Related papers: A Grover-Based Quantum Algorithm for Solving Perfe…
Unstructured search remains as one of the significant challenges in computer science, as classical search algorithms become increasingly impractical for large-scale systems due to their linear time complexity. Quantum algorithms, notably…
This paper discusses an improvement to Grover's algorithm for searches where target states are Hamming weight eigenstates and search space is not ordered. It is shown that under these conditions search efficiency depends on the smaller…
The main approach to hybrid quantum-classical neural networks (QNN) is employing quantum computing to build a neural network (NN) that has quantum features, which is then optimized classically. Here, we propose a different strategy: to use…
We study an oracle operation, along with its circuit design, which combined with the Grover diffusion operator boosts the probability of finding minimum or maximum solutions on a weighted directed graph. We focus on a geometry of…
In the Grover-type quantum search process a search operator is iteratively applied, say, k times, on the initial database state. We present an additive decomposition scheme such that the iteration process is expressed, in the computational…
We present the implementation of Grover's algorithm in a quantum simulator to perform a quantum search for preimages of two scaled hash functions, whose design only uses modular addition, word rotation, and bitwise exclusive or. Our…
This paper introduces a quantum-classical hybrid algorithm for generalized pattern search (GPS) algorithms. We introduce a quantum search step algorithm using amplitude amplification, which reduces the number of oracle calls needed during…
Grover's quantum search algorithm drives a quantum computer from a prepared initial state to a desired final state by using selective transformations of these states. Here, we analyze a framework when one of the selective trasformations is…
Grover adaptive search (GAS) is a quantum exhaustive search algorithm designed to solve binary optimization problems. In this paper, we propose higher-order binary formulations that can simultaneously reduce the numbers of qubits and gates…
We propose a couple of oracle construction methods for quantum pattern matching. We in turn show that one of the construct can be used with the Grover's search algorithm for exact and partial pattern matching, deterministically. The other…
An algebraic analysis of Grover's quantum search algorithm is presented for the case in which the initial state is an arbitrary pure quantum state of n qubits. This approach reveals the geometrical structure of the quantum search process,…
A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. A quantum system can undergo two types of operation, measurement and quantum…
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,…
In this paper we discuss Grover Adaptive Search (GAS) for Constrained Polynomial Binary Optimization (CPBO) problems, and in particular, Quadratic Unconstrained Binary Optimization (QUBO) problems, as a special case. GAS can provide a…
We present a continuous time quantum search algorithm analogous to Grover's. In particular, the optimal search time for this algorithm is proportional to $\sqrt{N}$, where $N$ is the database size. This search algorithm can be implemented…
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…
In the recent years, we have seen that Grover search algorithm (Proceedings, 28th annual ACM symposium on the theory of computing, pp. 212-219, 1996) by using quantum parallelism has revolutionized the field of solving huge class of NP…
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…
Grover's algorithm can solve NP-complete problems on quantum computers faster than all the known algorithms on classical computers. However, Grover's algorithm still needs exponential time. Due to the BBBV theorem, Grover's algorithm is…
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…