Related papers: Element Distinctness Revisited
Given $n$ elements, an integer $k$ and a parameter $\varepsilon$, we study to select an element with rank in $(k-n\varepsilon,k+n\varepsilon]$ using unreliable comparisons where the outcome of each comparison is incorrect independently with…
Quantum Search Algorithm made a big impact by being able to solve the search problem for a set with $N$ elements using only $O(\sqrt{N})$ steps. Unfortunately, it is impossible to reduce the order of the complexity of this problem, however,…
Identifying the $k$-partite entanglement and $k$-nonseparability of general $N$-partite quantum states are fundamental issues in quantum information theory. By use of computable inequalities of nonlinear operators, we present some simple…
In classical secretary problems, a sequence of $n$ elements arrive in a uniformly random order, and we want to choose a single item, or a set of size $K$. The random order model allows us to escape from the strong lower bounds for the…
Typical elements of quantum networks are made by identical systems, which are the basic particles constituting a resource for quantum information processing. Whether the indistinguishability due to particle identity is an exploitable…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
A quantum algorithm is exact if it always produces the correct answer, on any input. Coming up with exact quantum algorithms that substantially outperform the best classical algorithm has been a quite challenging task. In this paper, we…
Quantum entanglement is the core resource in quantum information processing and quantum computing. It is an significant challenge to effectively characterize the entanglement of quantum states. Recently, elegant separability criterion is…
We present a quantum algorithm solving the $k$-distinctness problem in $O(n^{1-2^{k-2}/(2^k-1)})$ queries with a bounded error. This improves the previous $O(n^{k/(k+1)})$-query algorithm by Ambainis. The construction uses a modified…
Discretizing Helmholtz problems via finite elements yields linear systems whose efficient solution remains a major challenge for classical computation. In this paper, we investigate how variational quantum algorithms could address this…
Suppose one has access to oracles generating samples from two unknown probability distributions P and Q on some N-element set. How many samples does one need to test whether the two distributions are close or far from each other in the…
Based on the partition of parameter space, two algorithms for computing the rational univariate representation of zero-dimensional ideals with parameters are presented in the paper. Unlike the rational univariate representation of…
We consider the problem of finding the minimum element in a list of length $N$ using a noisy comparator. The noise is modelled as follows: given two elements to compare, if the values of the elements differ by at least $\alpha$ by some…
Determining whether a given integer is prime or composite is a basic task in number theory. We present a primality test based on quantum order finding and the converse of Fermat's theorem. For an integer $N$, the test tries to find an…
An n-element set contains an unknown number of excellent elements, and our goal is to identify at least one of these elements. The members of a family of subsets can be asked if they contain at least one excellent element or not. At most…
The hidden shift problem is a natural place to look for new separations between classical and quantum models of computation. One advantage of this problem is its flexibility, since it can be defined for a whole range of functions and a…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…
Ever since entanglement was identified as a computational and cryptographic resource, researchers have sought efficient ways to tell whether a given density matrix represents an unentangled, or separable, state. This paper gives the first…
In this paper we investigate the problem of sorting a set of $n$ coins, each with distinct but unknown weights, using an unusual scale. The classical version of this problem, which has been well-studied, gives the user a binary scale,…
Binomial ideals are special polynomial ideals with many algorithmically and theoretically nice properties. We discuss the problem of deciding if a given polynomial ideal is binomial. While the methods are general, our main motivation and…