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We investigate quantum walks in multiple dimensions with different quantum coins. We augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases. This model enables us to study in detail…

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…

Quantum walks are roughly analogous to classical random walks, and like classical walks they have been used to find new (quantum) algorithms. When studying the behavior of large graphs or combinations of graphs it is useful to find the…

A quantum walk places a traverser into a superposition of both graph location and traversal "spin." The walk is defined by an initial condition, an evolution determined by a unitary coin/shift-operator, and a measurement based on the…

Classical and quantum walks on some finite paths are introduced. It is shown that these walks have explicit solutions given in terms of exceptional Krawtchouk polynomials and their properties are explored. In particular, fractional revival…

Random walks are a fundamental primitive used in many machine learning algorithms with several applications in clustering and semi-supervised learning. Despite their relevance, the first efficient parallel algorithm to compute random walks…

This work revisits quantum algorithms for the well-known welded tree problem, proposing a very succinct quantum algorithm based on the simplest coined quantum walks. It simply iterates the naturally defined coined quantum walk operator for…

We address the question of symmetries of an important type of quantum walks. We introduce all the necessary definitions and provide a rigorous formulation of the problem. Using a thorough analysis, we reach the complete answer by presenting…

Quantum walks are a well-established model for the study of coherent transport phenomena and provide a universal platform in quantum information theory. Dynamically influencing the walker's evolution gives a high degree of flexibility for…

Quantum walks are the quantum-mechanical analog of random walks, in which a quantum `walker' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution…

The Noisy Intermediate-Scale Quantum (NISQ) era of technology in which we currently find ourselves is defined by non-universality, susceptibility to errors and noise, and a search for useful applications. While demonstrations of practical…

A new model of quantum random walks is introduced, on lattices as well as on finite graphs. These quantum random walks take into account the behavior of open quantum systems. They are the exact quantum analogues of classical Markov chains.…

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…

In this paper we introduce a novel polynomial-time algorithm to compute graph invariants based on the modified random walk idea on graphs. However not proved to be a full graph invariant by now, our method gives the right answer for the…

Quantum computing has the potential to solve complex problems faster and more efficiently than classical computing. It can achieve speedups by leveraging quantum phenomena like superposition, entanglement, and tunneling. Quantum walks (QWs)…

We clarify that coined quantum walk is determined by only the choice of local quantum coins. To do so, we characterize coined quantum walks on graph by disjoint Euler circles with respect to symmetric arcs. In this paper, we introduce a new…

With photonics, the quantum computational advantage has been demonstrated on the task of boson sampling. Next, developing quantum-enhanced approaches for practical problems becomes one of the top priorities for photonic systems. Quantum…

The development of universal quantum computers has achieved remarkable success in recent years, culminating with the quantum supremacy reported by Google. Now is possible to implement short-depth quantum circuits with dozens of qubits and…

Quantum computers are believed to bring computational advantages in simulating quantum many body systems. However, recent works have shown that classical machine learning algorithms are able to predict numerous properties of quantum systems…

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…