Related papers: Using Approximating Polynomials in Partial-Global …
Fractional polynomial models are potentially useful for response surfaces investigations. With the availability of routines for fitting nonlinear models in statistical packages they are increasingly being used. However, as in all…
We present a simple derivation of a Feynman-Kac type formula to study fermionic systems. In this approach the real time or the imaginary time dynamics is expressed in terms of the evolution of a collection of Poisson processes. A computer…
We present a new approach to simulating Hamiltonian dynamics based on implementing linear combinations of unitary operations rather than products of unitary operations. The resulting algorithm has superior performance to existing simulation…
Given a graphical model (GM), computing its partition function is the most essential inference task, but it is computationally intractable in general. To address the issue, iterative approximation algorithms exploring certain local…
When implementing regular enough functions (e.g., elementary or special functions) on a computing system, we frequently use polynomial approximations. In most cases, the polynomial that best approximates (for a given distance and in a given…
In this paper, we propose a carefully optimized "half-gcd" algorithm for polynomials. We achieve a constant speed-up with respect to previous work for the asymptotic time complexity. We also discuss special optimizations that are possible…
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.…
In the simplified setting of the Schwinger model we present a systematic study on the simulation of dynamical fermions by global accept/reject steps that take into account the fermion determinant. A family of exact algorithms is developed,…
The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can only be applied to small systems. By contrast, we demonstrate that quantum…
We study a graph partitioning problem motivated by the simulation of the physical movement of multi-body systems on an atomistic level, where the forces are calculated from a quantum mechanical description of the electrons. Several advanced…
Understanding the behavior of interacting fermions is of fundamental interest in many fields ranging from condensed matter to high energy physics. Developing numerically efficient and accurate simulation methods is an indispensable part of…
Near-term quantum simulators are mostly based on qubit-based architectures. However, their imperfect nature significantly limits their practical application. The situation is even worse for simulating fermionic systems, which underlie most…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
We propose a general approach to find an optimal representation of a quantum many body wave function for a given error margin via global fermionic mode optimization. The stationary point on a fixed rank matrix product state manifold is…
Consider the collection of all binary matrices having a specific sequence of row and column sums and consider sampling binary matrices uniformly from this collection. Practical algorithms for exact uniform sampling are not known, but there…
In this paper, we propose a new and simple approach to the approximation algorithms that are modified and improved from our published results. The computational and graphical examples are presented with the aid of Maple procedures.
When using images to locate objects, there is the problem of correcting for distortion and misalignment in the images. An elegant way of solving this problem is to generate an error correcting function that maps points in an image to their…
This paper studies the polynomial optimization problem whose feasible set is a union of several basic closed semialgebraic sets. We propose a unified hierarchy of Moment-SOS relaxations to solve it globally. Under some assumptions, we prove…
Spectral polynomial approximation of smooth functions allows real-time manipulation of and computation with them, as in the Chebfun system. Extension of the technique to two-dimensional and three-dimensional functions on hyperrectangles has…
A thorough account is given of the derivation of uniform semiclassical approximations to the particle and kinetic energy densities of N noninteracting bounded fermions in one dimension. The employed methodology allows the inclusion of…