Related papers: Lackadaisical quantum walk in the hypercube to sea…
We present analytical treatment of quantum walks on multidimensional hyper-cycle graphs. We derive the analytical expression of the probability distribution for strong and weak decoherence regimes. Upper bound to mixing time is obtained.
This paper introduces in detail a non-variational quantum algorithm designed to solve a wide range of combinatorial optimisation problems, including constrained problems and problems with non-binary variables. The algorithm returns optimal…
This work focuses on the quantum mixing time, which is crucial for efficient quantum sampling and algorithm performance. We extend Richter's previous analysis of continuous time quantum walks on the periodic lattice $\mathbb{Z}_{n_1}\times…
This PhD thesis is dedicated to the study of the interplay between symmetries of quantum states and their self-similar properties. It consists of three connected threads of research: polynomial invariants for multiphoton states,…
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…
A single excitation in a quantum spin network described by the Heisenberg model can effect a variety of continuous-time quantum walks on unweighted graphs, including those governed by the discrete Laplacian, adjacency matrix, and signless…
Random walks on graphs are an essential primitive for many randomised algorithms and stochastic processes. It is natural to ask how much can be gained by running $k$ multiple random walks independently and in parallel. Although the cover…
In our previous works, we have studied quantum random walk search algorithm on hypercube, with traversing coin constructed by using generalized Householder reflection and a phase multiplier. When the same phases are used each iteration, the…
Shenvi, Kempe and Whaley's quantum random-walk search (SKW) algorithm [Phys. Rev. A 67, 052307 (2003)] is known to require $O(\sqrt N)$ number of oracle queries to find the marked element, where $N$ is the size of the search space. The…
We offer theoretical explanations for some recent observations in numerical simulations of quantum random walks (QRW). Specifically, in the case of a QRW on the line with one particle (walker) and two entangled coins, we explain the…
A randomly walking quantum particle evolving by Schr\"odinger's equation searches on $d$-dimensional cubic lattices in $O(\sqrt{N})$ time when $d \ge 5$, and with progressively slower runtime as $d$ decreases. This suggests that graph…
Given an undirected, weighted graph, with $n$ vertices and $m$ edges, and two special vertices $s$ and $t$, the problem is to find the shortest path between them. We give two bounded-error quantum algorithms with improved runtime in the…
We show that the hitting time of the discrete time quantum random walk on the n-bit hypercube from one corner to its opposite is polynomial in n. This gives the first exponential quantum-classical gap in the hitting time of discrete quantum…
We treat a quantum walk model with in- and out- flows at every time step from the outside. We show that this quantum walk can find the marked vertex of the complete graph with a high probability in the stationary state. In exchange of the…
With the constant flow of data from vast sources over the past decades, a plethora of advanced analytical techniques have been developed to extract relevant information from different data types ranging from labeled data, quasi-labeled…
Hitting the exit node from the entrance node faster on a graph is one of the properties that quantum walk algorithms can take advantage of to outperform classical random walk algorithms. Especially, continuous-time quantum walks on…
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…
A discrete-time staggered quantum walk was recently introduced as a generalization that allows to unify other versions, such as the coined and Szegedy's walk. However, it also produces new forms of quantum walks not covered by previous…
We show that with the addition of multiple walkers, quantum walks on a line can be transformed into lattice graphs of higher dimension. Thus, multi-walker walks can simulate single-walker walks on higher dimensional graphs and vice versa.…
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…