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It is demonstrated that in gate-based quantum computing architectures quantum walk is a natural mathematical description of quantum gates. It originates from field-matter interaction driving the system, but is not attached to specific qubit…
In this work, we generalize the recently-introduced graph composition framework to the non-boolean setting. A quantum algorithm in this framework is represented by a hypergraph, where each hyperedge is adjacent to multiple vertices. The…
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.…
Diverse facets Of the Theory of Quantum Walks on Graph are reviewed Till now .In specific, Quantum network routing, Quantum Walk Search Algorithm, Element distinctness associated to the eigenvalues of Graphs and the use of these relation…
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…
The connection between coined and continuous-time quantum walk models has been addressed in a number of papers. In most of those studies, the continuous-time model is derived from coined quantum walks by employing dimensional reduction and…
The formalism of continuous-time quantum walks on graphs has been widely used in the study of quantum transport of energy and information, as well as in the development of quantum algorithms. In experimental settings, however, there is…
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 show that non-abelian quantum statistics can be studied using certain topological invariants which are the homology groups of configuration spaces. In particular, we formulate a general framework for describing quantum statistics of…
Quantum walks in general graphs, or more specifically scattering on graphs, encompass enough complexity to perform universal quantum computation. Any given quantum circuit can be broken down into single- and two-qubit gates, which can then…
Multi-photon propagation in connected structures - a quantum walk - offers the potential for simulating complex physical systems and provides a route to universal quantum computation. Increasing the complexity of quantum photonic networks…
Quantum walks underlie an important class of quantum computing algorithms, and represent promising approaches in various simulations and practical applications. Here we design stroboscopically monitored quantum walks and their subsequent…
Random walks are at the heart of many existing deep learning algorithms for graph data. However, such algorithms have many limitations that arise from the use of random walks, e.g., the features resulting from these methods are unable to…
We explore the possibility of using quantum walks on graphs to find structural anomalies, such as extra edges or loops, on a graph. We focus our attention on star graphs, whose edges are like spokes coming out of a central hub. If there are…
The control of the quantum transport is an issue of current interest for the construction of new devices. In this work, we investigate this possibility in the realm of quantum graphs. The study allows the identification of two distinct…
Quantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the…
Matrix-based centrality measures have enjoyed significant popularity in network analysis, in no small part due to our ability to rigorously analyze their behavior as parameters vary. Recent work has considered the relationship between…
Quantum walks are powerful kernels in quantum computing protocols that possess strong capabilities in speeding up various simulation and optimisation tasks. One striking example is given by quantum walkers evolving on glued trees for their…
This paper investigates continuous-time quantum walks on directed bipartite graphs based on a graph's adjacency matrix. We prove that on bipartite graphs, probability transport between the two node partitions can be completely suppressed by…
We develop an equivariant theory of graphs with respect to quantum symmetries and present a detailed exposition of various examples. We portray unitary tensor categories as a unifying framework encompassing all finite classical simple…