Related papers: Robustness of Quantum Random Walk Search with mult…
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…
The quantum switch, a process enabling a coherent superposition of different orders of quantum channels, has garnered significant attention due to its ability to enable noiseless communications through noisy channels, such as…
Computational advantages gained by quantum algorithms rely largely on the coherence of quantum devices and are generally compromised by decoherence. As an exception, we present a quantum algorithm for graph isomorphism testing whose…
In this article we investigate the effects of shifting position decoherence, arisen from the tunneling effect in the experimental realization of the quantum walk, on the one-dimensional discreet time quantum walk. We show that in the regime…
Quantum Random Walks, which have drawn much attention over the past few decades for their distinctly non-classical behavior, is a promising subfield within Quantum Computing. Theoretical framework and applications for these walks have seen…
In this paper, we analyze the application of the Multi-self-loop Lackadaisical Quantum Walk on the hypercube that uses partial phase inversion to search for multiple adjacent marked vertices. We evaluate the influence of the relative…
Quantum computer algorithms can exploit the structure of random satisfiability problems. This paper extends a previous empirical evaluation of such an algorithm and gives an approximate asymptotic analysis accounting for both the average…
Recently, quantized versions of random walks have been explored as effective elements for quantum algorithms. In the simplest case of one dimension, the theory has remained divided into the discrete-time quantum walk and the continuous-time…
We present an experimental implementation of the coined discrete time quantum walk on a square using a three qubit liquid state nuclear magnetic resonance (NMR) quantum information processor (QIP). Contrary to its classical counterpart, we…
Random walks are a fundamental primitive used in many machine learning algorithms with several applications in clustering and semi-supervised learning. Despite their relevance, the first efficient parallel algorithm to compute random walks…
We present a mathematical formalism for the description of unrestricted quantum walks with entangled coins and one walker. The numerical behaviour of such walks is examined when using a Bell state as the initial coin state, two different…
We experimentally demonstrate a quantum walk on a line in phase space using one and two trapped ion. A walk with up to 23 steps is realized by subjecting an ion to state-dependent displacement operations interleaved with quantum coin…
Quantum walks are powerful tools not only to construct the quantum speedup algorithms but also to describe specific models in physical processes. Furthermore, the discrete time quantum walk has been experimentally realized in various…
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…
Quantum walks have been useful for designing quantum algorithms that outperform their classical versions for a variety of search problems. Most of the papers, however, consider a search space containing a single marked element only. We show…
We study quantum walk on a ladder with combination of conventional and split-step protocols. The two components of the walk resulting from periodic boundary conditions can be made to have three kinds of probability distributions. Two of…
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…
This work introduces a graph-phased Szegedy's quantum walk, which incorporates link phases and local arbitrary phase rotations (APR), unlocking new possibilities for quantum algorithm efficiency. We demonstrate how to adapt quantum circuits…
We identify a key difference between quantum search by discrete- and continuous-time quantum walks: a discrete-time walk typically performs one walk step per oracle query, whereas a continuous-time walk can effectively perform multiple walk…
The aim of this work is to develop a framework for realising quantum network algorithms with the use of prior knowledge about the structure of the network. We seek to obtain computational methods that allows us to locally determine network…