相关论文: Mathematical comparison of classical and quantum m…

It is first shown that when the Schr\"{o}dinger equation for a wave function is written in the polar form, complete information about the system's {\em quantum-ness} is separated out in a single term $Q$, the so called `quantum potential'.…

Computing the principal component (PC) of the adjacency matrix of an undirected graph has several applications ranging from identifying key vertices for influence maximization and controlling diffusion processes, to discovering densely…

Differential privacy has emerged as the main definition for private data analysis and machine learning. The {\em global} model of differential privacy, which assumes that users trust the data collector, provides strong privacy guarantees…

Contextuality is a defining feature that separates the quantum from the classical descriptions of physical systems. Within the marginal-scenario framework, noncontextual models are characterized by the existence of a single joint…

In the thermodynamics of nanoscopic systems the relation between classical and quantum mechanical description is of particular importance. To scrutinize this correspondence we study an anharmonic oscillator driven by a periodic external…

We characterize the minimum noise amplitude and power for noise-adding mechanisms in $(\epsilon, \delta)$-differential privacy for single real-valued query function. We derive new lower bounds using the duality of linear programming, and…

Current universal quantum computers have a limited number of noisy qubits. Because of this, it is difficult to use them to solve large-scale complex optimization problems. In this paper we tackle this issue by proposing a quantum…

Due to Csiszar and Koerner, the private capacity of classical wiretap channels has a single-letter characterization in terms of the private information. For quantum wiretap channels, however, it is known that regularization of the private…

Differential privacy is a mathematical framework for privacy-preserving data analysis. Changing the hyperparameters of a differentially private algorithm allows one to trade off privacy and utility in a principled way. Quantifying this…

Differentially-private histograms have emerged as a key tool for location privacy. While past mechanisms have included theoretical & experimental analysis, it has recently been observed that much of the existing literature does not fully…

In differentially private (DP) machine learning, the privacy guarantees of DP mechanisms are often reported and compared on the basis of a single $(\varepsilon, \delta)$-pair. This practice overlooks that DP guarantees can vary…

Many methods in differentially private model training rely on computing the similarity between a query point (such as public or synthetic data) and private data. We abstract out this common subroutine and study the following fundamental…

Privately counting distinct elements in a stream is a fundamental data analysis problem with many applications in machine learning. In the turnstile model, Jain et al. [NeurIPS2023] initiated the study of this problem parameterized by the…

Differential privacy is often applied with a privacy parameter that is larger than the theory suggests is ideal; various informal justifications for tolerating large privacy parameters have been proposed. In this work, we consider partial…

There have been several research works on the hidden shift problem, quantum algorithms for the problem, and their applications. However, all the results have focused on discrete groups with discrete oracle functions. In this paper, we…

Quantum computing has been regarded as a promising approach to accelerate power system optimization. However, challenges such as limited qubits and inherent noise hinder their widespread adoption in power systems. In this paper, we propose…

We introduce a refined differentially private (DP) data structure for kernel density estimation (KDE), offering not only improved privacy-utility tradeoff but also better efficiency over prior results. Specifically, we study the…

We construct for every connected locally finite graph $\Pi$ the quantum automorphism group $\text{QAut}\ \Pi$ as a locally compact quantum group. When $\Pi$ is vertex transitive, we associate to $\Pi$ a new unitary tensor category…

The classical shadow estimation protocol is a noise-resilient and sample-efficient quantum algorithm for learning the properties of quantum systems. Its performance depends on the choice of a unitary ensemble, which must be chosen by a user…

We study quantum differential privacy (QDP) by defining a notion of the order of informativeness between pairs of quantum states. In particular, we show that if the hypothesis testing divergence of one pair dominates over that of the other…