Related papers: Quantum search of partially ordered sets
We give an O(sqrt n log n)-query quantum algorithm for evaluating size-n AND-OR formulas. Its running time is poly-logarithmically greater after efficient preprocessing. Unlike previous approaches, the algorithm is based on a quantum walk…
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…
Presented here is a matrix inversion method utilizing quantum searching algorithm. In this method, huge Hilbert space as a whole spanned by myriad of eigen states is searched and evaluated efficiently by sequential reduction in dimension…
One of the significant breakthroughs in quantum computation is Grover's algorithm for unsorted database search. Recently, the applications of Grover's algorithm to solve global optimization problems have been demonstrated, where unknown…
Recent studies have been spurred on by the promise of advanced quantum computing technology, which has led to the development of quantum computer simulations on classical hardware. Grover's quantum search algorithm is one of the well-known…
We investigate the implementation of an oracle for the Subset Sum problem for quantum search using Grover's algorithm. Our work concerns reducing the number of qubits, gates, and multi-controlled gates required by the oracle. We describe…
We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be at most polynomial. We show that for average-case complexity under the…
The query model offers a concrete setting where quantum algorithms are provably superior to randomized algorithms. Beautiful results by Bernstein-Vazirani, Simon, Aaronson, and others presented partial Boolean functions that can be computed…
Many quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given by a black box. As in the classical version of decision trees, different kinds of quantum query algorithms are possible: exact,…
A general consideration on the phase rotations in quantum searching algorithm is taken in this work. As four phase rotations on the initial state, the marked states, and the states orthogonal to them are taken account, we deduce a phase…
We give a dimension independent formulation of the quantum search algorithm introduced in [L. K. Grover, Phys. Rev. Lett. {\bf 79}, 325 (1997)]. This algorithm provides a quadratic gain when compared to its classical counterpart by…
L. K. Grover's search algorithm in quantum computing gives an optimal, square-root speedup in the search for a single object in a large unsorted database. In this paper, we expound Grover's algorithm in a Hilbert-space framework that…
We consider the problem of finding a desired item out of $N$ items arranged on the sites of a two-dimensional lattice of size $\sqrt{N} \times \sqrt{N}$. The previous quantum walk based algorithms take $O(\sqrt{N}\log N)$ steps to solve…
Simon's problem is one of the most important problems demonstrating the power of quantum computing. Recently, an interesting distributed quantum algorithm for Simon's problem was proposed, where a key sorting operator requiring a large…
Quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given in a black box, but the aim is to compute function value for arbitrary input using as few queries as possible. In this paper we…
$k$-Clustering in $\mathbb{R}^d$ (e.g., $k$-median and $k$-means) is a fundamental machine learning problem. While near-linear time approximation algorithms were known in the classical setting for a dataset with cardinality $n$, it remains…
Despite the advent of Grover's algorithm for the unstructured search, its successful implementation on near-term quantum devices is still limited. We apply three strategies to reduce the errors associated with implementing quantum search…
A modification of Tulsi's quantum search algorithm with intermediate measurements of the control is presented. In order to analyze the effect of measurements in quantum searches, a different choice of the angular parameter is used. The…
We consider quantum search algorithms that have access to a noisy oracle that, for every oracle call, with probability $p>0$ completely depolarizes the query registers, while otherwise working properly. Previous results had not ruled out…
In this work we address two questions concerning Grover's algorithm. In the first we give an answer to the question how to employ Grover's algorithm for actual search over database. We introduce a quantum model of an unordered phone book…