Related papers: Quantum Property Testing Algorithm for the Concate…
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 initiate the systematic study of QMA algorithms in the setting of property testing, to which we refer as QMA proofs of proximity (QMAPs). These are quantum query algorithms that receive explicit access to a sublinear-size untrusted proof…
We present several new examples of speed-ups obtainable by quantum algorithms in the context of property testing. First, motivated by sampling algorithms, we consider probability distributions given in the form of an oracle $f:[n]\to[m]$.…
We present a trichotomy theorem for the quantum query complexity of regular languages. Every regular language has quantum query complexity Theta(1), ~Theta(sqrt n), or Theta(n). The extreme uniformity of regular languages prevents them from…
We explore potential quantum speedups for the fundamental problem of testing the properties of closeness and $k$-wise uniformity of probability distributions. Closeness testing is the problem of distinguishing whether two $n$-dimensional…
A language L has a property tester if there exists a probabilistic algorithm that given an input x only asks a small number of bits of x and distinguishes the cases as to whether x is in L and x has large Hamming distance from all y in L.…
We initiate a systematic study of the computational complexity of property testing, focusing on the relationship between query and time complexity. While traditional work in property testing has emphasized query complexity, relatively…
The goal of property testing is to quickly distinguish between objects which satisfy a property and objects that are $\epsilon$-far from satisfying the property. There are now several general results in this area which show that natural…
Property testers are fast, randomized "election polling"-type algorithms that determine if an input (e.g., graph or hypergraph) has a certain property or is $\varepsilon$-far from the property. In the dense graph model of property testing,…
The area of property testing tries to design algorithms that can efficiently handle very large amounts of data: given a large object that either has a certain property or is somehow "far" from having that property, a tester should…
Suppose one has access to oracles generating samples from two unknown probability distributions P and Q on some N-element set. How many samples does one need to test whether the two distributions are close or far from each other in the…
We study unitary property testing, where a quantum algorithm is given query access to a black-box unitary and has to decide whether it satisfies some property. In addition to containing the standard quantum query complexity model (where the…
Query complexity is a model of computation in which we have to compute a function $f(x_1, \ldots, x_N)$ of variables $x_i$ which can be accessed via queries. The complexity of an algorithm is measured by the number of queries that it makes.…
Given a Boolean function f, we study two natural generalizations of the certificate complexity C(f): the randomized certificate complexity RC(f) and the quantum certificate complexity QC(f). Using Ambainis' adversary method, we exactly…
Properties of Boolean functions can often be tested much faster than the functions can be learned. However, this advantage usually disappears when testers are limited to random samples of a function $f$--a natural setting for data…
We give a quantum algorithm for evaluating a class of boolean formulas (such as NAND trees and 3-majority trees) on a restricted set of inputs. Due to the structure of the allowed inputs, our algorithm can evaluate a depth $n$ tree using…
We present quantum query complexity bounds for testing algebraic properties. For a set S and a binary operation on S, we consider the decision problem whether $S$ is a semigroup or has an identity element. If S is a monoid, we want to…
Property testing has been extensively studied and its target is to determine whether a given object satisfies a certain property or it is far from the property. In this paper, we construct an efficient quantum algorithm which tests if a…
An atom of a regular language L with n (left) quotients is a non-empty intersection of uncomplemented or complemented quotients of L, where each of the n quotients appears in a term of the intersection. The quotient complexity of L, which…
This study examines clusterability testing for a signed graph in the bounded-degree model. Our contributions are two-fold. First, we provide a quantum algorithm with query complexity $\tilde{O}(N^{1/3})$ for testing clusterability, which…