Quantum simulation is a prominent application of quantum computers. While there is extensive previous work on simulating finite-dimensional systems, less is known about quantum algorithms for real-space dynamics. We conduct a systematic study of such algorithms. In particular, we show that the dynamics of a d-dimensional Schrödinger equation with η particles can be simulated with gate complexity O~(ηdFpoly(log⁡(g′/ϵ))), where ϵ is the discretization error, g′ controls the higher-order derivatives of the wave function, and F measures the time-integrated strength of the potential. Compared to the best previous results, this exponentially improves the dependence on ϵ and g′ from poly(g′/ϵ) to poly(log⁡(g′/ϵ)) and polynomially improves the dependence on T and d, while maintaining best known performance with respect to η. For the case of Coulomb interactions, we give an algorithm using η3(d+η)Tpoly(log⁡(ηdTg′/(Δϵ)))/Δ one- and two-qubit gates, and another using η3(4d)d/2Tpoly(log⁡(ηdTg′/(Δϵ)))/Δ one- and two-qubit gates and QRAM operations, where T is the evolution time and the parameter Δ regulates the unbounded Coulomb interaction. We give applications to several computational problems, including faster real-space simulation of quantum chemistry, rigorous analysis of discretization error for simulation of a uniform electron gas, and a quadratic improvement to a quantum algorithm for escaping saddle points in nonconvex optimization.

Interpretation is a well established theory that supports reasoning about the run-time behaviour of programs. It achieves tractable reasoning by considering abstractions of run-time states, rather than the states themselves. The chosen set of abstractions is referred to as the abstract domain. We develop a novel framework for combining (a possibly large number of) abstract domains. It achieves the effect of the so-called reduced product without requiring a quadratic number of functions to translate information among abstract domains. A central notion is a reference domain, a medium for information exchange. Our approach suggests a novel and simpler way to manage the integration of large numbers of abstract domains. We instantiate our framework in the context of string analysis. Browser-embedded dynamic programming languages such as JavaScript and PHP encourage the use of strings as a universal data type for both code and data values. The ensuing vulnerabilities have made string analysis a focus of much recent research. String analysis tends to combine many elementary string abstract domains, each designed to capture a specific aspect of strings. For this instance the set of regular languages, while too expensive to use directly for analysis, provides an attractive reference domain, enabling the efficient simulation of reduced products of multiple string abstract domains.

Language-based information flow control (IFC) aims to provide guarantees about information propagation in computer systems having multiple security levels. Existing IFC systems extend the lattice model of Denning’s, enforcing transitive security policies by tracking information flows along with a partially ordered set of security levels. They yield a transitive noninterference property of either confidentiality or integrity. In this paper, we explore IFC for security policies that are not necessarily transitive. Such nontransitive security policies avoid unwanted or unexpected information flows implied by transitive policies and naturally accommodate high-level coarse-grained security requirements in modern component-based software. We present a novel security type system for enforcing nontransitive security policies. Unlike traditional security type systems that verify information propagation by subtyping security levels of a transitive policy, our type system relaxes strong transitivity by inferring information flow history through security levels and ensuring that they respect the nontransitive policy in effect. Such a type system yields a new nontransitive noninterference property that offers more flexible information flow relations induced by security policies that do not have to be transitive, therefore generalizing the conventional transitive noninterference. This enables us to directly reason about the extent of information flows in the program and restrict interactions between security-sensitive and untrusted components.

Adversarial attacks hamper the functionality and accuracy of deep neural networks (DNNs) by meddling with subtle perturbations to their inputs. In this work, we propose a new mask-based adversarial defense scheme (MAD) for DNNs to mitigate the negative effect from adversarial attacks. Our method preprocesses multiple copies of a potential adversarial image by applying random masking, before the outputs of the DNN on all the randomly masked images are combined. As a result, the combined final output becomes more tolerant to minor perturbations on the original input. Compared with existing adversarial defense techniques, our method does not need any additional denoising structure or any change to a DNN’s architectural design. We have tested this approach on a collection of DNN models for a variety of datasets, and the experimental results confirm that the proposed method can effectively improve the defense abilities of the DNNs against all of the tested adversarial attack methods. In certain scenarios, the DNN models trained with MAD can improve classification accuracy by as much as $90\%$ compared to the original models when given adversarial inputs.