Related papers: Faster Quantum Concentration via Grover's Search
We establish a lower bound concerning the computational complexity of Grover's algorithms on fractal networks. This bound provides general predictions for the quantum advantage gained for searching unstructured lists. It yields a…
We find that the Measurement Based Quantum Computing (MBQC) search algorithm on an unsorted list is not the same as Grover's search algorithm (GSA).
The search task is one of the most difficult when it comes to execution speed, and reducing the latter is important both when working with large data and with small samples, if they need to be processed frequently and in a limited time.…
For the unsorted database quantum search with the unknown fraction $\lambda$ of target items, there are mainly two kinds of methods, i.e., fixed-point or trail-and-error. (i) In terms of the fixed-point method, Yoder et al. [Phys. Rev.…
We present three quantum algorithms for clustering graphs based on higher-order patterns, known as motif clustering. One uses a straightforward application of Grover search, the other two make use of quantum approximate counting, and all of…
The Grover search algorithm performs an unstructured search of a marked item in a database quadratically faster than classical algorithms and is shown to be optimal. Here, we show that if the search space is divided into two blocks with the…
The closest pair problem is a fundamental problem of computational geometry: given a set of $n$ points in a $d$-dimensional space, find a pair with the smallest distance. A classical algorithm taught in introductory courses solves this…
Grover's algorithm is one of the pioneering demonstrations of the advantages of quantum computing over its classical counterpart, providing - at most - a quadratic speed-up over the classical solution for unstructured database search. The…
We discuss the quantum search algorithm using complex queries that has recently been published by Grover (quant-ph/9706005). We recall the algorithm adding some details showing which complex query has to be evaluated. Based on this version…
Identifying jets formed in high-energy particle collisions requires solving optimization problems over potentially large numbers of final-state particles. In this work, we consider the possibility of using quantum computers to speed up jet…
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points. A choice among these…
We generalize Grover's unstructured quantum search algorithm to enable it to use an arbitrary starting superposition and an arbitrary unitary matrix simultaneously. We derive an exact formula for the probability of the generalized Grover's…
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…
The Grover quantum search algorithm is generalized to deal with an arbitrary mixed initial state. The probability to measure a marked state as a function of time is calculated, and found to depend strongly on the specific initial state. The…
Grover's database search algorithm is the optimal algorithm for finding a desired object from an unsorted collection of items. Although it was discovered in the context of quantum computation, it is simple and versatile enough to be…
Quantum search is among the most important algorithms in quantum computing. At its core is quantum amplitude amplification, a technique that achieves a quadratic speedup over classical search by combining two global reflections: the oracle,…
The study of quantum computation has been motivated by the hope of finding efficient quantum algorithms for solving classically hard problems. In this context, quantum algorithms by local adiabatic evolution have been shown to solve an…
We describe an algorithm to solve the problem of Boolean CNF-Satisfiability when the input formula is chosen randomly. We build upon the algorithms of Sch{\"{o}}ning 1999 and Dantsin et al.~in 2002. The Sch{\"{o}}ning algorithm works by…
We consider the quantum time complexity of the all pairs shortest paths (APSP) problem and some of its variants. The trivial classical algorithm for APSP and most all pairs path problems runs in $O(n^3)$ time, while the trivial algorithm in…
Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum…