Related papers: Multi-self-loop Lackadaisical Quantum Walk with Pa…
Quantum walks are powerful tools for building quantum search algorithms or quantum sampling algorithms named the construction of quantum stationary state. However, the success probability of those algorithms are all far away from 1.…
We present a novel methodological framework for quantum spatial search, generalising the Childs & Goldstone ($\mathcal{CG}$) algorithm via alternating applications of marked-vertex phase shifts and continuous-time quantum walks. We…
This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schr\"{o}dinger equation or wavefunctions. Unlike the standard QM…
Quantum walks have by now been realized in a large variety of different physical settings. In some of these, particularly with trapped ions, the walk is implemented in phase space, where the corresponding position states are not orthogonal.…
Quantum walk is a potent technique for building quantum algorithms. This paper examines the quantum walk search algorithm on complete multipartite graphs with multiple marked vertices, which has not been explored before. Two specific cases…
In this paper, a study on discrete-time coined quantum walks on the line is presented. Clear mathematical foundations are still lacking for this quantum walk model. As a step towards this objective, the following question is being…
Exploiting multi-dimensional quantum walks as feasible platforms for quantum computation and quantum simulation is attracting constantly growing attention from a broad experimental physics community. Here, we propose a two-dimensional…
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…
Fast computational algorithms are in constant demand, and their development has been driven by advances such as quantum speedup and classical acceleration. This paper intends to study search algorithms based on quantum walks in quantum…
Quantum walks are standard tools for searching graphs for marked vertices, and they often yield quadratic speedups over a classical random walk's hitting time. In some exceptional cases, however, the system only evolves by sign flips,…
Quantum walks are versatile simulators of topological phases and phase transitions as observed in condensed matter physics. Here, we utilize a step dependent coin in quantum walks and investigate what topological phases we can simulate with…
We construct a quantum random walk algorithm, based on the Dirac operator instead of the Laplacian. The algorithm explores multiple evolutionary branches by superposition of states, and does not require the coin toss instruction of…
In this tutorial, which contains some original results, we bridge the fields of quantum computing algorithms, conservation laws, and many-body quantum systems by examining three algorithms for searching an unordered database of size $N$…
In this study we show a way of achieving the reverse evolution of n-dimensional quantum walks by introducing interventions on the coin degree of freedom during the forward progression of the coin-walker system. Only a single intervention is…
This work proposes a computational procedure that uses a quantum walk in a complete graph to train classical artificial neural networks. The idea is to apply the quantum walk to search the weight set values. However, it is necessary to…
Computing using a continuous-time evolution, based on the natural interaction Hamiltonian of the quantum computer hardware, is a promising route to building useful quantum computers in the near-term. Adiabatic quantum computing, quantum…
We analyze the realization of a quantum-walk search algorithm in a passive, linear optical network. The specific model enables us to consider the effect of realistic sources of noise and losses on the search efficiency. Photon loss uniform…
We propose a new method for designing quantum search algorithms for finding a "marked" element in the state space of a classical Markov chain. The algorithm is based on a quantum walk \'a la Szegedy (2004) that is defined in terms of the…
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…
We investigate the role of a time and spin-dependent phase shift on the evolution of one-dimensional discrete-time quantum walks. By employing Floquet engineering, a time and spin-dependent phase shift ($\phi$) is imprinted onto the…