly increasing to support complicated tasks and to improve model accuracy. Correspondingly, the amount of computations and required memory footprint increase as well.…
Polynomial approximations to the inverse of the fermion matrix are used to filter the dynamics of the upper energy scales in HMC simulations. The use of a multiple time-scale integration scheme allows the filtered pseudofermions to be…