Quantitative Robustness Analysis of Quantum Programs (Extended Version)

Quantum computation is a topic of significant recent interest, with practical advances coming from both research and industry. A major challenge in quantum programming is dealing with errors (quantum noise) during execution. Because quantum resources (e.g., qubits) are scarce, classical error correction techniques applied at the level of the architecture are currently cost-prohibitive. But while this reality means that quantum programs are almost certain to have errors, there as yet exists no principled means to reason about erroneous behavior. This paper attempts to fill this gap by developing a semantics for erroneous quantum while-programs, as well as a logic for reasoning about them. This logic permits proving a property we have identified, called $\epsilon$-robustness, which characterizes possible "distance" between an ideal program and an erroneous one. We have proved the logic sound, and showed its utility on several case studies, notably: (1) analyzing the robustness of noisy versions of the quantum Bernoulli factory (QBF) and quantum walk (QW); (2) demonstrating the (in)effectiveness of different error correction schemes on single-qubit errors; and (3) analyzing the robustness of a fault-tolerant version of QBF.Comment: 34 pages, LaTeX; v2: fixed typo

On the stability of impulsive functional differential equations with infinite delays

In this paper, the stability problem of impulsive functional differential equations with infinite delays is considered. By using Lyapunov functions and the Razumikhin technique, some new theorems on the uniform stability and uniform asymptotic stability are obtained. The obtained results are milder and more general than several recent works. Two examples are given to demonstrate the advantages of the results

On exploiting social relationship and personal background for content discovery in P2P networks

International audienceContent discovery is a critical issue in unstructured Peer-to-Peer (P2P) networks as nodes maintain only local network information. However, similarly without global information about human networks, one still can find specific persons via his/her friends by using social information. Therefore, in this paper, we investigate the problem of how social information (i.e., friends and background information) could benefit content discovery in P2P networks. We collect social information of 384, 494 user profiles from Facebook, and build a social P2P network model based on the empirical analysis. In this model, we enrich nodes in P2P networks with social information and link nodes via their friendships. Each node extracts two types of social features-Knowledge and Similarity-and assigns more weight to the friends that have higher similarity and more knowledge. Furthermore, we present a novel content discovery algorithm which can explore the latent relationships among a node's friends. A node computes stable scores for all its friends regarding their weight and the latent relationships. It then selects the top friends with higher scores to query content. Extensive experiments validate performance of the proposed mechanism. In particular, for personal interests searching, the proposed mechanism can achieve 100% of Search Success Rate by selecting the top 20 friends within two-hop. It also achieves 6.5 Hits on average, which improves 8x the performance of the compared methods

On exploiting social relationship and personal background for content discovery in P2P networks

Content discovery is a critical issue in unstructured Peer-to-Peer (P2P) networks as nodes maintain only local network information. However, similarly without global information about human networks, one still can find specific persons via his/her friends by using social information. Therefore, in this paper, we investigate the problem of how social information (i.e., friends and background information) could benefit content discovery in P2P networks. We collect social information of 384,494 user profiles from Facebook, and build a social P2P network model based on the empirical analysis. In this model, we enrich nodes in P2P networks with social information and link nodes via their friendships. Each node extracts two types of social features – Knowledge and Similarity – and assigns more weight to the friends that have higher similarity and more knowledge. Furthermore, we present a novel content discovery algorithm which can explore the latent relationships among a node’s friends. A node computes stable scores for all its friends regarding their weight and the latent relationships. It then selects the top friends with higher scores to query content. Extensive experiments validate performance of the proposed mechanism. In particular, for personal interests searching, the proposed mechanism can achieve 100% of Search Success Rate by selecting the top 20 friends within two-hop. It also achieves 6.5 Hits on average, which improves 8x the performance of the compared methods.This work has been funded by the European Union under the project eCOUSIN (EU-FP7-318398) and the project SITAC (ITEA2-11020). It also has been partially funded by the Spanish Government through the MINEC eeCONTENT project (TEC2011-29688-C02-02)

Quantum algorithm for estimating volumes of convex bodies

Estimating the volume of a convex body is a central problem in convex geometry and can be viewed as a continuous version of counting. We present a quantum algorithm that estimates the volume of an $n$-dimensional convex body within multiplicative error $\epsilon$ using $\tilde{O}(n^{3}+n^{2.5}/\epsilon)$ queries to a membership oracle and $\tilde{O}(n^{5}+n^{4.5}/\epsilon)$ additional arithmetic operations. For comparison, the best known classical algorithm uses $\tilde{O}(n^{4}+n^{3}/\epsilon^{2})$ queries and $\tilde{O}(n^{6}+n^{5}/\epsilon^{2})$ additional arithmetic operations. To the best of our knowledge, this is the first quantum speedup for volume estimation. Our algorithm is based on a refined framework for speeding up simulated annealing algorithms that might be of independent interest. This framework applies in the setting of "Chebyshev cooling", where the solution is expressed as a telescoping product of ratios, each having bounded variance. We develop several novel techniques when implementing our framework, including a theory of continuous-space quantum walks with rigorous bounds on discretization error. To complement our quantum algorithms, we also prove that volume estimation requires $\Omega(\sqrt n+1/\epsilon)$ quantum membership queries, which rules out the possibility of exponential quantum speedup in $n$ and shows optimality of our algorithm in $1/\epsilon$ up to poly-logarithmic factors.Comment: 61 pages, 8 figures. v2: Quantum query complexity improved to $\tilde{O}(n^{3}+n^{2.5}/\epsilon)$ and number of additional arithmetic operations improved to $\tilde{O}(n^{5}+n^{4.5}/\epsilon)$. v3: Improved Section 4.3.3 on nondestructive mean estimation and Section 6 on quantum lower bounds; various minor change

Group DETR v2: Strong Object Detector with Encoder-Decoder Pretraining

We present a strong object detector with encoder-decoder pretraining and finetuning. Our method, called Group DETR v2, is built upon a vision transformer encoder ViT-Huge~\cite{dosovitskiy2020image}, a DETR variant DINO~\cite{zhang2022dino}, and an efficient DETR training method Group DETR~\cite{chen2022group}. The training process consists of self-supervised pretraining and finetuning a ViT-Huge encoder on ImageNet-1K, pretraining the detector on Object365, and finally finetuning it on COCO. Group DETR v2 achieves $\textbf{64.5}$ mAP on COCO test-dev, and establishes a new SoTA on the COCO leaderboard https://paperswithcode.com/sota/object-detection-on-cocoComment: Tech report, 3 pages. We establishes a new SoTA (64.5 mAP) on the COCO test-de