Related papers: Deutsch-Jozsa and Bernstein-Vazirani algorithm usi…
We make and generalize the observation that summing of probability amplitudes of a discrete-time quantum walk over partitions of the walking graph consistent with the step operator results in a unitary evolution on the reduced graph which…
Szegedy developed a generic method for quantizing classical algorithms based on random walks [Proceedings of FOCS, 2004, pp. 32-41]. A major contribution of his work was the construction of a walk unitary for any reversible random walk.…
Quantum algorithms theoretically outperform classical algorithms in solving problems of increasing size, but computational errors must be kept to a minimum to realize this potential. Despite the development of increasingly capable quantum…
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…
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…
Quantum random walks are shown to have non-intuitive dynamics, which makes them an attractive area of study for devising quantum algorithms for well-known classical problems as well as those arising in the field of quantum computing. In…
Based on the Dirac representation of Maxwell equations we present an explicit, discrete space-time, quantum walk-inspired algorithm suitable for simulating the electromagnetic wave propagation and scattering from inhomogeneities within…
We present the first robust implementation of a coined quantum walk over five steps using only passive optical elements. By employing a fiber network loop we keep the amount of required resources constant as the walker's position Hilbert…
A hybrid model of the Deutsch-Jozsa algorithm is presented, inspired by the proposals of hybrid computation by S. Lloyd and P. van Loock et. al. The model is based on two observations made about both the discrete and continuous algorithms…
Signaled by non-analyticities in the time evolution of physical observables, dynamic quantum phase transitions (DQPTs) emerge in quench dynamics of topological systems and possess an interesting geometric origin captured by dynamic…
High-energy physics simulations traditionally rely on classical Monte Carlo methods to model complex particle interactions, often incurring significant computational costs. In this paper, we introduce a novel quantum-enhanced simulation…
We present an approach to induce localization of a Bose-Einstein condensate in a one-dimensional lattice under the influence of unitary quantum walk evolution using disordered quantum coin operation. We introduce a discrete-time quantum…
A proposal for the implementation of quantum walks using cold atom technology is presented. It consists of one atom trapped in time varying optical superlattices. The required elements are presented in detail including the preparation…
For the ever-growing field of quantum information processing, large-scale, efficient multi-port interferometers serving as photonic processors are required. In this context, the suitability of quantum walks as the interferometric base for…
We propose a physical implementation of the step operator of the discrete quantum walk for an electron in a one-dimensional chain of quantum dots. The operating principle of the step operator is based on locally enhanced Zeeman splitting…
We present an idealized quantum continuous variable analog of the Deutsch-Jozsa algorithm which can be implemented on a perfect continuous variable quantum computer. Using the Fourier transformation and XOR gate appropriate for continuous…
Quantum walks, in virtue of the coherent superposition and quantum interference, possess exponential superiority over its classical counterpart in applications of quantum searching and quantum simulation. The quantum enhanced power is…
Quantum correlations have been pointed out as the most likely source of the speed-up in quantum computation. Here we analyzed the presence of quantum correlations in the implementation of Deutsch-Jozsa algorithm running in the DQC1 and DQCp…
Quantum entanglement and coherence are crucial resources in quantum information theory. In some scenarios, however, it is not necessary to directly estimate entanglement or coherence measures to quantify the capabilities of a state in…
A long-standing aim of quantum information research is to understand what gives quantum computers their advantage. This requires separating problems that need genuinely quantum resources from those for which classical resources are enough.…