Related papers: PolyQEnt: A Polynomial Quantified Entailment Solve…
Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. In this paper, an effective algorithm is presented for computing the…
The derivative polynomials introduced by Knuth and Buckholtz in their calculations of the tangent and secant numbers are extended to a multivariable $q$--environment. The $n$-th $q$-derivatives of the classical $q$-tangent and $q$-secant…
Effective computation of resultants is a central problem in elimination theory and polynomial system solving. Commonly, we compute the resultant as a quotient of determinants of matrices and we say that there exists a determinantal formula…
We prove that the results of a finite set of general quantum measurements on an arbitrary dimensional quantum system can be simulated using a polynomial (in measurements) number of hidden-variable states. In the limit of infinitely many…
PolySAT is a word-level decision procedure supporting bit-precise SMT reasoning over polynomial arithmetic with large bit-vector operations. The PolySAT calculus extends conflict-driven clause learning modulo theories with two key…
Recently, it has been presented some algorithms and physical models which give prospects for construction of quantum computers capable to solve systems of linear equations. The common feature which is shared in these works is the use of…
We present a systematic pathway for solving differential equations within the quantum linear systems framework by combining block encoding with Quantum Singular Value Transformation (QSVT). The approach is demonstrated on a complex…
Reducing the conditions under which a given set satisfies the stipulations of the subset sum proposition to a set of linear relationships, the question of whether a set satisfies subset sum may be answered in a polynomial number of steps by…
We present a mapping which associates pure N-qubit states with a polynomial. The roots of the polynomial characterize the state completely. Using the properties of the polynomial we construct a way to determine the separability and the…
Block encoding is a key ingredient in the recently developed quantum singular value transformation (QSVT) framework, which provides a unifying description for many quantum algorithms. Initially introduced to simplify and optimize resource…
With the rapid advances in quantum computer architectures and the emerging prospect of large-scale quantum memory, it is becoming essential to classically verify that remote devices genuinely allocate the promised quantum memory with…
This paper presents a program analysis method that generates program summaries involving polynomial arithmetic. Our approach builds on prior techniques that use solvable polynomial maps for summarizing loops. These techniques are able to…
Polymer quantization is as a useful toy model for the mathematical aspects of loop quantum gravity and is interesting in its own right. Analyzing entropies of physically equivalent states in the standard Hilbert space and the polymer…
The paradigm behind digital quantum computing inherits the idea of using binary information processing. Nature in fact gives much more rich structures of physical objects that can be used for encoding information, which is especially…
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 entanglement was first recognized as a feature of quantum mechanics in the famous paper of Einstein, Podolsky and Rosen [18]. Recently it has been realized that quantum entanglement is a key ingredient in quantum computation,…
We prove that all polynomials in several variables can be decomposed as the sums of $k$th powers: $P(x_1,...,x_n) = Q_1(x_1,...,x_n)^k+...+ Q_s(x_1,...,x_n)^k$, provided that elements of the base field are themselves sums of $k$th powers.…
The symmetrized quartic polynomial oscillator is shown to admit an sl(2,$\R$) algebraization. Some simple quasi-exactly solvable (QES) solutions are exhibited. A new symmetrized sextic polynomial oscillator is introduced and proved to be…
We present entcalc, a Python and MATLAB package for estimating the geometric entanglement of multipartite quantum states. The package operates as follows: given a multipartite quantum state as input, it outputs an estimate of its geometric…
Quantile is an important risk measure quantifying the stochastic system random behaviors. This paper studies a pooled quantile estimator, which is the sample quantile of detailed simulation outputs after directly pooling independent sample…