Related papers: Quantum walks with memory on cycles
The first general analytic solutions for the one-dimensional walk in position and momentum space are derived. These solutions reveal, among other things, new symmetry features of quantum walk probability densities and further insight into…
We analyze final-time dependent discrete-time quantum walks in one dimension. We compute asymptotics of the return probability of the quantum walk by a path counting approach. Moreover, we discuss a relation between the quantum walk and the…
Quantum walks are quantum counterparts of Markov chains. In this article, we give a brief overview of quantum walks, with emphasis on their algorithmic applications.
We introduce a multi-coin discrete quantum random walk where the amplitude for a coin flip depends upon previous tosses. Although the corresponding classical random walk is unbiased, a bias can be introduced into the quantum walk by varying…
We study the simulation of the topological phases in three subsequent dimensions with quantum walks. We are mainly focused on the completion of a table for the protocols of the quantum walk that could simulate different family of the…
For a generalized step reinforced random walk, starting from the origin, the first step is taken according to the first element of an innovation sequence. Then in subsequent epochs, it recalls a past epoch with probability proportional to a…
The rapid development of quantum computing has led to increasing interest in quantum algorithms for a variety of different applications. Quantum walks have also experienced a surge in interest due to their potential use in quantum…
The quantum walk is the quantum analogue of the well-known random walk, which forms the basis for models and applications in many realms of science. Its properties are markedly different from the classical counterpart and might lead to…
In this paper, we work on a quantum walk whose system is manipulated by a five-diagonal unitary matrix, and present long-time limit distributions. The quantum walk launches off a location and delocalizes in distribution as its system is…
Quantum random walks use interference to obtain faster state space exploration, which can be used for algorithmic purposes. Photonic technologies provide a natural platform for many recent experimental demonstrations. Here we analyze…
We discuss a particular kind of quantum walk on a general graph. We affix two semi-infinite lines to a general finite graph, which we call tails. On the tails, the particle making the walk simply advances one unit at each time step, so that…
Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available for these processes. Here we solve exactly a model with long range memory where…
Recurrence in the classical random walk is well known and described by the P\'olya number. For quantum walks, recurrence is similarly understood in terms of the probability of a localized quantum walker to return to its origin. Under…
The study of quantum walk processes has been widely divided into two standard variants, the discrete-time quantum walk (DTQW) and the continuous-time quantum walk (CTQW). The connection between the two variants has been established by…
Since a limit distribution of a discrete-time quantum walk on the line was derived in 2002, a lot of limit theorems for quantum walks with a localized initial state have been reported. On the other hand, in quantum probability theory, there…
Quantum versions of random walks on the line and cycle show a quadratic improvement in their spreading rate and mixing times respectively. The addition of decoherence to the quantum walk produces a more uniform distribution on the line, and…
We study numerically the behavior of continuous-time quantum walks over networks which are topologically equivalent to square lattices. On short time scales, when placing the initial excitation at a corner of the network, we observe a fast,…
The "quantum walk" has emerged recently as a paradigmatic process for the dynamic simulation of complex quantum systems, entanglement production and quantum computation. Hitherto, photonic implementations of quantum walks have mainly been…
The development of universal quantum computers has achieved remarkable success in recent years, culminating with the quantum supremacy reported by Google. Now is possible to implement short-depth quantum circuits with dozens of qubits and…
Randomness plays a key role in the design of attacks on cryptographic systems and cyber security algorithms in general. Random walks and quantum walks are powerful tools for mastering random phenomena. In this article, I propose a…