Related papers: Implementation of Continuous-Time Quantum Walk on …
Quantum walks, both discrete (coined) and continuous time, on a general graph of N vertices with undirected edges are reviewed in some detail. The resource requirements for implementing a quantum walk as a program on a quantum computer are…
Large-scale quantum computation requires to be performed in the fault-tolerant manner. One crucial challenge of fault-tolerant quantum computing (FTQC) is reducing the overhead of implementing logical gates. Recently work proposed…
We study the classical and quantum transport processes on some finite networks and model them by continuous-time random walks (CTRW) and continuous-time quantum walks (CTQW), respectively. We calculate the classical and quantum transition…
In this work we introduce, test and discuss three quantum methods for computing hub and authority centrality scores in directed networks. The methods are based on unitary, continuous-time quantum walks; the construction of a suitable…
In this work we explain the necessity for consistently labeled rotation maps for efficiently computing coined discrete time quantum walks on regular graphs.
Quantum random walks represent a powerful tool for the implementation of various quantum algorithms. We consider a convolution problem for the graphs which provide quantum and classical random walks. We suggest a new method for lattices and…
The discrete time quantum walk (DTQW) is a universal quantum computational model. Significant relationships between discrete and corresponding continuous quantum systems have been studied since the work of Pauli and Feynman. This work…
Discrete-time quantum walks (DTQW) have topological phases that are richer than those of time-independent lattice Hamiltonians. Even the basic symmetries, on which the standard classification of topological insulators hinges, have not yet…
This manuscript gathers and subsumes a long series of works on using QW to simulate transport phenomena. Quantum Walks (QWs) consist of single and isolated quantum systems, evolving in discrete or continuous time steps according to a…
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 Continuous-Time Quantum Walks (CTQW) model for one-dimensional Dirac dynamics simulation with higher-order approximation. Our model bridges CTQW with a discrete-time model called Dirac Cellular Automata (DCA) via Quantum…
A new approach to quantum walks is presented. Considering a quantum system undergoing some unitary discrete-time evolution in a directed graph G, we think of the vertices of G as sites that are occupied by the quantum system, whose internal…
Arbitrary exponentially large unitaries cannot be implemented efficiently by quantum circuits. However, we show that quantum circuits can efficiently implement any unitary provided it has at most polynomially many nonzero entries in any row…
In this paper, we consider a continuous-time quantum walk based search algorithm. We introduce equitable partition of the graph and perfect state transfer on it. By these two methods, we can calculate the success probability and the finding…
Program implementation and simulation are essential for research in the field of quantum algorithms. However, complex and large-scale quantum algorithms can pose challenges for existing quantum programming languages and simulators. Here, we…
In this paper, we present an abstract model of continuous-time quantum walk (CTQW) based on Bernoulli functionals and show that the model has perfect state transfer (PST), among others. Let $\mathfrak{h}$ be the space of square integrable…
In this paper we study continuous-time quantum walks on Cayley graphs of the symmetric group, and prove various facts concerning such walks that demonstrate significant differences from their classical analogues. In particular, we show that…
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…
Early but promising results in quantum computing have been enabled by the concurrent development of quantum algorithms, devices, and materials. Classical simulation of quantum programs has enabled the design and analysis of algorithms and…
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…