相关论文: Private learning implies quantum stability

The exponential scaling of the wave function is a fundamental property of quantum systems with far reaching implications in our ability to process quantum information. A problem where these are particularly relevant is quantum state…

We continue the study of the computational complexity of differentially private PAC learning and how it is situated within the foundations of machine learning. A recent line of work uncovered a qualitative equivalence between the private…

Shadow tomography for quantum states provides a sample efficient approach for predicting the properties of quantum systems when the properties are restricted to expectation values of $2$-outcome POVMs. However, these shadow tomography…

We study binary classification algorithms for which the prediction on any point is not too sensitive to individual examples in the dataset. Specifically, we consider the notions of uniform stability (Bousquet and Elisseeff, 2001) and…

The constantly increasing dimensionality of artificial quantum systems demands for highly efficient methods for their characterization and benchmarking. Conventional quantum tomography fails for larger systems due to the exponential growth…

Suppose we have many copies of an unknown $n$-qubit state $\rho$. We measure some copies of $\rho$ using a known two-outcome measurement $E_{1}$, then other copies using a measurement $E_{2}$, and so on. At each stage $t$, we generate a…

We consider the problem of learning stabilizer states with noise in the Probably Approximately Correct (PAC) framework of Aaronson (2007) for learning quantum states. In the noiseless setting, an algorithm for this problem was recently…

The ability of quantum computers to directly manipulate and analyze quantum states stored in quantum memory allows them to learn about aspects of our physical world that would otherwise be invisible given a modest number of measurements.…

We consider online and PAC learning of Littlestone classes subject to the constraint of approximate differential privacy. Our main result is a private learner to online-learn a Littlestone class with a mistake bound of…

We prove that every concept class with finite Littlestone dimension can be learned by an (approximate) differentially-private algorithm. This answers an open question of Alon et al. (STOC 2019) who proved the converse statement (this…

We give new differentially private algorithms for the classic problems of learning decision lists and large-margin halfspaces in the PAC and online models. In the PAC model, we give a computationally efficient algorithm for learning…

The problem of efficient quantum state learning, also called shadow tomography, aims to comprehend an unknown $d$-dimensional quantum state through POVMs. Yet, these states are rarely static; they evolve due to factors such as measurements,…

The complete learning of an $n$-qubit quantum state requires samples exponentially in $n$. Several works consider subclasses of quantum states that can be learned in polynomial sample complexity such as stabilizer states or high-temperature…

We construct a universally Bayes consistent learning rule that satisfies differential privacy (DP). We first handle the setting of binary classification and then extend our rule to the more general setting of density estimation (with…

We study the problems of quantum tomography and shadow tomography using measurements performed on individual, identical copies of an unknown $d$-dimensional state. We first revisit a known lower bound due to Haah et al. (2017) on quantum…

Learning quantum state properties is both a fundamental and practical problem in quantum information theory. Classical shadows have emerged as an efficient method for estimating properties of unknown quantum states, with rigorous…

This work explores the connection between differential privacy (DP) and online learning in the context of PAC list learning. In this setting, a $k$-list learner outputs a list of $k$ potential predictions for an instance $x$ and incurs a…

In differential privacy (DP), we want to query a database about n users, in a way that "leaks at most eps about any individual user," even conditioned on any outcome of the query. Meanwhile, in gentle measurement, we want to measure n…

We study the computational relationship between replicability (Impagliazzo et al. [STOC `22], Ghazi et al. [NeurIPS `21]) and other stability notions. Specifically, we focus on replicable PAC learning and its connections to differential…

In this work we analyze the sample complexity of classification by differentially private algorithms. Differential privacy is a strong and well-studied notion of privacy introduced by Dwork et al. (2006) that ensures that the output of an…