Related papers: Applications of the Adversary Method in Quantum Qu…
We study the problem of learning an unknown graph provided via an oracle using a quantum algorithm. We consider three query models. In the first model ("OR queries"), the oracle returns whether a given subset of the vertices contains any…
We present quantum complexity lower and upper bounds for independent set problems in graphs. In particular, we give quantum algorithms for computing a maximal and a maximum independent set in a graph. We present applications of these…
The edge list model is arguably the simplest input model for graphs, where the graph is specified by a list of its edges. In this model, we study the quantum query complexity of three variants of the triangle finding problem. The first asks…
We study quantum algorithms for testing bipartiteness and expansion of bounded-degree graphs. We give quantum algorithms that solve these problems in time O(N^(1/3)), beating the Omega(sqrt(N)) classical lower bound. For testing expansion,…
We show that in the quantum query model the complexity of detecting a triangle in an undirected graph on $n$ nodes can be done using $O(n^{1+{3\over 7}}\log^{2}n)$ quantum queries. The same complexity bound applies for outputting the…
We study the quantum query complexity of minor-closed graph properties, which include such problems as determining whether an $n$-vertex graph is planar, is a forest, or does not contain a path of a given length. We show that most…
The (negative-weighted) quantum adversary bound is a tight characterisation of the quantum query complexity for any partial function. We analyse the extent to which this bound can be generalised. Ambainis et al. [arXiv:1012.2112] and Lee et…
The general adversary dual is a powerful tool in quantum computing because it gives a query-optimal bounded-error quantum algorithm for deciding any Boolean function. Unfortunately, the algorithm uses linear qubits in the worst case, and…
We investigate query-to-communication lifting theorems for models related to the quantum adversary bounds. Our results are as follows: 1. We show that the classical adversary bound lifts to a lower bound on randomized communication…
In this work, we initiate the study of learning quantum processes from quantum statistical queries. We focus on two fundamental learning tasks in this new access model: shadow tomography of quantum processes and process tomography with…
We study the quantum query algorithms for simplex finding, a generalization of triangle finding to hypergraphs. This problem satisfies a rank-reduction property: a quantum query algorithm for finding simplices in rank-$r$ hypergraphs can be…
We prove tight $\Omega(n^{1/3})$ lower bounds on the quantum query complexity of the Collision and the Set Equality problems, provided that the size of the alphabet is large enough. We do this using the negative-weight adversary method.…
In this paper we present a quantum algorithm solving the triangle finding problem in unweighted graphs with query complexity $\tilde O(n^{5/4})$, where $n$ denotes the number of vertices in the graph. This improves the previous upper bound…
We present several quantum algorithms for performing nearest-neighbor learning. At the core of our algorithms are fast and coherent quantum methods for computing distance metrics such as the inner product and Euclidean distance. We prove…
Quantum computing (QC) is a new computational paradigm whose foundations relate to quantum physics. Notable progress has been made, driving the birth of a series of quantum-based algorithms that take advantage of quantum computational…
Machine learning algorithms are powerful tools for data driven tasks such as image classification and feature detection, however their vulnerability to adversarial examples - input samples manipulated to fool the algorithm - remains a…
The problems of computing eccentricity, radius, and diameter are fundamental to graph theory. These parameters are intrinsically defined based on the distance metric of the graph. In this work, we propose quantum algorithms for the diameter…
Quantum Machine Learning is where nowadays machine learning meets quantum information science. In order to implement this new paradigm for novel quantum technologies, we still need a much deeper understanding of its underlying mechanisms,…
We present new quantum algorithms for Triangle Finding improving its best previously known quantum query complexities for both dense and spare instances.For dense graphs on $n$ vertices, we get a query complexity of $O(n^{5/4})$ without any…
The polynomial and the adversary methods are the two main tools for proving lower bounds on query complexity of quantum algorithms. Both methods have found a large number of applications, some problems more suitable for one method, some for…