Related papers: Quantum Property Testing of Group Solvability
This paper employs a powerful argument, called an algorithmic argument, to prove lower bounds of the quantum query complexity of a multiple-block ordered search problem in which, given a block number i, we are to find a location of a target…
We study the probability of making an error if, by querying an oracle a fixed number of times, we declare constant a randomly chosen n-bit Boolean function. We compare the classical and the quantum case, and we determine for how many…
We call a group $G$ {\it algorithmically finite} if no algorithm can produce an infinite set of pairwise distinct elements of $G$. We construct examples of recursively presented infinite algorithmically finite groups and study their…
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…
The hidden shift problem is a natural place to look for new separations between classical and quantum models of computation. One advantage of this problem is its flexibility, since it can be defined for a whole range of functions and a…
This article surveys the state of the art in quantum computer algorithms, including both black-box and non-black-box results. It is infeasible to detail all the known quantum algorithms, so a representative sample is given. This includes a…
We study the problem of transmission of information over classical and classical-quantum channels in the one-shot regime where the underlying codes are constrained to be group codes. In the achievability part, we introduce a new input…
Consider a very large (infinite) population of items, where each item independent from the others is defective with probability p, or good with probability q=1-p. The goal is to identify N good items as quickly as possible. The following…
Most measurements are designed to tell you which of several alternatives have occurred, but it is also possible to make measurements that eliminate possibilities and tell you an alternative that did not occur. Measurements of this type have…
Given two testable properties $\mathcal{P}_{1}$ and $\mathcal{P}_{2}$, under what conditions are the union, intersection or set-difference of these two properties also testable? We initiate a systematic study of these basic set-theoretic…
PARITY is the problem of determining the parity of a string $f$ of $n$ bits given access to an oracle that responds to a query $x\in\{0,1,...,n-1\}$ with the $x^{\rm th}$ bit of the string, $f(x)$. Classically, $n$ queries are required to…
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…
We give a classification and complete algebraic description of groups allowing only finitely many (left multiplication invariant) circular orders. In particular, they are all solvable groups with a specific semi-direct product…
The goal of group testing is to efficiently identify a few specific items, called positives, in a large population of items via tests. A test is an action on a subset of items which returns positive if the subset contains at least one…
The ultimate objective of this paper is to create a stepping stone to the development of new quantum algorithms. The strategy chosen is to begin by focusing on the class of abelian quantum hidden subgroup algorithms, i.e., the class of…
We describe a method to upper bound the quantum query complexity of Boolean formula evaluation problems, using fundamental theorems about the general adversary bound. This nonconstructive method can give an upper bound on query complexity…
Efficiently counting or detecting defective items is a crucial task in various fields ranging from biological testing to quality control to streaming algorithms. The \emph{group testing estimation problem} concerns estimating the number of…
Group testing is the process of pooling arbitrary subsets from a set of $n$ items so as to identify, with a minimal number of tests, a "small" subset of $d$ defective items. In "classical" non-adaptive group testing, it is known that when…
Quantum systems, in general, output data that cannot be simulated efficiently by a classical computer, and hence is useful for solving certain mathematical problems and simulating quantum many-body systems. This also implies, unfortunately,…
Oracle quantum programs are a fundamental class of quantum programs that serve as a critical bridge between quantum computing and classical computing. Many important quantum algorithms are built upon oracle quantum programs, making it…