Related papers: Lackadaisical quantum walk for spatial search
The spatial search problem consists in minimizing the number of steps required to find a given site in a network, under the restriction that only oracle queries or translations to neighboring sites are allowed. In this paper, a quantum…
In this work, we consider the spatial search for a general marked state on graphs by continuous time quantum walks. As a simplest case, we compute the amplitude expression of the search for the multi-vertex uniform superposition state on…
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…
Nature of quantum walk in presence of multiple marked state has been studied by Nahimovs and Rivosh \cite{10.1007/978-3-662-49192-8_31}. They have shown that if the marked states are arranged in a $\sqrt{k} \times \sqrt{k}$ cluster in a…
Spatial search is an important problem in quantum computation, which aims to find a marked vertex on a graph. We propose a novel approach for designing deterministic quantum search algorithms on a variety of graphs via alternating quantum…
Since Grover's seminal work which provides a way to speed up combinatorial search, quantum search has been studied in great detail. We propose a new method for designing quantum search algorithms for finding a marked element in the state…
We study quantum algorithms for spatial search on finite dimensional grids. Patel et al. and Falk have proposed algorithms based on a quantum walk without a coin, with different operators applied at even and odd steps. Until now, such…
The quantum walk (QW) is the term given to a family of algorithms governing the evolution of a discrete quantum system and as such has a founding role in the study of quantum computation. We contribute to the investigation of QW phenomena…
We provide numerical evidence that the nonlinear searching algorithm introduced by Wong and Meyer \cite{meyer2013nonlinear}, rephrased in terms of quantum walks with effective nonlinear phase, can be extended to the finite 2-dimensional…
The problem of finding a marked node in a graph can be solved by the spatial search algorithm based on continuous-time quantum walks (CTQW). However, this algorithm is known to run in optimal time only for a handful of graphs. In this work,…
A powerful strategy to accelerate quantum-walk-based search algorithms leverages on resetting protocols, where a detector monitors a target site and the evolution of the walker is restarted if no detection occurs within a fixed time…
Continuous-time quantum walks provide an alternative method for quantum search problems. Most of the earlier studies confirmed that quadratic speedup exists in some synthetic Hamiltonians, but whether there is quadratic speedup in real…
In typical discrete-time quantum walk algorithms, one measures the position of the walker while ignoring its internal spin/coin state. Rather than neglecting the information in this internal state, we show that additionally measuring it…
Continuous-time quantum walks (CTQWs) on dynamic graphs, referred to as dynamic CTQWs, are a recently introduced universal model of computation that offers a new paradigm in which to envision quantum algorithms. In this work we develop an…
A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. Searching in this mathematical framework has interested the community since a long time. However, most results consider spatial search…
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…
Quantum walks contribute significantly to developing quantum algorithms and quantum simulations. Here, we introduce a first of its kind one-dimensional quantum walk in the $d$-dimensional quantum domain, where $d>2$, and show its…
A two-dimensional discrete-time quantum walk (DTQW) can be realized by alternating a two-state DTQW in one spatial dimension followed by an evolution in the other dimension. This was shown to reproduce a probability distribution for a…
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…
Quantum walk has emerged as an essential tool for searching marked vertices on various graphs. Recent advances in the discrete-time quantum walk search algorithm have enabled it to effectively handle multiple marked vertices, expanding its…