Related papers: Solid State Implementation of Quantum Random Walks…

The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial: pure quantum…

We propose to implement quantum computing based on electronic spin qubits by controlling the propagation of the electron wave packets through the helical edge states of quantum spin Hall systems (QSHs). Specfically, two non-commutative…

We formulate three current models of discrete-time quantum walks in a combinatorial way. These walks are shown to be closely related to rotation systems and 1-factorizations of graphs. For two of the models, we compute the traces and total…

The rotation of subspaces by a chosen angle is a fundamental quantum computing operation, with applications in error correction and quantum algorithms such as the Quantum Approximate Optimization Algorithm, the Variational Quantum…

Recently, several groups have investigated quantum analogues of random walk algorithms, both on a line and on a circle. It has been found that the quantum versions have markedly different features to the classical versions. Namely, the…

We discuss an efficient physical realization of topological quantum walks on a finite lattice. The $N$-point lattice is realized with $\log_2 N$ qubits, and the quantum circuit utilizes a number of quantum gates which is polynomial in the…

Quantum walks, being the quantum analogue of classical random walks, are expected to provide a fruitful source of quantum algorithms. A few such algorithms have already been developed, including the `glued trees' algorithm, which provides…

This letter treats the quantum random walk on the line determined by a 2 times 2 unitary matrix U. A combinatorial expression for the mth moment of the quantum random walk is presented by using 4 matrices, P, Q, R and S given by U. The…

We propose a scheme to implement the one-dimensional coined quantum walk with electrons transported through a two-dimensional network of spintronic semiconductor quantum rings. The coin degree of freedom is represented by the spin of the…

Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or…

Motivated by the immense success of random walk and Markov chain methods in the design of classical algorithms, we consider_quantum_ walks on graphs. We analyse in detail the behaviour of unbiased quantum walk on the line, with the example…

A crucial requirement for scalable quantum-information processing is the realization of multiple-qubit quantum gates. Universal multiple-qubit gates can be implemented by a set of universal single qubit gates and any one kind of two-qubit…

Quantum walks provide a framework for understanding and designing quantum algorithms that is both intuitive and universal. To leverage the computational power of these walks, it is important to be able to programmably modify the graph a…

Photonics provide an efficient way to implement quantum walks, the quantum analogue of classical random walk that demonstrates rich physics with potential applications. However, most photonic quantum walks do not involve photon…

The efficient control of a large number of qubits is one of most challenging aspects for practical quantum computing. Current approaches in solid-state quantum technology are based on brute-force methods, where each and every qubit requires…

We consider quantum walks defined on arbitrary infinite graphs, parameterized by a family of scattering matrices attached to the vertices. Multiplying each scattering matrix by an i.i.d. random phase, we obtain a random scattering quantum…

We consider quantum walks on the cycle in the non-stationary case where the `coin' operation is allowed to change at each time step. We characterize, in algebraic terms, the set of possible state transfers and prove that, as opposed to the…

We introduce the quantum stochastic walk (QSW), which determines the evolution of generalized quantum mechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all…

Quantum random walks (QRWs) can be used to perform both quantum simulations and quantum algorithms. In order to exploit this potential, quantum walks on different types of graphs must be physically implemented. To this end we design, model…

Quantum measurements play a fundamental role in quantum mechanics and quantum information processing, but it is not easy to implement generalized measurements, the most powerful measurements allowed by quantum mechanics. Here we propose a…