Related papers: New Results on Quantum Property Testing
Lin and Lin have recently shown how starting with a classical query algorithm (decision tree) for a function, we may find upper bounds on its quantum query complexity. More precisely, they have shown that given a decision tree for a…
An algorithm for structured database searching is presented and used to solve the set partition problem. O(n) oracle calls are required in order to obtain a solution, but the probability that this solution is optimal decreases exponentially…
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,…
Quantum programs exhibit inherent non-deterministic behavior, which poses more significant challenges for error discovery compared to classical programs. While several testing methods have been proposed for quantum programs, they often…
Software under test can be analyzed dynamically, while it is being executed, to find defects. However, as the number and possible values of input parameters increase, the cost of dynamic testing rises. This paper examines whether quantum…
Grover's algorithm, orginally conceived as a means of searching an unordered database, can also be used to extract solutions from the result sets generated by quantum computations. The Grover algorithm exploits the concept of an oracle…
We consider a probabilistic quantum implementation of a variable of the Pocklington-Lehmer $N-1$ primality test using Shor's algorithm. O($\log^3 N \log\log N \log\log\log N$) elementary q-bit operations are required to determine the…
Consider a fixed universe of $N=2^n$ elements and the uniform distribution over elements of some subset of size $K$. Given samples from this distribution, the task of complement sampling is to provide a sample from the complementary subset.…
The quantum computer algorithm by Peter Shor for factorization of integers is studied. The quantum nature of a QC makes its outcome random. The output probability distribution is investigated and the chances of a successful operation is…
Quantum algorithms have demonstrated promising speed-ups over classical algorithms in the context of computational learning theory - despite the presence of noise. In this work, we give an overview of recent quantum speed-ups, revisit the…
We engineer a new probabilistic Monte-Carlo algorithm for isomorphism testing. Most notably, as opposed to all other solvers, it implicitly exploits the presence of symmetries without explicitly computing them. We provide extensive…
Functions are a fundamental object in mathematics, with countless applications to different fields, and are usually classified based on certain properties, given their domains and images. An important property of a real-valued function is…
A recent model for property testing of probability distributions (Chakraborty et al., ITCS 2013, Canonne et al., SICOMP 2015) enables tremendous savings in the sample complexity of testing algorithms, by allowing them to condition the…
In this work, we propose a new way to (non-interactively, verifiably) demonstrate quantum advantage by solving the average-case $\mathsf{NP}$ search problem of finding a solution to a system of (underdetermined) constant degree multivariate…
Search-base algorithms have widespread applications in different scenarios. Grover's quantum search algorithms and its generalization, amplitude amplification, provide a quadratic speedup over classical search algorithms for unstructured…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
One of the most fundamental problems in distribution testing is the identity testing problem: given samples $x_1,\ldots,x_s$, the goal is to determine whether the samples are drawn from a target distribution $\mathcal{D}$. When…
Two new omnibus tests of uniformity for data on the hypersphere are proposed. The new test statistics exploit closed-form expressions for orthogonal polynomials, feature tuning parameters, and are related to a "smooth maximum" function and…
We create a variety of new quantum algorithms that use Grover's algorithm and similar techniques to give polynomial speedups over their classical counterparts. We begin by introducing a set of tools that carefully minimize the impact of…
We are interested in testing properties of distributions with systematically mislabeled samples. Our goal is to make decisions about unknown probability distributions, using a sample that has been collected by a confused collector, such as…