This is a textbook about quantum walks and quantum search algorithms. The readers will
take advantage of the pedagogical aspects and learn the topics faster and make less effort …

A discrete-time quantum walk (QW) is essentially an operator driving the evolution of a
single particle on the lattice, through local unitaries. Some QWs admit a continuum limit …

Through introducing controlled alternate quantum walks, we present controlled alternate
quantum walks (CAQW) based quantum hash function. CAQW based quantum hash …

We propose a multidimensional discrete-time quantum walk (DTQW), whose continuum limit
is an extended multidimensional Dirac equation, which can be further mapped to the …

The aim of this paper is to build quantum circuits that implement discrete-time quantum
walks having an arbitrary position-dependent coin operator. The position of the walker is …

In this work, the quantum random walk search algorithm with a walk coin constructed by
generalized Householder reflection and phase multiplier has been studied. The coin register …

Bloch oscillations appear when an electric field is superimposed on a quantum particle that
evolves on a lattice with a tight-binding Hamiltonian (TBH), ie, evolves via what we call an …

Quantum walks hold enormous potential applications in various areas such as quantum
computing and quantum simulation. Discrete-time quantum walks on a ladder offer greater …

We extend to the gamut of functional forms of the probability distribution of the time-
dependent step-length a previous model dubbed Elephant Quantum Walk, which considers …

Quantum walks are a useful platform for studying high-efficiency energy transport. In this
paper, we study the probability transfer in the discrete-time quantum walk (DTQW) in detail …