Related papers: Binary Subdivision for Quantum Search
We introduce a structured quantum search algorithm that leverages entanglement maps and a fixed-point method to minimize oracle query complexity in unsorted datasets. By partitioning qubits into rows based on their entanglement order, the…
Given an item and a list of values of size $N$. It is required to decide if such item exists in the list. Classical computer can search for the item in O(N). The best known quantum algorithm can do the job in $O(\sqrt{N})$. In this paper, a…
A quantum algorithm for general combinatorial search that uses the underlying structure of the search space to increase the probability of finding a solution is presented. This algorithm shows how coherent quantum systems can be matched to…
A new quantum algorithm for a search problem and its computational complexity are discussed. It is shown in the search problem containing 2^n objects that our algorithm runs in polynomial time.
A quantum algorithm for combinatorial search is presented that provides a simple framework for utilizing search heuristics. The algorithm is evaluated in a new case that is an unstructured version of the graph coloring problem. It performs…
We investigate the generalisation of quantum search of unstructured and totally ordered sets to search of partially ordered sets (posets). Two models for poset search are considered. In both models, we show that quantum algorithms can…
Quantum mechanical search induces polynomial speed up in an unsorted database search process. In case of classical linear search the computational time increases with the dimensionality of the query. However, quantum parallelism, inherent…
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…
Detection of symmetry is vital to problem solving. Most of the problems of computer vision and computer graphics and machine intelligence in general, can be reduced to symmetry detection problem. Unstructured search problem can also be…
This paper shows that a quantum mechanical algorithm that can query information relating to multiple items of the database, can search a database in a single query (a query is defined as any question to the database to which the database…
A simple circuit implementation of the oracle for Grover's quantum search of a real unstructured classical database is proposed. The oracle contains a kind of quantumly accessible classical memory, which stores the database.
This paper shows how a basic property of unitary transformations can be used for meaningful computations. This approach immediately leads to search-type applications, where it improves the number of steps by a square-root - a simple minded…
Withdrawn by the author due to irreparable errors. We present a quantum algorithm that in the black-box model performs a search in an ordered list of N elements. Using 3/4 log N + O(1) queries, it achieves a success probability of at least…
Quantum Search Algorithm made a big impact by being able to solve the search problem for a set with $N$ elements using only $O(\sqrt{N})$ steps. Unfortunately, it is impossible to reduce the order of the complexity of this problem, however,…
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…
We consider the problem of finding one or more desired items out of an unsorted database. Patel has shown that if the database permits quantum queries, then mere digitization is sufficient for efficient search for one desired item. The…
In this paper, we will use a quantum operator which performs the inversion about the mean operation only on a subspace of the system ({\it Partial Diffusion Operator}) to propose a quantum search algorithm runs in $O(\sqrt N/M})$ for…
In the quantum database search problem we are required to search for an item in a database. In this paper, we consider a generalization of this problem, where we are provided d identical copes of a database each with N items which we can…
We consider the problem of search of an unstructured list for a marked element, when one is given advice as to where this element might be located, in the form of a probability distribution. The goal is to minimise the expected number of…
In this paper we will present a quantum algorithm which works very efficiently in case of multiple matches within the search space and in the case of few matches, the algorithm performs classically. This allows us to propose a hybrid…