Related papers: Quantum walks through generalized graph compositio…
We explore the use of machine-learning techniques to detect quantum speedup in random walks on graphs. Specifically, we investigate the performance of three different neural-network architectures (variations on fully connected and…
In this paper, we analyze the potential for new types of searches using the formalism of scattering random walks on Quantum Computers. Given a particular type of graph consisting of nodes and connections, a "Tree Maze", we would like to…
This work examines the time complexity of quantum search algorithms on combinatorial $t$-designs with multiple marked elements using the continuous-time quantum walk. Through a detailed exploration of $t$-designs and their incidence…
One of the significant breakthroughs in quantum computation is Grover's algorithm for unsorted database search. Recently, the applications of Grover's algorithm to solve global optimization problems have been demonstrated, where unknown…
The task of finding an element in an unstructured database is known as spatial search and can be expressed as a quantum walk evolution on a graph. In this article, we modify the usual search problem by adding an extra trapping vertex to the…
We introduce a new tool for quantum algorithms called quantum fast-forwarding (QFF). The tool uses quantum walks as a means to quadratically fast-forward a reversible Markov chain. More specifically, with $P$ the Markov chain transition…
We use quantum walks to construct a new quantum algorithm for element distinctness and its generalization. For element distinctness (the problem of finding two equal items among N given items), we get an O(N^{2/3}) query quantum algorithm.…
In this paper, we analyze the dynamics of quantum walks on a graph structure resulting from the integration of a main connected graph $G$ and a secondary connected graph $G'$. This composite graph is formed by a disjoint union of $G$ and…
We propose a new method for designing quantum search algorithms for finding a "marked" element in the state space of a classical Markov chain. The algorithm is based on a quantum walk \'a la Szegedy (2004) that is defined in terms of the…
In this paper, we show reduction methods for search algorithms on graphs using quantum walks. By using a graph partitioning method called equitable partition for the the given graph, we determine "effective subspace" for the search…
We introduce quantized bipartite walks, compute their spectra, generalize the algorithms of Grover \cite{g} and Ambainis \cite{amb03} and interpret them as quantum walks with memory. We compare the performance of walk based classical and…
Continuous-time quantum walks are typically effected by either the discrete Laplacian or the adjacency matrix. In this paper, we explore a third option: the signless Laplacian, which has applications in algebraic graph theory and may arise…
Quantum random walks have received much interest due to their non-intuitive dynamics, which may hold the key to a new generation of quantum algorithms. What remains a major challenge is a physical realization that is experimentally viable…
Quantum computing promises to improve the information processing power to levels unreachable by classical computation. Quantum walks are heading the development of quantum algorithms for searching information on graphs more efficiently than…
In this paper we isolate the combinatorial property responsible (at least in part) for the computational speedups recently observed in some quantum walk algorithms. We find that continuous-time quantum walks can exploit the covering space…
Quantum walks (QW) are of crucial importance in the development of quantum information processing algorithms. Recently, several quantum algorithms have been proposed to implement network analysis, in particular to rank the centrality of…
We consider the problem of finding a marked vertex in a graph from an arbitrary starting distribution, using a quantum walk based algorithm. We work in the framework introduced by Belovs which showed how to detect the existence of a marked…
We give a quantum algorithm for a novel type of black-box problem: identifying a hidden $d$-regular base graph $G$ on $n$ vertices from oracle access to an obfuscated version of it, rather than traversing it. From $G$ we build the spired…
An important tool in algorithm design is the ability to build algorithms from other algorithms that run as subroutines. In the case of quantum algorithms, a subroutine may be called on a superposition of different inputs, which complicates…
Given the extensive application of classical random walks to classical algorithms in a variety of fields, their quantum analogue in quantum walks is expected to provide a fruitful source of quantum algorithms. So far, however, such…