Related papers: Optimal lower bounds for Quantum Learning via Info…
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…
Cumulative memory -- the sum of space used per step over the duration of a computation -- is a fine-grained measure of time-space complexity that was introduced to analyze cryptographic applications like password hashing. It is a more…
Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…
The fundamental theorem of statistical learning states that for binary classification problems, any Empirical Risk Minimization (ERM) learning rule has close to optimal sample complexity. In this paper we seek for a generic optimal learner…
One of the most basic lower bounds in machine learning is that in nearly any nontrivial setting, it takes $\textit{at least}$ $1/\epsilon$ samples to learn to error $\epsilon$ (and more, if the classifier being learned is complex). However,…
Standard quantum inference converts quantum data into classical outputs. We study an alternative inference setting in which the desired output is quantum, preserving coherence. Such settings include quantum purity amplification (QPA),…
The standard definition of PAC learning (Valiant 1984) requires learners to succeed under all distributions -- even ones that are intractable to sample from. This stands in contrast to samplable PAC learning (Blum, Furst, Kearns, and Lipton…
We introduce a notion of the quantum query complexity of a certificate structure. This is a formalisation of a well-known observation that many quantum query algorithms only require the knowledge of the disposition of possible certificates…
We study the complexity of two closely related learning problems, one quantum and one classical. In the quantum setting, we consider agnostic tomography for the natural class of product mixed states. Given $N$ copies of an $n$-qubit state…
In 2008, Kasiviswanathan et al. defined private learning as a combination of PAC learning and differential privacy. Informally, a private learner is applied to a collection of labeled individual information and outputs a hypothesis while…
We consider the problem of distribution-free learning for Boolean function classes in the PAC and agnostic models. Generalizing a beautiful work of Malach and Shalev-Shwartz (2022) that gave tight correlational SQ (CSQ) lower bounds for…
We study several questions in the reliable agnostic learning framework of Kalai et al. (2009), which captures learning tasks in which one type of error is costlier than others. A positive reliable classifier is one that makes no false…
Adversarially robust PAC learning has proved to be challenging, with the currently best known learners [Montasser et al., 2021a] relying on improper methods based on intricate compression schemes, resulting in sample complexity exponential…
We study the sample complexity of differentially private optimization of quasi-concave functions. For a fixed input domain $\mathcal{X}$, Cohen et al. (STOC 2023) proved that any generic private optimizer for low sensitive quasi-concave…
Quantum machine learning algorithms could provide significant speed-ups over their classical counterparts; however, whether they could also achieve good generalization remains unclear. Recently, two quantum perceptron models which give a…
Quantum state tomography is the fundamental physical task of learning a complete classical description of an unknown state of a quantum system given coherent access to many identical samples of it. The complexity of this task is commonly…
We consider the process consisting of preparation, transmission through a quantum channel, and subsequent measurement of quantum states. The communication complexity of the channel is the minimal amount of classical communication required…
In this paper, we consider the problem of replicable realizable PAC learning. We construct a particularly hard learning problem and show a sample complexity lower bound with a close to $(\log|H|)^{3/2}$ dependence on the size of the…
Instance discriminative self-supervised representation learning has been attracted attention thanks to its unsupervised nature and informative feature representation for downstream tasks. In practice, it commonly uses a larger number of…
We work out a theory of approximate quantum error correction that allows us to derive a general lower bound for the entanglement fidelity of a quantum code. The lower bound is given in terms of Kraus operators of the quantum noise. This…