Related papers: Quantitative approach to Grover's quantum walk on …
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…
In this paper, we consider continuous-time quantum walks (CTQWs) on finite graphs determined by the Laplacian matrices. By introducing fully interconnected graph decomposition of given graphs, we show a decomposition method for the…
We review Grover's algorithm by means of a detailed geometrical interpretation and a worked out example. Some basic concepts of Quantum Mechanics and quantum circuits are also reviewed. This work is intended for non-specialists which have…
With the growing interest in quantum machine learning, the perceptron -- a fundamental building block in traditional machine learning -- has emerged as a valuable model for exploring quantum advantages. Two quantum perceptron algorithms…
Large scale complex systems, such as social networks, electrical power grid, database structure, consumption pattern or brain connectivity, are often modeled using network graphs. Valuable insight can be gained by measuring the similarity…
Quantum algorithms for several problems in graph theory are considered. Classical algorithms for finding the lowest weight path between two points in a graph and for finding a minimal weight spanning tree involve searching over some space.…
Grover's algorithm achieves a quadratic speedup over classical algorithms, but it is considered necessary to know the value of $\lambda$ exactly [Phys. Rev. Lett. 95, 150501 (2005); Phys. Rev. Lett. 113, 210501 (2014)], where $\lambda$ is…
Graph partition is a fundamental problem of parallel computing for big graph data. Many graph partition algorithms have been proposed to solve the problem in various applications, such as matrix computations and PageRank, etc., but none has…
In this paper we introduce a novel polynomial-time algorithm to compute graph invariants based on the modified random walk idea on graphs. However not proved to be a full graph invariant by now, our method gives the right answer for the…
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…
In this paper, we extend a previously presented Grover-based heuristic to tackle general combinatorial optimization problems with linear constraints. We further describe the introduced method as a framework that enables performance…
We introduce a novel quantum algorithm for similar subgraph identification in form of an NP-hard cardinality-constrained binary quadratic optimization problem. Given a weighted reference graph with Laplacian $\boldsymbol{B}$, our algorithm…
In this paper, we consider a continuous-time quantum walk based search algorithm. We introduce equitable partition of the graph and perfect state transfer on it. By these two methods, we can calculate the success probability and the finding…
Quantum counting is a key quantum algorithm that aims to determine the number of marked elements in a database. This algorithm is based on the quantum phase estimation algorithm and uses the evolution operator of Grover's algorithm because…
The spatial search problem aims to find a marked vertex of a finite graph using a dynamic with two constraints: (1) The walker has no compass and (2) the walker can check whether a vertex is marked only after reaching it. This problem is a…
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…
We demonstrate that continuous time quantum walks on several types of branching graphs, including graphs with loops, are identical to quantum walks on simpler linear chain graphs. We also show graph types for which such equivalence does not…
We address the correspondence search problem among multiple graphs with complex properties while considering the matching consistency. We describe each pair of graphs by combining multiple attributes, then jointly match them in a unified…
In the emerging domain of quantum algorithms, the Grover's quantum search is certainly one of the most significant. It is relatively simple, performs a useful task and more importantly, does it in an optimal way. However, due to the success…
The quantum circuit model essentially treats every quantum algorithm as a straight-line program. While this view is universal, recent work has shown that it is inconvenient for using different-length quantum subroutines in superposition.…