Related papers: Quantum and classical query complexities for deter…
This paper initiates the study of quantum algorithms for matroid property problems. It is shown that quadratic quantum speedup is possible for the calculation problem of finding the girth or the number of circuits (bases, flats,…
The Maximum Matching problem has a quantum query complexity lower bound of $\Omega(n^{3/2})$ for graphs on $n$ vertices represented by an adjacency matrix. The current best quantum algorithm has the query complexity $O(n^{7/4})$, which is…
It has recently been shown that starting with a classical query algorithm (decision tree) and a guessing algorithm that tries to predict the query answers, we can design a quantum algorithm with query complexity $O(\sqrt{GT})$ where $T$ is…
The matroid intersection problem is a fundamental problem that has been extensively studied for half a century. In the classic version of this problem, we are given two matroids $\mathcal{M}_1 = (V, \mathcal{I}_1)$ and $\mathcal{M}_2 = (V,…
We consider classical and quantum algorithms which have a duality property: roughly, either the algorithm provides some nontrivial improvement over random or there exist many solutions which are significantly worse than random. This enables…
Quantum computing promises to solve difficult optimization problems in chemistry, physics and mathematics more efficiently than classical computers, but requires fault-tolerant quantum computers with millions of qubits. To overcome errors…
Quantum algorithms could efficiently solve certain classically intractable problems by exploiting quantum parallelism. To date, whether the quantum entanglement is useful or not for quantum computing is still a question of debate. Here, we…
The standard oracle model for matroid algorithms assumes that each independence query can be answered in constant time, regardless of the size of the queried set. While this abstraction has underpinned much of the theoretical progress in…
This study examines clusterability testing for a signed graph in the bounded-degree model. Our contributions are two-fold. First, we provide a quantum algorithm with query complexity $\tilde{O}(N^{1/3})$ for testing clusterability, which…
It is known that quantum computers yield a speed-up for certain discrete problems. Here we want to know whether quantum computers are useful for continuous problems. We study the computation of the integral of functions from the classical…
Query complexity is a model of computation in which we have to compute a function $f(x_1, \ldots, x_N)$ of variables $x_i$ which can be accessed via queries. The complexity of an algorithm is measured by the number of queries that it makes.…
The problem of efficient multiplication of large numbers has been a long-standing challenge in classical computation and has been extensively studied for centuries. It appears that the existing classical algorithms are close to their…
We present a quantum algorithm which identifies with certainty a hidden subgroup of an arbitrary finite group G in only a polynomial (in log |G|) number of calls to the oracle. This is exponentially better than the best classical algorithm.…
Genetic algorithms are heuristic optimization techniques inspired by Darwinian evolution. Quantum computation is a new computational paradigm which exploits quantum resources to speed up information processing tasks. Therefore, it is…
In the oracle identification problem, we are given oracle access to an unknown N-bit string x promised to belong to a known set C of size M and our task is to identify x. We present a quantum algorithm for the problem that is optimal in its…
In the matroid intersection problem, we are given two matroids of rank $r$ on a common ground set $E$ of $n$ elements and the goal is to find the maximum set that is independent in both matroids. In this note, we show that Cunningham's…
Simon's problem is an essential example demonstrating the faster speed of quantum computers than classical computers for solving some problems. The optimal separation between exact quantum and classical query complexities for Simon's…
In this paper we construct quantum algorithms for matrix products over several algebraic structures called semirings, including the (max,min)-matrix product, the distance matrix product and the Boolean matrix product. In particular, we…
Many recent investigations conclude, based on asymptotic complexity analyses, that quantum computers could accelerate combinatorial optimization (CO) tasks relative to a purely classical computer. However, asymptotic analysis alone cannot…
Quantum annealing (QA) has the potential to significantly improve solution quality and reduce time complexity in solving combinatorial optimization problems compared to classical optimization methods. However, due to the limited number of…