Related papers: Universal quantum computation by discontinuous qua…
At present, several models for quantum computation have been proposed. Adiabatic quantum computation scheme particularly offers this possibility and is based on a slow enough time evolution of the system, where no transitions take place. In…
Quantum networks are complex systems formed by the interaction among quantum processors through quantum channels. Analogous to classical computer networks, quantum networks allow for the distribution of quantum operations among quantum…
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…
This tutorial article showcases the many varieties and uses of quantum walks. Discrete time quantum walks are introduced as counterparts of classical random walks. The emphasis is on the connections and differences between the two types of…
The physics of quantum walks on graphs is formulated in Hamiltonian language, both for simple quantum walks and for composite walks, where extra discrete degrees of freedom live at each node of the graph. It is shown how to map between…
Quantum walks contribute significantly to developing quantum algorithms and quantum simulations. Here, we introduce a first of its kind one-dimensional quantum walk in the $d$-dimensional quantum domain, where $d>2$, and show its…
Classical random walk formalism shows a significant role across a wide range of applications. As its quantum counterpart, the quantum walk is proposed as an important theoretical model for quantum computing. By exploiting the quantum…
The quantum walk dynamics obey the laws of quantum mechanics with an extra locality constraint, which demands that the evolution operator is local in the sense that the walker must visit the neighboring locations before endeavoring to…
The nonadiabatic holonomic quantum computation based on the geometric phase is robust against the built-in noise and decoherence. In this work, we theoretically propose a scheme to realize nonadiabatic holonomic quantum gates in a surface…
We discuss the model of a one-dimensional, discrete-time walk on a line with spatial heterogeneity in the form of a variable set of ultrametric barriers. Inspired by the homogeneous quantum walk on a line, we develop a formalism by which…
A scheme of universal quantum computation on a chain of qubits is described that does not require local control. All the required operations, an Ising-type interaction and spatially uniform simultaneous one-qubit gates, are…
The adjacency matrix of a graph G is the Hamiltonian for a continuous-time quantum walk on the vertices of G. Although the entries of the adjacency matrix are integers, its eigenvalues are generally irrational and, because of this, the…
Previously it was shown that (almost) perfect state transfer can be achieved on the complete bipartite graph by a discrete-time coined quantum walk based algorithm when both the sender and receiver vertices are in the same partition of the…
Quantum random walks are shown to have non-intuitive dynamics, which makes them an attractive area of study for devising quantum algorithms for well-known classical problems as well as those arising in the field of quantum computing. In…
Multi-dimensional quantum walks can exhibit highly non-trivial topological structure, providing a powerful tool for simulating quantum information and transport systems. We present a flexible implementation of a 2D optical quantum walk on a…
It is well-known that any quantum gate can be decomposed into the universal gate set {T, H, CNOT}, and recent results have shown that each of these gates can be implemented using a dynamic quantum walk, which is a continuous-time quantum…
Recently, it has been shown that one-dimensional quantum walks can mix more quickly than classical random walks, suggesting that quantum Monte Carlo algorithms can outperform their classical counterparts. We study two quantum walks on the…
Quantum random walks are shown to have non-intuitive dynamics which makes them an attractive area of study for devising quantum algorithms for long-standing open problems as well as those arising in the field of quantum computing. In the…
Quantum walks have emerged as an interesting candidate for the implementation of quantum information processing protocols. Optical implementations of quantum walks have been demonstrated by various groups and some have received high-profile…
A discrete-time quantum walk is the quantum analogue of a Markov chain on a graph. Zhan [J. Algebraic Combin. 53(4):1187-1213, 2020] proposes a model of discrete-time quantum walk whose transition matrix is given by two reflections, using…