Related papers: A polynomial quantum computing algorithm for solvi…
How many quantum queries are required to determine the coefficients of a degree-$d$ polynomial in $n$ variables? We present and analyze quantum algorithms for this multivariate polynomial interpolation problem over the fields…
In this paper, we present a quantum algorithm for dynamic programming approach for problems on directed acyclic graphs (DAGs). The running time of the algorithm is $O(\sqrt{\hat{n}m}\log \hat{n})$, and the running time of the best known…
Motivated by the need to uncover some underlying mathematical structure of optimal quantum computation, we carry out a systematic analysis of a wide variety of quantum algorithms from the majorization theory point of view. We conclude that…
The clock synchronization problem is to determine the time difference $\Delta$ between two spatially separated clocks. When message delivery times between the two clocks are uncertain, $O(2^{2n})$ classical messages must be exchanged…
We give an algorithm for computing all roots of polynomials over a univariate power series ring over an exact field $\mathbb{K}$. More precisely, given a precision $d$, and a polynomial $Q$ whose coefficients are power series in $x$, the…
Quantum signal processing is a framework for implementing polynomial functions on quantum computers. To implement a given polynomial $P$, one must first construct a corresponding complementary polynomial $Q$. Existing approaches to this…
The query model offers a concrete setting where quantum algorithms are provably superior to randomized algorithms. Beautiful results by Bernstein-Vazirani, Simon, Aaronson, and others presented partial Boolean functions that can be computed…
Let M be a manifold with an action of a Lie group G, $\A$ the function algebra on M. The first problem we consider is to construct a $U_h(\g)$ invariant quantization, $\A_h$, of $\A$, where $U_h(\g)$ is a quantum group corresponding to G.…
Both bilevel and robust optimization are established fields of mathematical optimization and operations research. However, only until recently, the similarities in their mathematical structure has neither been studied theoretically nor…
Quantum computing holds the promise of solving computational mechanics problems in polylogarithmic time, meaning computational time scales as $\mathscr{O}((\log N)^c)$, where $N$ is the problem size and $c$ a constant. We propose a quantum…
This article fits in the area of research that investigates the application of topological duality methods to problems that appear in theoretical computer science. One of the eventual goals of this approach is to derive results in…
Complex linear differential equations with entire coefficients are studied in the situation where one of the coefficients is an exponential polynomial and dominates the growth of all the other coefficients. If such an equation has an…
We consider the problem of computing the Boolean convolution (with wraparound) of $n$~vectors of dimension $m$, or, equivalently, the problem of computing the sumset $A_1+A_2+\ldots+A_n$ for $A_1,\ldots,A_n \subseteq \mathbb{Z}_m$. Boolean…
It is known a method for converting a system of Boolean polynomial equations to a single Boolean polynomial equation with less variables. In this paper, we show a formula for systems of Boolean polynomial equations which is based on the…
A randomized algorithm for a search problem is *pseudodeterministic* if it produces a fixed canonical solution to the search problem with high probability. In their seminal work on the topic, Gat and Goldwasser posed as their main open…
The noise sensitivity of a Boolean function $f: \{0,1\}^n \rightarrow \{0,1\}$ is one of its fundamental properties. A function of a positive noise parameter $\delta$, it is denoted as $NS_{\delta}[f]$. Here we study the algorithmic problem…
This work deals with the definability problem by quantifier-free first-order formulas over a finite algebraic structure. We show the problem to be coNP-complete and present two decision algorithms based on a semantical characterization of…
The phenomenon of quantum entanglement is fundamental to the implementation of quantum computation, and requires at least two qubits for its demonstration. However, both Deutsch algorithm and Grover's search algorithm for two bits do not…
Conditions on sure-success decidability of weights of Boolean functions are presented for a given number of generalized Grover iterations. It is shown that the decidability problem reduces to a system of algebraic equations of a single…
Many quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given by a black box. As in the classical version of decision trees, different kinds of quantum query algorithms are possible: exact,…