Related papers: Efficient long division via Montgomery multiply
Splitting methods are widely used for solving initial value problems (IVPs) due to their ability to simplify complicated evolutions into more manageable subproblems which can be solved efficiently and accurately. Traditionally, these…
I will present a new method for thinking about and for computing loop integrals based on differential equations. All required information is obtained by algebraic means and is encoded in a small set of simple quantities that I will…
Faced with saturation of Moore's law and increasing dimension of data, system designers have increasingly resorted to parallel and distributed computing. However, distributed computing is often bottle necked by a small fraction of slow…
The BMR16 circuit garbling scheme introduces gadgets that allow for ciphertext-free modular addition, while the multiplication of private inputs modulo a prime p can be done with 2(p - 1) ciphertexts as described in Malkin, Pastro, and…
We propose a novel multi-dimensional integration algorithm using a machine learning (ML) technique. After training a ML regression model to mimic a target integrand, the regression model is used to evaluate an approximation of the integral.…
It is well known that the repeated square and multiply algorithm is an efficient way of modular exponentiation. The obvious question to ask is if this algorithm has an inverse which would calculate the discrete logarithm efficiently. The…
We present a novel and efficient in terms of circuit depth design for Shor's quantum factorization algorithm. The circuit effectively utilizes a diverse set of adders based on the quantum Fourier transform (QFT) Draper's adders to build…
We propose two coded schemes for the distributed computing problem of multiplying a matrix by a set of vectors. The first scheme is based on partitioning the matrix into submatrices and applying maximum distance separable (MDS) codes to…
We study algorithms for the fast computation of modular inverses. Newton-Raphson iteration over $p$-adic numbers gives a recurrence relation computing modular inverse modulo $p^m$, that is logarithmic in $m$. We solve the recurrence to…
It is shown how to compute quotients efficiently in non-commutative univariate polynomial rings. This extends earlier work where efficient generic quotients were studied with a primary focus on commutative domains. Fast algorithms are given…
The inversion of extremely high order matrices has been a challenging task because of the limited processing and memory capacity of conventional computers. In a scenario in which the data does not fit in memory, it is worth to consider…
We obtain two new algorithms for partial fraction decompositions; the first is over algebraically closed fields, and the second is over general fields. These algorithms takes $O(M^2)$ time, where $M$ is the degree of the denominator of the…
This article describes a lightweight additive homomorphic algorithm with the same encryption and decryption keys. Compared to standard additive homomorphic algorithms like Paillier, this algorithm reduces the computational cost of…
Performing exact Bayesian inference for complex models is computationally intractable. Markov chain Monte Carlo (MCMC) algorithms can provide reliable approximations of the posterior distribution but are expensive for large datasets and…
As quantum devices continue to scale, distributed quantum computing emerges as a promising strategy for executing large-scale tasks across modular quantum processors. A central challenge in this paradigm is verifying the correctness of…
In quantum computing the decoherence time of the qubits determines the computation time available and this time is very limited when using current hardware. In this paper we minimize the execution time (the depth) for a class of circuits…
NISQ (Noisy, Intermediate-Scale Quantum) computing requires error mitigation to achieve meaningful computation. Our compilation tool development focuses on the fact that the error rates of individual qubits are not equal, with a goal of…
To effectively implement quantum algorithms on noisy intermediate-scale quantum (NISQ) processors is a central task in modern quantum technology. NISQ processors feature tens to a few hundreds of noisy qubits with limited coherence times…
Quantum multi-programming is a method utilizing contemporary noisy intermediate-scale quantum computers by executing multiple quantum circuits concurrently. Despite early research on it, the research remains on quantum gates or small-size…
The most widely used algorithm for floating point complex division, known as Smith's method, may fail more often than expected. This document presents two improved complex division algorithms. We present a proof of the robustness of the…