Niklas Pirnay

Niklas Pirnay, Ryan Sweke, Jens Eisert et al.

Density modelling is the task of learning an unknown probability density function from samples, and is one of the central problems of unsupervised machine learning. In this work, we show that there exists a density modelling problem for which fault-tolerant quantum computers can offer a super-polynomial advantage over classical learning algorithms, given standard cryptographic assumptions. Along the way, we provide a variety of additional results and insights, of potential interest for proving future distribution learning separations between quantum and classical learning algorithms. Specifically, we (a) provide an overview of the relationships between hardness results in supervised learning and distribution learning, and (b) show that any weak pseudo-random function can be used to construct a classically hard density modelling problem. The latter result opens up the possibility of proving quantum-classical separations for density modelling based on weaker assumptions than those necessary for pseudo-random functions.

Niklas Pirnay, Anna Pappa, Jean-Pierre Seifert

Physical Unclonable Functions (PUFs) have been proposed as a way to identify and authenticate electronic devices. Recently, several ideas have been presented that aim to achieve the same for quantum devices. Some of these constructions apply single-qubit gates in order to provide a secure fingerprint of the quantum device. In this work, we formalize the class of Classical Readout Quantum PUFs (CR-QPUFs) using the statistical query (SQ) model and explicitly show insufficient security for CR-QPUFs based on single qubit rotation gates, when the adversary has SQ access to the CR-QPUF. We demonstrate how a malicious party can learn the CR-QPUF characteristics and forge the signature of a quantum device through a modelling attack using a simple regression of low-degree polynomials. The proposed modelling attack was successfully implemented in a real-world scenario on real IBM Q quantum machines. We thoroughly discuss the prospects and problems of CR-QPUFs where quantum device imperfections are used as a secure fingerprint.