Related papers: Efficient Non-Adaptive Quantum Algorithms for Tole…
In this note, we develop a bounded-error quantum algorithm that makes $\tilde O(n^{1/4}\varepsilon^{-1/2})$ queries to a Boolean function $f$, accepts a monotone function, and rejects a function that is $\varepsilon$-far from being…
Inspired by a recent classical distribution-free junta tester by Chen, Liu, Serverdio, Sheng, and Xie (STOC'18), we construct a quantum tester for the same problem with complexity $O(k/\varepsilon)$, which constitutes a quadratic…
The model of relative-error property testing of Boolean functions has been the subject of significant recent research effort [CDH+24][CPPS25a][CPPS25b] In this paper we consider the problem of relative-error testing an unknown and arbitrary…
Given a black-box representing an unknown Boolean function $f$ of $n$ variables, in this paper we propose a fast quantum algorithm to test whether or not a certain variable in the function $f$ is a junta variable. The proposed algorithm…
We study the power of nonadaptive quantum query algorithms, which are algorithms whose queries to the input do not depend on the result of previous queries. First, we show that any bounded-error nonadaptive quantum query algorithm that…
Quantum-phase-estimation algorithms are critical subroutines in many applications for quantum computers and in quantum-metrology protocols. These algorithms estimate the unknown strength of a unitary evolution. By using coherence or…
We give an adaptive algorithm which tests whether an unknown Boolean function $f\colon \{0, 1\}^n \to\{0, 1\}$ is unate, i.e. every variable of $f$ is either non-decreasing or non-increasing, or $\epsilon$-far from unate with one-sided…
We consider the problem of enumerating relevant features hidden in other irrelevant information for multi-labeled data, which is formalized as learning juntas. A $k$-junta function is a function which depends on only $k$ coordinates of the…
We give an algorithm for learning symmetric k-juntas (boolean functions of $n$ boolean variables which depend only on an unknown set of $k$ of these variables) in the PAC model under the uniform distribution, which runs in time n^{O(k/\log…
Khot and Shinkar (RANDOM, 2016) recently describe an adaptive, $O(n \log(n)/\varepsilon)$-query tester for unateness of Boolean functions $f:\{0,1\}^n \to \{0,1\}$. In this note we describe a simple non-adaptive, $O(n…
The problem of tolerant junta testing is a natural and challenging problem which asks if the property of a function having some specified correlation with a $k$-Junta is testable. In this paper we give an affirmative answer to this…
In this paper, we consider the problem of tolerant junta testing for boolean function. Compared with the prior work by Blais et al., we provide improved results in terms of both the parameter gap and query complexity. Compared with the…
A Boolean function $f:\{0,1\}^n\to \{0,1\}$ is $k$-linear if it returns the sum (over the binary field $F_2$) of $k$ coordinates of the input. In this paper, we study property testing of the classes $k$-Linear, the class of all $k$-linear…
We present an adaptive tester for the unateness property of Boolean functions. Given a function $f:\{0,1\}^n \to \{0,1\}$ the tester makes $O(n \log(n)/\epsilon)$ adaptive queries to the function. The tester always accepts a unate function,…
We give the first super-polynomial (in fact, mildly exponential) lower bounds for tolerant testing (equivalently, distance estimation) of monotonicity, unateness, and juntas with a constant separation between the "yes" and "no" cases.…
We consider the problem of Clifford testing, which asks whether a black-box $n$-qubit unitary is a Clifford unitary or at least $\varepsilon$-far from every Clifford unitary. We give the first 4-query Clifford tester, which decides this…
A natural problem in high-dimensional inference is to decide if a classifier $f:\mathbb{R}^n \rightarrow \{-1,1\}$ depends on a small number of linear directions of its input data. Call a function $g: \mathbb{R}^n \rightarrow \{-1,1\}$, a…
We design a nonadaptive algorithm that, given oracle access to a function $f: \{0,1\}^n \to \{0,1\}$ which is $\alpha$-far from monotone, makes poly$(n, 1/\alpha)$ queries and returns an estimate that, with high probability, is an…
We consider the basic statistical problem of detecting truncation of the uniform distribution on the Boolean hypercube by juntas. More concretely, we give upper and lower bounds on the problem of distinguishing between i.i.d. sample access…
A Boolean function f over n variables is said to be q-locally correctable if, given a black-box access to a function g which is "close" to an isomorphism f_sigma of f, we can compute f_sigma(x) for any x in Z_2^n with good probability using…