相关论文: Quadratically optimized polynomials for fermion si…
Least-squares optimized polynomials are discussed which are needed in the two-step multi-bosonic algorithm for Monte Carlo simulations of quantum field theories with fermions. A recurrence scheme for the calculation of necessary…
Smeared link fermionic actions can be straightforwardly simulated with partial-global updating. The efficiency of this simulation is greatly increased if the fermionic matrix is written as a product of several near-identical terms. Such a…
We discuss a simulation algorithm for dynamical fermions, which combines the multiboson technique with the Hybrid Monte Carlo algorithm. The algorithm turns out to give a substantial gain over standard methods in practical simulations and…
L\"uscher's local bosonic algorithm for Monte Carlo simulations of quantum field theories with fermions is applied to the simulation of a possibly supersymmetric Yang-Mills theory with a Majorana fermion in the adjoint representation.…
Quaternion optimization has attracted significant interest due to its broad applications, including color face recognition, video compression, and signal processing. Despite the growing literature on quadratic and matrix quaternion…
We present a simulation algorithm for dynamical fermions that combines the multiboson technique with the Hybrid Monte Carlo algorithm. We find that the algorithm gives a substantial gain over the standard methods in practical simulations.…
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…
Three topics concerning fermion simulation algorithms are discussed: 1.) A performance comparison of the multiboson technique to simulate dynamical fermions and the Kramers equation algorithm, 2.) the question of reversibility in the Hybrid…
Fast algorithms for arithmetic on real or complex polynomials are well-known and have proven to be not only asymptotically efficient but also very practical. Based on Fast Fourier Transform (FFT), they for instance multiply two polynomials…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
We present and analyse a Monte-Carlo algorithm to compute the minimal polynomial of an $n\times n$ matrix over a finite field that requires $O(n^3)$ field operations and O(n) random vectors, and is well suited for successful practical…
We present an exact local bosonic algorithm for the simulation of dynamical fermions in lattice QCD. It is based on a non-hermitian polynomial approximation of the inverse of the quark matrix and a global Metropolis accept/reject correction…
Many quantum algorithms for ground-state preparation and energy estimation require the implementation of high-degree polynomials of a Hamiltonian to achieve better convergence rates. Their circuit implementation typically relies on quantum…
We provide in this work a form of Modular Quantum Signal Processing that we call iterated quantum signal processing. This method recursively applies quantum signal processing to the outputs of other quantum signal processing steps, allowing…
An algorithm is presented for the efficient and accurate computation of the coefficients of the characteristic polynomial of a general square matrix. The algorithm is especially suited for the evaluation of canonical traces in determinant…
Factorization of polynomials arises in numerous areas in symbolic computation. It is an important capability in many symbolic and algebraic computation. There are two type of factorization of polynomials. One is convention polynomial…
Polynomial factorization and root finding are among the most standard themes of computational mathematics. Yet still, little has been done for polynomials over quaternion algebras, with the single exception of Hamiltonian quaternions for…
Finding suitable points for multivariate polynomial interpolation and approximation is a challenging task. Yet, despite this challenge, there has been tremendous research dedicated to this singular cause. In this paper, we begin by…
We present an exact local bosonic algorithm for the simulation of dynamical fermions in lattice QCD. We show that this algorithm is a viable alternative to the Hybrid Monte Carlo algorithm.
Quantum computing is a promising way to systematically solve the longstanding computational problem, the ground state of a many-body fermion system. Many efforts have been made to realise certain forms of quantum advantage in this problem,…