相关论文: Worst-Case Sample Complexity Bounds for Distribute…

In this paper we revisit the classical method of partitioning classification and study its convergence rate under relaxed conditions, both for observable (non-privatised) and for privatised data. We consider the problem of classification in…

Efficient global optimization is a widely used method for optimizing expensive black-box functions such as tuning hyperparameter, and designing new material, etc. Despite its popularity, less attention has been paid to analyzing the…

We present an algorithm for performing quantum process tomography on an unknown $n$-qubit unitary $C$ from the Clifford group. Our algorithm uses Bell basis measurements to deterministically learn $C$ with $4n + 3$ queries, which is the…

Shadow estimation is a recent protocol that allows estimating exponentially many expectation values of a quantum state from ``classical shadows'', obtained by applying random quantum circuits and computational basis measurements. In this…

We study the power of local test for bipartite quantum states. Our central result is that, for properties of bipartite pure states, unitary invariance on one part implies an optimal (over all global testers) local tester acting only on the…

We consider the problem of identifying, from statistics, a distribution of discrete random variables $X_1,\ldots,X_n$ that is a mixture of $k$ product distributions. The best previous sample complexity for $n \in O(k)$ was $(1/\zeta)^{O(k^2…

Quantum learning encounters fundamental challenges when estimating non-linear properties, owing to the inherent linearity of quantum mechanics. Although recent advances in single-copy randomized measurement protocols have achieved optimal…

We study quantum soft covering and privacy amplification against quantum side information. The former task aims to approximate a quantum state by sampling from a prior distribution and querying a quantum channel. The latter task aims to…

A circuit $\mathcal{C}$ samples a distribution $\mathbf{X}$ with an error $\epsilon$ if the statistical distance between the output of $\mathcal{C}$ on the uniform input and $\mathbf{X}$ is $\epsilon$. We study the hardness of sampling a…

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…

As small quantum computers are becoming available on different physical platforms, a benchmarking task known as cross-platform verification has been proposed that aims to estimate the fidelity of states prepared on two quantum computers.…

We give new characterizations of the sample complexity of answering linear queries (statistical queries) in the local and central models of differential privacy: *In the non-interactive local model, we give the first approximate…

We prove a Carbery-Wright style anti-concentration inequality for the unitary Haar measure, by showing that the probability of a polynomial in the entries of a random unitary falling into an $\varepsilon$ range is at most a polynomial in…

We address the fundamental network design problem of constructing approximate minimum spanners. Our contributions are for the distributed setting, providing both algorithmic and hardness results. Our main hardness result shows that an…

We consider differentially private approximate singular vector computation. Known worst-case lower bounds show that the error of any differentially private algorithm must scale polynomially with the dimension of the singular vector. We are…

We study policy evaluation of offline contextual bandits subject to unobserved confounders. Sensitivity analysis methods are commonly used to estimate the policy value under the worst-case confounding over a given uncertainty set. However,…

We study the following distribution clustering problem: Given a hidden partition of $k$ distributions into two groups, such that the distributions within each group are the same, and the two distributions associated with the two clusters…

We study the problem of testing the covariance matrix of a high-dimensional Gaussian in a robust setting, where the input distribution has been corrupted in Huber's contamination model. Specifically, we are given i.i.d. samples from a…

We introduce a Pauli-measurement-based algorithm to certify the Schmidt number of $n$-qubit pure states. Our protocol achieves an average-case sample complexity of $\caO(\mathrm{poly}(n)\chi^2)$, a substantial improvement over the $\caO(2^n…

Worst-case bounds on the expected shortfall risk given only limited information on the distribution of the random variables has been studied extensively in the literature. In this paper, we develop a new worst-case bound on the expected…