Related papers: Optimal lower bounds for Quantum Learning via Info…
A basic question in the PAC model of learning is whether proper learning is harder than improper learning. In the classical case, there are examples of concept classes with VC dimension $d$ that have sample complexity $\Omega\left(\frac…
We revisit the problem of characterising the complexity of Quantum PAC learning, as introduced by Bshouty and Jackson [SIAM J. Comput. 1998, 28, 1136-1153]. Several quantum advantages have been demonstrated in this setting, however, none…
$ \newcommand{\eps}{\varepsilon} $In learning theory, the VC dimension of a concept class $C$ is the most common way to measure its "richness." In the PAC model $$ \Theta\Big(\frac{d}{\eps} + \frac{\log(1/\delta)}{\eps}\Big) $$ examples are…
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…
Studies addressing the question "Can a learner complete the learning securely?" have recently been spurred from the standpoints of fundamental theory and potential applications. In the relevant context of this question, we present a…
We study how efficiently a $k$-element set $S\subseteq[n]$ can be learned from a uniform superposition $|S\rangle$ of its elements. One can think of $|S\rangle=\sum_{i\in S}|i\rangle/\sqrt{|S|}$ as the quantum version of a uniformly random…
Learning tasks play an increasingly prominent role in quantum information and computation. They range from fundamental problems such as state discrimination and metrology over the framework of quantum probably approximately correct (PAC)…
The polynomial method by Beals, Buhrman, Cleve, Mosca, and de Wolf (FOCS 1998, J. ACM 2001), the adversary method by Ambainis (STOC 2000, J. Comput. Syst. Sci. 2002), and the compressed oracle method by Zhandry (CRYPTO 2019) have been shown…
An increasing number of communication and computational schemes with quantum advantages have recently been proposed, which implies that quantum technology has fertile application prospects. However, demonstrating these schemes…
We consider quantum versions of two well-studied classical learning models: Angluin's model of exact learning from membership queries and Valiant's Probably Approximately Correct (PAC) model of learning from random examples. We give…
We generalize the PAC (probably approximately correct) learning model to the quantum world by generalizing the concepts from classical functions to quantum processes, defining the problem of \emph{PAC learning quantum process}, and study…
Here we study the comparative power of classical and quantum learners for generative modelling within the Probably Approximately Correct (PAC) framework. More specifically we consider the following task: Given samples from some unknown…
Over decades traditional information theory of source and channel coding advances toward learning and effective extraction of information from data. We propose to go one step further and offer a theoretical foundation for learning classical…
This paper studies quantum supervised learning for classical inference from quantum states. In this model, a learner has access to a set of labeled quantum samples as the training set. The objective is to find a quantum measurement that…
Recent years have seen significant activity on the problem of using data for the purpose of learning properties of quantum systems or of processing classical or quantum data via quantum computing. As in classical learning, quantum learning…
Understanding the power of quantum data in machine learning is central to many proposed applications of quantum technologies. While access to quantum data can offer exponential advantages for carefully designed learning tasks and often…
Using quantum algorithms, we obtain, for accuracy $\epsilon>0$ and confidence $1-\delta,0<\delta<1,$ a new sample complexity upper bound of $O((\mbox{log}(\frac{1}{\delta}))/\epsilon)$ as $\epsilon,\delta\rightarrow 0$ for a general…
Quantum samplers are believed capable of sampling efficiently from distributions that are classically hard to sample from. We consider a sampler inspired by the classical Ising model. It is nonadaptive and therefore experimentally amenable.…
This paper surveys various results in the field of Quantum Learning theory, specifically focusing on learning quantum-encoded classical concepts in the Probably Approximately Correct (PAC) framework. The cornerstone of this work is the…
We consider the quantum decoding problem. It consists in recovering a codeword given a superposition of noisy versions of this codeword. By measuring the superposition, we get back to the classical decoding problem. It appears for the first…