Related papers: Numerical evaluation of multiple polylogarithms
We describe a new C++ library for multiprecision arithmetic for numbers in the order of 100--500 bits, i.e., representable with just a few limbs. The library is written in "optimizing-compiler-friendly" C++, with an emphasis on the use of…
This study considers implementations of error correction in a simulation language on a classical computer. Error correction will be necessarily in quantum computing and quantum information. We will give some examples of the implementations…
Numerical continuation methods track a solution path defined by a homotopy. The systems we consider are defined by polynomials in several variables with complex coefficients. For larger dimensions and degrees, the numerical conditioning…
This paper presents methodological improvements to variational quantum algorithms (VQAs) for solving multicriteria optimization problems. We introduce two key contributions. First, we reformulate the parameter optimization task of VQAs as a…
Polynomial optimization problems over binary variables can be expressed as integer programs using a linearization with extra monomials in addition to those arising in the given polynomial. We characterize when such a linearization yields an…
We give a technique to reduce the error probability of quantum algorithms that determine whether its input has a specified property of interest. The standard process of reducing this error is statistical processing of the results of…
Loop invariants are properties of a program loop that hold before and after each iteration of the loop. They are often employed to verify programs and ensure that algorithms consistently produce correct results during execution.…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
We analyse the axioms of Euclidean geometry according to standard object-oriented software development methodology. We find a perfect match: the main undefined concepts of the axioms translate to object classes. The result is a suite of C++…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
Quantum computation must be performed in a fault-tolerant manner to be realizable in practice. Recent progress has uncovered quantum error-correcting codes with sparse connectivity requirements and constant qubit overhead. Existing schemes…
Quantum computation has received great attention in recent years for its possible application to difficult problem in classical calculation. Despite the experimental problems of implementing quantum devices, theoretical physicists have…
Quantum field theory provides the framework for the most fundamental physical theories to be confirmed experimentally and has enabled predictions of unprecedented precision. However, calculations of physical observables often require great…
Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…
Multiobjective discrete programming is a well-known family of optimization problems with a large spectrum of applications. The linear case has been tackled by many authors during the last years. However, the polynomial case has not been…
The growing demand for solving large-scale, data-intensive linear and conic optimization problems, particularly in applications such as artificial intelligence and machine learning, has highlighted the limitations of classical interior…
Convex polyhedra are the basis for several abstractions used in static analysis and computer-aided verification of complex and sometimes mission critical systems. For such applications, the identification of an appropriate…
Much algorithmic research in NLP aims to efficiently manipulate rich formal structures. An algorithm designer typically seeks to provide guarantees about their proposed algorithm -- for example, that its running time or space complexity is…
In this paper, we present fast algorithms for the product of two multivariate polynomials in sparse representation. The bit complexity of our algorithms are studied in detail for various types of coefficients, and we derive new complexity…
A unique decoding algorithm for general AG codes, namely multipoint evaluation codes on algebraic curves, is presented. It is a natural generalization of the previous decoding algorithm which was only for one-point AG codes. As such, it…