Related papers: Quantum algorithm for tree size estimation, with a…
We consider the problem of estimating the expected outcomes of Monte Carlo processes whose outputs are described by multidimensional random variables. We tightly characterize the quantum query complexity of this problem for various choices…
Searching and sorting used as a subroutine in many important algorithms. Quantum algorithm can find a target item in a database faster than any classical algorithm. One can trade accuracy for speed and find a part of the database (a block)…
The Quantum Approximate Optimization Algorithm can be applied to search problems on graphs with a cost function that is a sum of terms corresponding to the edges. When conjugating an edge term, the QAOA unitary at depth p produces an…
Quantum computers have the potential of solving certain problems exponentially faster than classical computers. Recently, Harrow, Hassidim and Lloyd proposed a quantum algorithm for solving linear systems of equations: given an $N\times{N}$…
We consider two combinatorial problems. The first we call "search with wildcards": given an unknown n-bit string x, and the ability to check whether any subset of the bits of x is equal to a provided query string, the goal is to output x.…
Enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum game with the problem of data clustering, and then develop a quantum-game-based clustering algorithm, in which data points…
The current era of quantum computing has yielded several algorithms that promise high computational efficiency. While the algorithms are sound in theory and can provide potentially exponential speedup, there is little guidance on how to…
In this work I describe a classical analog of Grover's quantum searching algorithm, explaining why a quantum algorithm should be able to perform search in O(sqrtN) steps and also acting as a useful pedagogic demonstration.
In a fundamental paper [Phys. Rev. Lett. 78, 325 (1997)] Grover showed how a quantum computer can find a single marked object in a database of size N by using only O(N^{1/2}) queries of the oracle that identifies the object. His result was…
In the search with wildcards problem [Ambainis, Montanaro, Quantum Inf.~Comput.'14], one's goal is to learn an unknown bit-string $x \in \{-1,1\}^n$. An algorithm may, at unit cost, test equality of any subset of the hidden string with a…
In this work, we present a quantum query algorithm for searching a word of length $m$ in an unsorted dictionary of size $n$. The algorithm uses $O(\sqrt{n})$ queries (Grover operators), like previously known algorithms. What is new is that…
Quantum walk is a potent technique for building quantum algorithms. This paper examines the quantum walk search algorithm on complete multipartite graphs with multiple marked vertices, which has not been explored before. Two specific cases…
In Noisy Intermediate-Scale Quantum (NISQ) era, quantum processing units (QPUs) suffer from, among others, highly limited connectivity between physical qubits. To make a quantum circuit effectively executable, a circuit transformation…
This paper initiates the study of quantum algorithms for matroid property problems. It is shown that quadratic quantum speedup is possible for the calculation problem of finding the girth or the number of circuits (bases, flats,…
This paper develops a measure for bounding the performance of AND/OR search algorithms for solving a variety of queries over graphical models. We show how drawing a connection to the recent notion of hypertree decompositions allows to…
The treedepth of a graph $G$ is the least possible depth of an elimination forest of $G$: a rooted forest on the same vertex set where every pair of vertices adjacent in $G$ is bound by the ancestor/descendant relation. We propose an…
We introduce two quantum algorithms for solving structured prediction problems. We first show that a stochastic gradient descent that uses the quantum minimum finding algorithm and takes its probabilistic failure into account solves the…
High dimensional integration is essential to many areas of science, ranging from particle physics to Bayesian inference. Approximating these integrals is hard, due in part to the difficulty of locating and sampling from regions of the…
The kernel method is a potential approach to analyzing structured data such as sequences, trees, and graphs; however, unordered trees have not been investigated extensively. Kimura et al. (2011) proposed a kernel function for unordered…
Quantum search is a technique for searching N possibilities in only O(sqrt(N)) steps. It has been applied in the design of quantum algorithms for several structured problems. Many of these algorithms require significant amount of quantum…