Related papers: Quantum walk-based search algorithms with multiple…
Quantum random walks represent a powerful tool for the implementation of various quantum algorithms. We consider a convolution problem for the graphs which provide quantum and classical random walks. We suggest a new method for lattices and…
In this paper, we study Grover's search algorithm focusing on continuous-time quantum walk on graphs. We propose an alternative optimization approach to Grover's algorithm on graphs that can be summarized as follows: instead of finding…
Quantum walks are at the heart of modern quantum technologies. They allow to deal with quantum transport phenomena and are an advanced tool for constructing novel quantum algorithms. Quantum walks on graphs are fundamentally different from…
We consider the problem of searching a general $d$-dimensional lattice of $N$ vertices for a single marked item using a continuous-time quantum walk. We demand locality, but allow the walk to vary periodically on a small scale. By…
Quantum search on the two-dimensional lattice with one marked vertex and cyclic boundary conditions is an important problem in the context of quantum algorithms with an interesting unfolding. It avails to test the ability of quantum walk…
The lackadaisical quantum walk, which is a quantum walk with a weighted self-loop at each vertex, has been shown to speed up dispersion on the line and improve spatial search on the complete graph and periodic square lattice. In these…
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…
Quantum random walks have been shown to be powerful quantum algorithms for certain tasks on graphs like database searching, quantum simulations etc. In this work we focus on its applications for the graph isomorphism problem. In particular…
Lackadaisical quantum walk(LQW) has been an efficient technique in searching a target state from a database which is distributed on a two-dimensional lattice. We numerically study the quantum search algorithm based on the lackadaisical…
Continuous-time quantum walks (CTQW) have shown the capability to perform efficiently the spatial search of a marked site on many kinds of graphs. However, most of such graphs are hard to realize in an experimental setting. Here we study…
We introduce an object called a \emph{subspace graph} that formalizes the technique of multidimensional quantum walks. Composing subspace graphs allows one to seamlessly combine quantum and classical reasoning, keeping a classical structure…
The quantum SearchRank algorithm is a promising tool for a future quantum search engine based on PageRank quantization. However, this algorithm loses its functionality when the $N/M$ ratio between the network size $N$ and the number of…
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 and random walks have been shown to be equivalent in the following sense: a time-dependent random walk can be constructed such that its vertex distribution at all time instants is identical to the vertex distribution of any…
This article presents a novel and succinct algorithmic framework via alternating quantum walks, unifying quantum spatial search, state transfer and uniform sampling on a large class of graphs. Using the framework, we can achieve exact…
We introduce a continuous-time quantum walk on an ultrametric space corresponding to the set of p-adic integers and compute its time-averaged probability distribution. It is shown that localization occurs for any location of the ultrametric…
The so-called welded tree problem provides an example of a black-box problem that can be solved exponentially faster by a quantum walk than by any classical algorithm. Given the name of a special ENTRANCE vertex, a quantum walk can find…
In the present paper, we study the continuous-time quantum walk on quotient graphs. On such graphs, there is a straightforward reduction of problem to a subspace that can be considerably smaller than the original one. Along the lines of…
The defining feature of memoryless quantum walks is that they operate on the vertex space of a graph, and therefore can be used to produce search algorithms with minimal memory. We present a memoryless walk that can find a unique marked…
Quantum walks in an elaborately designed graph, is a powerful tool simulating physical and topological phenomena, constructing analog quantum algorithms and realizing universal quantum computing. Integrated photonics technology has emerged…