Armando Angrisani | LIP6 - Équipe QI

A unifying framework for differentially private quantum algorithms

Sun, 24 Nov 2024 00:00:00 +0000

Differential privacy is a widely used notion of security that enables the processing of sensitive information. In short, differentially private algorithms map “neighbouring” inputs to close output distributions. Prior work proposed several quantum extensions of differential privacy, each of them built on substantially different notions of neighbouring quantum states. In this paper, we propose a novel and general definition of neighbouring quantum states. We demonstrate that this definition captures the underlying structure of quantum encodings and can be used to provide exponentially tighter privacy guarantees for quantum measurements. Our approach combines the addition of classical and quantum noise and is motivated by the noisy nature of near-term quantum devices. Moreover, we also investigate an alternative setting where we are provided with multiple copies of the input state. In this case, differential privacy can be ensured with little loss in accuracy combining concentration of measure and noise-adding mechanisms. En route, we prove the advanced joint convexity of the quantum hockey-stick divergence and we demonstrate how this result can be applied to quantum differential privacy. Finally, we complement our theoretical findings with an empirical estimation of the certified adversarial robustness ensured by differentially private measurements.

The disparate impact of noise on quantum learning algorithms

Mon, 11 Dec 2023 00:00:00 +0000

Les algorithmes quantiques offrent un potentiel remarquable, promettant de résoudre plusieurs problèmes computationnels de manière exponentiellement plus rapide que leurs homologues classiques.

Cependant, les dispositifs quantiques disponibles aujourd’hui sont confrontés à des limitations majeures, notamment un niveau élevé de bruit et une capacité d’intrication limitée. Par conséquent, l’efficacité pratique de ces dispositifs reste incertaine.

Motivée par cette situation, cette thèse explore l’impact profond du bruit sur les algorithmes d’apprentissage quantique en trois dimensions clés.

Tout d’abord, elle examine l’influence du bruit sur les algorithmes quantiques variationnels, en particulier les méthodes quantiques ‘à noyaux’. Nos résultats révèlent des disparités marquées entre le bruit unital et non-unital, remettant en question les conclusions antérieures sur ces algorithmes bruyants.

Ensuite, elle aborde l’apprentissage des dynamiques quantiques avec des mesures binaires bruyantes de l’état de Choi-Jamiolkowski, en utilisant des requêtes statistiques quantiques. Nous prouvons que l’algorithme de Goldreich-Levin peut être implémenté ainsi, et que plusieurs unitaires sont apprenables de manière efficace dans ce modèle.

Enfin, la thèse contribue à la confidentialité différentielle quantique, montrant comment le bruit quantique peut renforcer la sécurité statistique. Nous proposons une nouvelle définition d’états quantiques voisins, qui capture la structure des encodages quantiques, offrant ainsi des garanties de confidentialité plus strictes. De plus, nous établissons une équivalence entre les requêtes statistiques quantiques et la confidentialité différentielle quantique locale, avec des applications à des tâches telles que le test d’hypothèse asymétrique.

The disparate impact of noise on quantum learning algorithms

Mon, 11 Dec 2023 00:00:00 +0000

Quantum computing, one of the most exciting scientific journeys of our time, holds remarkable potential by promising to rapidly solve computational problems. However, the practical implementation of these algorithms poses an immense challenge, with a universal and error-tolerant quantum computer remaining an elusive goal. Currently, short-term quantum devices are emerging, but they face significant limitations, including high levels of noise and limited entanglement capacity. The practical effectiveness of these devices, particularly due to quantum noise, is a subject of debate. Motivated by this situation, this thesis explores the profound impact of noise on quantum learning algorithms in three key dimensions. Firstly, it focuses on the influence of noise on variational quantum algorithms, especially quantum kernel methods. Our results reveal significant disparities between unital and non-unital noise, challenging previous conclusions on these noisy algorithms. Next, it addresses learning quantum dynamics with noisy binary measurements of the Choi-Jamiolkowski state, using quantum statistical queries. The Goldreich-Levin algorithm can be implemented in this way, and we demonstrate the efficiency of learning in our model. Finally, the thesis contributes to quantum differential privacy, demonstrating how quantum noise can enhance statistical security. A new definition of neighboring quantum states captures the structure of quantum encodings, providing stricter privacy guarantees. In the local model, we establish an equivalence between quantum statistical queries and local quantum differential privacy, with applications to tasks like asymmetric hypothesis testing. The results are illustrated by the efficient learning of parity functions in this model, compared to a classically demanding task.

Learning unitaries with quantum statistical queries

Tue, 03 Oct 2023 00:00:00 +0000

We propose several algorithms for learning unitary operators from quantum statistical queries (QSQs) with respect to their Choi-Jamiolkowski state. Quantum statistical queries capture the capabilities of a learner with limited quantum resources, which receives as input only noisy estimates of expected values of measurements. Our methods hinge on a novel technique for estimating the Fourier mass of a unitary on a subset of Pauli strings with a single quantum statistical query, generalizing a previous result for uniform quantum examples. Exploiting this insight, we show that the quantum Goldreich-Levin algorithm can be implemented with quantum statistical queries, whereas the prior version of the algorithm involves oracle access to the unitary and its inverse. Moreover, we prove that Oplog nqjuntas and quantum Boolean functions with constant total influence are efficiently learnable in our model, and constant-depth circuits are learnable sample-efficiently with quantum statistical queries. On the other hand, all previous algorithms for these tasks require direct access to the Choi-Jamiolkowski state or oracle access to the unitary. In addition, our upper bounds imply that the actions of those classes of unitaries on locally scrambled ensembles can be efficiently learned. We also demonstrate that, despite these positive results, quantum statistical queries lead to an exponentially larger sample complexity for certain tasks, compared to separable measurements to the Choi-Jamiolkowski state. In particular, we show an exponential lower bound for learning a class of phase-oracle unitaries and a double exponential lower bound for testing the unitarity of channels, adapting to our setting previous arguments for quantum states. Finally, we propose a new definition of average-case surrogate models, showing a potential application of our results to hybrid quantum machine learning.

A unifying framework for differentially private quantum algorithms

Mon, 10 Jul 2023 00:00:00 +0000

Differential Privacy Amplification in Quantum and Quantum-inspired Algorithms

Thu, 17 Nov 2022 00:00:00 +0000

Differential privacy provides a theoretical framework for processing a dataset about n users, in a way that the output reveals a minimal information about any single user. Such notion of privacy is usually ensured by noise-adding mechanisms and amplified by several processes, including subsampling, shuffling, iteration, mixing and diffusion. In this work, we provide privacy amplification bounds for quantum and quantum-inspired algorithms. In particular, we show for the first time, that algorithms running on quantum encoding of a classical dataset or the outcomes of quantum-inspired classical sampling, amplify differential privacy. Moreover, we prove that a quantum version of differential privacy is amplified by the composition of quantum channels, provided that they satisfy some mixing conditions.

Quantum Local Differential Privacy and Quantum Statistical Query Model

Wed, 17 Aug 2022 00:00:00 +0000

The problem of private learning has been extensively studied in classical computer science. Notably, a striking equivalence between local differentially private learning and statistical query learning has been shown. In addition, the statistical query model has been recently extended to quantum computation. In this work, we give a formal definition of quantum local differential privacy and we extend the aforementioned result to quantum computation.

Bridging the gap between technology and policy in GDPR compliance: the role of differential privacy

Wed, 06 Apr 2022 00:00:00 +0000

Probably approximately correct quantum source coding

Tue, 04 Jan 2022 00:00:00 +0000

Information-theoretic lower bounds are often encountered in several branches of computer science, including learning theory and cryptography. In the quantum setting, Holevo’s and Nayak’s bounds give an estimate of the amount of classical information that can be stored in a quantum state. Previous works have shown how to combine information-theoretic tools with a counting argument to lower bound the sample complexity of distribution-free quantum probably approximately correct (PAC) learning. In our work, we establish the notion of Probably Approximately Correct Source Coding and we show two novel applications in quantum learning theory and delegated quantum computation with a purely classical client. In particular, we provide a lower bound of the sample complexity of a quantum learner for arbitrary functions under the Zipf distribution, and we improve the security guarantees of a classically-driven delegation protocol for measurement-based quantum computation (MBQC).