Related papers: Google In A Photonic Lattice
Quantum computing promises to improve the information processing power to levels unreachable by classical computation. Quantum walks are heading the development of quantum algorithms for searching information on graphs more efficiently than…
With photonics, the quantum computational advantage has been demonstrated on the task of boson sampling. Next, developing quantum-enhanced approaches for practical problems becomes one of the top priorities for photonic systems. Quantum…
Quantum walks provide a powerful framework for achieving algorithmic speedup in quantum computing. This paper presents a quantum search algorithm for 2-tessellable graphs, a generalization of bipartite graphs, achieving a quadratic speedup…
Fluid flow simulations marshal our most powerful computational resources. In many cases, even this is not enough. Quantum computers provide an opportunity to speed up traditional algorithms for flow simulations. We show that lattice-based…
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…
We analyse the eigenvalue and eigenvector structure of the flip-flop quantum walk on regular graphs, explicitly demonstrating how it is quadratically faster than the classical random walk. Then we use it in a controlled spatial search…
We demonstrate that a site-dependent driving of a periodic potential allows for the controlled manipulation of a quantum particle on length scales of the lattice spacing. Specifically we observe for distinct driving frequencies a near…
The task of finding an entry in an unsorted list of $N$ elements famously takes $O(N)$ queries to an oracle for a classical computer and $O(\sqrt{N})$ queries for a quantum computer using Grover's algorithm. Reformulated as a spatial search…
We introduce a simple diagrammatic approach for estimating how a randomly walking quantum particle searches on a graph in continuous-time, which involves sketching small weighted graphs with self-loops and considering degenerate…
This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics (QM) results without using its mathematical formulation. The proposed model only uses integer-valued quantities and operations on…
In quantum computing, the quantum walk search algorithm is designed for locating fixed marked nodes within a graph. However, when multiple marked nodes exist, the conventional search algorithm lacks the capacity to simultaneously amplify…
A series of quantum search algorithms have been proposed recently providing an algebraic speedup compared to classical search algorithms from $N$ to $\sqrt{N}$, where $N$ is the number of items in the search space. In particular, devising…
Quantum walks are at the heart of modern quantum technologies. They allow to deal with quantum transport phenomena and are an advanced tool for constructing novel quantum algorithms. Quantum walks on graphs are fundamentally different from…
Quantum algorithm is an algorithm for solving mathematical problems using quantum systems encoded as information, which is found to outperform classical algorithms in some specific cases. The objective of this study is to develop a quantum…
It is shown that a Dirac(-type) equation for a rank-two bi-spinor field on Minkowski (configuration) spacetime furnishes a Lorentz-covariant quantum-mechanical wave equation in position-space representation for a single free photon. This…
Inspired by the classical phenomenon of random walk, the concept of quantum walk has emerged recently as a powerful platform for the dynamical simulation of complex quantum systems, entanglement production and universal quantum computation.…
Quantum tomography is an essential method of the photonic technology toolbox and is routinely used for evaluation of experimentally prepared states of light and characterization of devices transforming such states. The tomography procedure…
Heat kernel pagerank is a variation of Personalized PageRank given in an exponential formulation. In this work, we present a sublinear time algorithm for approximating the heat kernel pagerank of a graph. The algorithm works by simulating…
We consider the problem of finding a desired item out of $N$ items arranged on the sites of a two-dimensional lattice of size $\sqrt{N} \times \sqrt{N}$. The previous quantum walk based algorithms take $O(\sqrt{N}\log N)$ steps to solve…
We study numerically the spectrum and eigenstate properties of the Google matrix of various examples of directed networks such as vocabulary networks of dictionaries and university World Wide Web networks. The spectra have gapless structure…