Related papers: Quantum Algorithm for the Fixed-Radius Neighbor Se…
Filtered Approximate Nearest Neighbor (ANN) search retrieves the closest vectors for a query vector from a dataset. It enforces that a specified set of discrete labels $S$ for the query must be included in the labels of each retrieved…
Approximate nearest neighbor search (ANNS) has emerged as a crucial component of database and AI infrastructure. Ever-increasing vector datasets pose significant challenges in terms of performance, cost, and accuracy for ANNS services. None…
Large-scale approximate nearest neighbor search (ANN) has been gaining attention along with the latest machine learning researches employing ANNs. If the data is too large to fit in memory, it is necessary to search for the most similar…
The closest pair problem (CPP) is one of the well studied and fundamental problems in computing. Given a set of points in a metric space, the problem is to identify the pair of closest points. Another closely related problem is the fixed…
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…
Simulating quantum circuits using classical computers can accelerate the development and validation of quantum algorithms. Our newly developed algorithm, variational quantum search (VQS), has shown an exponential advantage over Grover's…
The paper considers the problem of finding a given substring in a text. It is known that the complexity of a classical search query in an unordered database is linear in the length of the text and a given substring. At the same time,…
Effective access points (APs) selection is a crucial step in localization systems. It directly affects both localization accuracy and computational efficiency. Classical APs selection algorithms are usually computationally expensive,…
Most natural language processing tasks can be formulated as the approximated nearest neighbor search problem, such as word analogy, document similarity, machine translation. Take the question-answering task as an example, given a question…
Searching for collisions in random functions is a fundamental computational problem, with many applications in symmetric and asymmetric cryptanalysis. When one searches for a single collision, the known quantum algorithms match the query…
Searching large databases is an important problem with broad applications. The Grover search algorithm provides a powerful method for quantum computers to perform searches with a quadratic speedup in the number of required database queries…
This paper presents a quantum search approach to combinatorial constraint satisfaction problems, demonstrated through the generation of magic squares. We reformulate magic square construction as a quantum search problem in which a…
Existing methods for retrieving k-nearest neighbours suffer from the curse of dimensionality. We argue this is caused in part by inherent deficiencies of space partitioning, which is the underlying strategy used by most existing methods. We…
We study the unsorted database search problem with items $N$ from the viewpoint of unitary discrimination. Instead of considering the famous $O(\sqrt{N})$ Grover's the bounded-error algorithm for the original problem, we seek for the…
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…
We prove that any exact quantum algorithm searching an ordered list of N elements requires more than \frac{1}{\pi}(\ln(N)-1) queries to the list. This improves upon the previously best known lower bound of {1/12}\log_2(N) - O(1). Our proof…
Quantum search algorithm (also known as Grover's algorithm) lays the foundation for many other quantum algorithms. Although it is very simple, its implementation is limited on noisy intermediate-scale quantum (NISQ) processors. Grover's…
A quantum algorithm is known that solves an unstructured search problem in a number of iterations of order $\sqrt{d}$, where $d$ is the dimension of the search space, whereas any classical algorithm necessarily scales as $O(d)$. It is shown…
Grover's search algorithm is renowned for its dramatic speedup in solving many important scientific problems. The recently proposed Variational Quantum Search (VQS) algorithm has shown an exponential advantage over Grover's algorithm for up…
Approximate Nearest Neighbor Search (ANNS) plays a critical role in various disciplines spanning data mining and artificial intelligence, from information retrieval and computer vision to natural language processing and recommender systems.…