Related papers: Laplacian versus Adjacency Matrix in 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…
Quantum walks and random walks bear similarities and divergences. One of the most remarkable disparities affects the probability of finding the particle at a given location: typically, almost a flat function in the first case and a…
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…
In network science, graphs obtained by taking the Kronecker or tensor power of the adjacency matrix of an initiator graph are used to construct complex networks. In this paper, we analytically prove sufficient conditions under which such…
A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. Searching in this mathematical framework has interested the community since a long time. However, most results consider spatial search…
We propose a quantum walk defined by digraphs (mixed graphs). This is like Grover walk that is perturbed by a certain complex-valued function defined by digraphs. The discriminant of this quantum walk is a matrix that is a certain…
One of the most important algorithmic applications of quantum walks is to solve spatial search problems. A widely used quantum algorithm for this problem, introduced by Childs and Goldstone [Phys. Rev. A 70, 022314 (2004)], finds a marked…
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 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.…
A quantum walk is the quantum analogue of a random walk. While it is relatively well understood how quantum walks can speed up random walk hitting times, it is a long-standing open question to what extent quantum walks can speed up the…
Incorporating higher-order interactions in information processing enables us to build more accurate models, gain deeper insights into complex systems, and address real-world challenges more effectively. However, existing methods, such as…
We survey the equations of continuous-time quantum walks on simple one-dimensional lattices, which include the finite and infinite lines and the finite cycle, and compare them with the classical continuous-time Markov chains. The focus of…
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…
Quantum walk followed by some amplitude amplification technique has been successfully used to search for marked vertices on various graphs. Lackadaisical quantum walk can search for target vertices on graphs without the help of any…
In quantum computing, the quantum walk search algorithm is designed for locating fixed marked nodes within a graph. However, when multiple marked nodes exist, the conventional search algorithm lacks the capacity to simultaneously amplify…
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…
One approach to the development of quantum search algorithms is the quantum walk. A spatial search can be effected by the continuous-time evolution of a single quantum particle on a graph containing a marked site. In many physical…
The quantum walk is the quantum analogue of the well-known random walk, which forms the basis for models and applications in many realms of science. Its properties are markedly different from the classical counterpart and might lead to…
Random walk algorithms are crucial for sampling and approximation problems in statistical physics and theoretical computer science. The mixing property is necessary for Markov chains to approach stationary distributions and is facilitated…
An ideal quantum walk transitions from one vertex to another with perfect fidelity, but in physical systems, the particle may be hindered by potential energy barriers. Then the particle has some amplitude of tunneling through the barriers,…