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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…
We simulate Grover's algorithm in a classical computer by means of a stochastic method using the Hubbard-Stratonovich decomposition of n-qubit gates into one-qubit gates integrated over auxiliary fields. The problem reduces to finding the…
We investigate a set of discrete-time quantum search algorithms on the n-dimensional hypercube following a proposal by Shenvi, Kempe and Whaley. We show that there exists a whole class of quantum search algorithms in the symmetry reduced…
This paper presents an enhancement to Grover's search algorithm for instances where the number of items (or the size of the search problem) $N$ is not a power of 2. By employing an efficient algorithm for the preparation of uniform quantum…
The hybrid quantum-classical learning scheme provides a prominent way to achieve quantum advantages on near-term quantum devices. A concrete example towards this goal is the quantum neural network (QNN), which has been developed to…
We report the implementation of Grover's quantum search algorithm in the scalable system of trapped atomic ion quantum bits. Any one of four possible states of a two-qubit memory is marked, and following a single query of the search space,…
The search for "a quantum needle in a quantum haystack" is a metaphor for the problem of finding out which one of a permissible set of unitary mappings---the oracles---is implemented by a given black box. Grover's algorithm solves this…
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…
Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing…
We propose a new quantum circuit for the quantum search problem. The quantum circuit is superior to Grover's algorithm in some realistic cases. The reasons for the superiority are in short as follows: In the quantum circuit proposed in this…
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…
In this article we consider an experimental study showing the influence of emotion regulation strategies on human memory performance: part of such experimental results are difficult to explain within a classic cognitive allocation model. We…
We describe a simulation method for a quantum spin model of a generic, general purpose quantum computer. The use of this quantum computer simulator is illustrated through several implementations of Grover's database search algorithm. Some…
A proof-of-concept application of a quantum algorithm to multiloop Feynman integrals in the Loop-Tree Duality (LTD) framework is applied to a representative four-loop topology. Bootstrapping causality in the LTD formalism, is a suitable…
Generic quantum search algorithm searches for target entity in an unsorted database by repeatedly applying canonical Grover's quantum rotation transform to reach near the vicinity of the target entity represented by a basis state in the…
These notes begin in Chapter 1 with a review of linear algebra and the postulates of quantum mechanics, leading to an explanation of single- and multi-qubit gates. Chapter 2 explores the challenge of constructing arbitrary quantum states…
Grover's algorithm is a quantum query algorithm solving the unstructured search problem of size $N$ using $O(\sqrt{N})$ queries. It provides a significant speed-up over any classical algorithm \cite{Gro96}. The running time of the…
One of the most important quantum algorithms ever discovered is Grover's algorithm for searching an unordered set. We give a new lower bound in the query model which proves that Grover's algorithm is exactly optimal. Similar to existing…
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…
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…