Related papers: Quantum Algorithm for Identifying Hidden Graphs: S…
How efficiently can we find an unknown graph using distance queries between its vertices? We assume that the unknown graph is connected, unweighted, and has bounded degree. The goal is to find every edge in the graph. This problem admits a…
This work describes a new algorithm for creating a superposition over the edge set of a graph, encoding a quantum sample of the random walk stationary distribution. The algorithm requires a number of quantum walk steps scaling as…
A quantum walk algorithm can detect the presence of a marked vertex on a graph quadratically faster than the corresponding random walk algorithm (Szegedy, FOCS 2004). However, quantum algorithms that actually find a marked element…
We study the phase discrimination problem, in which we want to decide whether the eigenphase $\theta\in(-\pi,\pi]$ of a given eigenstate $|\psi\rangle$ with eigenvalue $e^{i\theta}$ is zero or not, using applications of the unitary $U$…
We show that the quantum query complexity of detecting if an $n$-vertex graph contains a triangle is $O(n^{9/7})$. This improves the previous best algorithm of Belovs making $O(n^{35/27})$ queries. For the problem of determining if an…
One of the most important algorithmic applications of quantum walks is to solve spatial search problems. A widely used quantum algorithm for this problem, introduced by Childs and Goldstone [Phys. Rev. A 70, 022314 (2004)], finds a marked…
Quantum walk followed by some amplitude amplification technique has been successfully used to search for marked vertices on various graphs. Lackadaisical quantum walk can search for target vertices on graphs without the help of any…
The quantum walk is a powerful tool to develop quantum algorithms, which usually are based on searching for a vertex in a graph with multiple marked vertices, Ambainis's quantum algorithm for solving the element distinctness problem being…
The Scattering Quantum Random Walk scheme has found success as a basis for search algorithms on highly symmetric graph structures. In this paper we examine its effectiveness at locating a specially marked vertex on square grid graphs,…
Span program is a linear-algebraic model of computation originally proposed for studying the complexity theory. Recently, it has become a useful tool for designing quantum algorithms. In this paper, we present a time-efficient…
We study scattering quantum walks on highly symmetric graphs and use the walks to solve search problems on these graphs. The particle making the walk resides on the edges of the graph, and at each time step scatters at the vertices. All of…
With the constant flow of data from vast sources over the past decades, a plethora of advanced analytical techniques have been developed to extract relevant information from different data types ranging from labeled data, quasi-labeled…
We show a simple generalization of the quantum walk algorithm for search in backtracking trees by Montanaro (ToC 2018) to the case where vertices can have different times of computation. If a vertex $v$ in the tree of depth $D$ is computed…
Quantum walks, both discrete and continuous, serve as fundamental tools in quantum information processing with diverse applications. This work introduces a hybrid quantum walk model that integrates the coin mechanism of discrete walks with…
We present a quantum algorithm which identifies with certainty a hidden subgroup of an arbitrary finite group G in only a polynomial (in log |G|) number of calls to the oracle. This is exponentially better than the best classical algorithm.…
The identification of an unknown quantum gate is a significant issue in quantum technology. In this paper, we propose a quantum gate identification method within the framework of quantum process tomography. In this method, a series of pure…
Some of the quantum searching models have been given by perturbed quantum walks. Driving some perturbed quantum walks, we may quickly find one of the targets with high probability. In this paper, we construct a quantum searching model…
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…
Let $H$ be a fixed $k$-vertex graph with $m$ edges and minimum degree $d >0$. We use the learning graph framework of Belovs to show that the bounded-error quantum query complexity of determining if an $n$-vertex graph contains $H$ as a…
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…