Related papers: From Bit-Parallelism to Quantum String Matching fo…
We present a quantum algorithm for sampling random spanning trees from a weighted graph in $\widetilde{O}(\sqrt{mn})$ time, where $n$ and $m$ denote the number of vertices and edges, respectively. Our algorithm has sublinear runtime for…
We introduce a quantum dynamic programming framework that allows us to directly extend to the quantum realm a large body of classical dynamic programming algorithms. The corresponding quantum dynamic programming algorithms retain the same…
We study a variant of the subgraph isomorphism problem that is of high interest to the quantum computing community. Our results give an algorithm to perform pattern matching in quantum circuits for many patterns simultaneously,…
Exact pattern matching in labeled graphs is the problem of searching paths of a graph $G=(V,E)$ that spell the same string as the pattern $P[1..m]$. This basic problem can be found at the heart of more complex operations on variation graphs…
In this paper we study quantum algorithms for NP-complete problems whose best classical algorithm is an exponential time application of dynamic programming. We introduce the path in the hypercube problem that models many of these dynamic…
In this paper we present an efficiently scaling quantum algorithm which finds the size of the maximum common edge subgraph for a pair of arbitrary graphs and thus provides a meaningful measure of graph similarity. The algorithm makes use of…
In this paper we revisit the classical regular expression matching problem, namely, given a regular expression $R$ and a string $Q$, decide if $Q$ matches one of the strings specified by $R$. Let $m$ and $n$ be the length of $R$ and $Q$,…
Quantum computers can sometimes exponentially outperform classical ones, but only for problems with sufficient structure. While it is well known that query problems with full permutation symmetry can have at most polynomial quantum speedup…
Though quantum algorithm acts as an important role in quantum computation science, not only for providing a great vision for solving classically unsolvable problems, but also due to the fact that it gives a potential way of understanding…
We study quantum algorithms for several fundamental string problems, including Longest Common Substring, Lexicographically Minimal String Rotation, and Longest Square Substring. These problems have been widely studied in the stringology…
The graph isomorphism problem is theoretically interesting and also has many practical applications. The best known classical algorithms for graph isomorphism all run in time super-polynomial in the size of the graph in the worst case. An…
Quantum contextuality is a limitation on deterministic hidden variable models, testable in measurement scenarios where outcomes differ under quantum or classical descriptions due to a common set of constraints. When considering measurements…
We study space and time efficient quantum algorithms for two graph problems -- deciding whether an $n$-vertex graph is a forest, and whether it is bipartite. Via a reduction to the s-t connectivity problem, we describe quantum algorithms…
The $d$-dimensional pattern matching problem is to find an occurrence of a pattern of length $m \times \dots \times m$ within a text of length $n \times \dots \times n$, with $n \ge m$. This task models various problems in text and image…
Classical optimization algorithms in machine learning often take a long time to compute when applied to a multi-dimensional problem and require a huge amount of CPU and GPU resource. Quantum parallelism has a potential to speed up machine…
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 give a new upper bound on the quantum query complexity of deciding $st$-connectivity on certain classes of planar graphs, and show the bound is sometimes exponentially better than previous results. We then show Boolean formula evaluation…
Quantum algorithms for several problems in graph theory are considered. Classical algorithms for finding the lowest weight path between two points in a graph and for finding a minimal weight spanning tree involve searching over some space.…
Continuous-time quantum walks provide a natural framework to tackle the fundamental problem of finding a node among a set of marked nodes in a graph, known as spatial search. Whether spatial search by continuous-time quantum walk provides a…
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…