Related papers: Quantum Pattern Matching
The essential operations of a quantum computer can be accomplished using solely optical elements, with different polarization or spatial modes representing the individual qubits. We present a simple all-optical implementation of Grover's…
Some of the secret sharing schemes having unique quantum features like parallelism and entanglement are supposed to be relatively secure. Different schemes proposed by various researchers over the years have features which could be specific…
The simplest technique for simulating a quantum algorithm - QA described based on the direct matrix representation of the quantum operators. Using this approach, it is relatively simple to simulate the operation of a QA and to perform…
We present a method for realizing efficiently Grover's search algorithm in an array of coupled cavities doped with three-level atoms. We show that by encoding information in the lowest two ground states of the dopants and through the…
In this paper, we present a novel formulation of traditional sampling-based motion planners as database-oracle structures that can be solved via quantum search algorithms. We consider two complementary scenarios: for simpler sparse…
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…
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 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…
The task of finding an entry in an unsorted list of $N$ elements famously takes $O(N)$ queries to an oracle for a classical computer and $O(\sqrt{N})$ queries for a quantum computer using Grover's algorithm. Reformulated as a spatial search…
This article highlights some of the key operating principles of Grover algorithm. These principles were used to develop a new oracle function, that illustrates the possibility of using Grover algorithm for solving more realistic and…
Quantum amplitude estimation is a key sub-routine of a number of quantum algorithms with various applications. We propose an adaptive algorithm for interval estimation of amplitudes. The quantum part of the algorithm is based only on…
We review some of quantum algorithms for search problems: Grover's search algorithm, its generalization to amplitude amplification, the applications of amplitude amplification to various problems and the recent quantum algorithms based on…
Quantum sampling, a fundamental subroutine in numerous quantum algorithms, involves encoding a given probability distribution in the amplitudes of a pure state. Given the hefty cost of large-scale quantum storage, we initiate the study of…
We study quantum algorithms for several fundamental string problems, including Longest Common Substring, Lexicographically Minimal String Rotation, and Longest Square Substring. These problems have been widely studied in the stringology…
We present a systematic construction of quantum circuits implementing Grover's database search algorithm for arbitrary number of targets. We introduce a new operator which flips the sign of the targets and evaluate its circuit complexity.…
It is well known that Grover's algorithm asymptotically transforms an equal superposition state into an eigenstate (of a given basis). Here, we demonstrate a verification algorithm based on weak measurement which can achieve the same…
Many important computer science problems can be reduced to clause satisfaction problem. We are given $n$ Boolean variables $x_{k}$ and $m$ clauses $c_{j}$ where each clause is a function of values of some of the variables. We want to find…
Quantum multi-programming is a method utilizing contemporary noisy intermediate-scale quantum computers by executing multiple quantum circuits concurrently. Despite early research on it, the research remains on quantum gates or small-size…
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…
In this work I describe a classical analog of Grover's quantum searching algorithm, explaining why a quantum algorithm should be able to perform search in O(sqrtN) steps and also acting as a useful pedagogic demonstration.