Related papers: Quantum algorithms for search with wildcards and c…
Quantum computing has evolved quickly in recent years and is showing significant benefits in a variety of fields, especially in the realm of cybersecurity. The combination of software used to locate the most frequent hashes and $n$-grams…
We construct a new quantum algorithm for the graph collision problem; that is, the problem of deciding whether the set of marked vertices contains a pair of adjacent vertices in a known graph G. The query complexity of our algorithm is…
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…
We present an algorithm for the generalized search problem (searching $k$ marked items among $N$ items) based on a continuous Hamiltonian and exploiting resonance. This resonant algorithm has the same time complexity $O(\sqrt{N/k})$ as the…
We present deterministic algorithms for the Hidden Subgroup Problem. The first algorithm, for abelian groups, achieves the same asymptotic worst-case query complexity as the optimal randomized algorithm, namely O($\sqrt{ n}\,$), where $n$…
This paper addresses the problem of finding the densest $k$-vertex subgraph in an arbitrary graph. This problem is NP-hard and has important applications in social network analysis, fraud detection, recommendation systems, and…
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…
We study quantum algorithms for spatial search on finite dimensional grids. Patel et al. and Falk have proposed algorithms based on a quantum walk without a coin, with different operators applied at even and odd steps. Until now, such…
Spatial search is the problem of finding a marked vertex in a graph. A continuous-time quantum walk in the single-excitation subspace of an $n$ spin system solves the problem of spatial search by finding the marked vertex in $O(\sqrt{n})$…
It is known that the dual of the general adversary bound can be used to build quantum query algorithms with optimal complexity. Despite this result, not many quantum algorithms have been designed this way. This paper shows another example…
We present a quantum algorithmic routine that extends the realm of Grover-based heuristics for tackling combinatorial optimization problems with arbitrary efficiently computable objective and constraint functions. Building on previously…
Grover's algorithm, orginally conceived as a means of searching an unordered database, can also be used to extract solutions from the result sets generated by quantum computations. The Grover algorithm exploits the concept of an oracle…
A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. A quantum system can undergo two types of operation, measurement and quantum…
We study the problem of learning an unknown graph provided via an oracle using a quantum algorithm. We consider three query models. In the first model ("OR queries"), the oracle returns whether a given subset of the vertices contains any…
Quantum contextuality is a limitation on deterministic hidden variable models, testable in measurement scenarios where outcomes differ under quantum or classical descriptions due to a common set of constraints. When considering measurements…
This paper shows that, if we could examine the entire history of a hidden variable, then we could efficiently solve problems that are believed to be intractable even for quantum computers. In particular, under any hidden-variable theory…
Combinatorial optimization is considered a promising class of problems in which quantum computers can show significant advantages. However, problems of practical relevance typically have more variables than current or foreseeable quantum…
We use a Bayesian approach to optimally solve problems in noisy binary search. We deal with two variants: 1. Each comparison can be erroneous with some probability $1 - p$. 2. At each stage $k$ comparisons can be performed in parallel and a…
We study the problem of indexing text with wildcard positions, motivated by the challenge of aligning sequencing data to large genomes that contain millions of single nucleotide polymorphisms (SNPs)---positions known to differ between…
Consider a database most of whose entries are marked but the precise fraction of marked entries is not known. What is known is that the fraction of marked entries is 1-X, where X is a random variable that is uniformly distributed in the…