Related papers: Efficient quantum walk on the grid with multiple m…
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…
We show how multi-walker quantum walks can be implemented in a quantum quincunx created via cavity quantum electrodynamics. The implementation of a quantum walk with a multi-walker opens up the interesting possibility to introduce…
In this letter we introduce the concept of a driven quantum walk. This work is motivated by recent theoretical and experimental progress that combines quantum walks and parametric down- conversion, leading to fundamentally different…
We show a simple generalization of the quantum walk algorithm for search in backtracking trees by Montanaro (ToC 2018) to the case where vertices can have different times of computation. If a vertex $v$ in the tree of depth $D$ is computed…
We show that it is possible to use a quantum walk to find a path from one marked vertex to another. In the specific case of $M$ stars connected in a chain, one can find the path from the first star to the last one in $O(M\sqrt{N})$ steps,…
Quantum walks are recognizably useful for the development of new quantum algorithms, as well as for the investigation of several physical phenomena in quantum systems. Actual implementations of quantum walks face technological difficulties…
The quantum walk dynamics obey the laws of quantum mechanics with an extra locality constraint, which demands that the evolution operator is local in the sense that the walker must visit the neighboring locations before endeavoring to…
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links.…
We present an introduction to coined quantum walks on regular graphs, which have been developed in the past few years as an alternative to quantum Fourier transforms for underpinning algorithms for quantum computation. We then describe our…
Up to now, relatively few exponential quantum speed-ups have been achieved. Out of them, the welded tree problem (Childs, Cleve, Deotto, Farhi, Gutmann, and Spielman'2003) is one of the unusual examples, as the exponential speed-up is…
Quantum versions of random walks on the line and the cycle show a quadratic improvement over classical random walks in their spreading rates and mixing times respectively. Non-unitary quantum walks can provide a useful optimisation of these…
Quantum walks (QWs) are of interest as examples of uniquely quantum behavior and are applicable in a variety of quantum search and simulation models. Implementing QWs on quantum devices is useful from both points of view. We describe a…
Quantum walks have been very successful in the development of search algorithms in quantum information, in particular in the development of spatial search algorithms. However, the construction of continuous-time quantum search algorithms in…
Rydberg atoms provide a highly promising platform for quantum computation, leveraging their strong tunable interactions to encode and manipulate information in the electronic states of individual atoms. Key advantages of Rydberg atoms…
The Maximum Matching problem has a quantum query complexity lower bound of $\Omega(n^{3/2})$ for graphs on $n$ vertices represented by an adjacency matrix. The current best quantum algorithm has the query complexity $O(n^{7/4})$, which is…
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…
We demonstrate an implementation of the hitting time of a discrete time quantum random walk on cubelike graphs using IBM's Qiskit platform. Our implementation is based on efficient circuits for the Grover and Shift operators. We verify the…
This work describes a new algorithm for creating a superposition over the edge set of a graph, encoding a quantum sample of the random walk stationary distribution. The algorithm requires a number of quantum walk steps scaling as…
Mixing properties of discrete-time quantum walks on two-dimensional grids with torus-like boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an…
The coined quantum walk is a discretization of the Dirac equation of relativistic quantum mechanics, and it is the basis of many quantum algorithms. We investigate how it searches the complete bipartite graph of $N$ vertices for one of $k$…