Learning DNFs under product distributions via {\mu}-biased quantum Fourier sampling

We show that DNF formulae can be quantum PAC-learned in polynomial time under product distributions using a quantum example oracle. The best classical algorithm (without access to membership queries) runs in superpolynomial time. Our result extends the work by Bshouty and Jackson (1998) that proved that DNF formulae are efficiently learnable under the uniform distribution using a quantum example oracle. Our proof is based on a new quantum algorithm that efficiently samples the coefficients of a {\mu}-biased Fourier transform.Comment: 17 pages; v3 based on journal version; minor corrections and clarification

Stabilisers as a design tool for new forms of Lechner-Hauke-Zoller Annealer

In a recent paper Lechner, Hauke and Zoller (LHZ) described a means to translate a Hamiltonian of $N$ spin-$\frac{1}{2}$ particles with 'all-to-all' interactions into a larger physical lattice with only on-site energies and local parity constraints. LHZ used this mapping to propose a novel form of quantum annealing. Here we provide a stabiliser-based formulation within which we can describe both this prior approach and a wide variety of variants. Examples include a triangular array supporting all-to-all connectivity, and moreover arrangements requiring only $2N$ or $N\log N$ spins but providing interesting bespoke connectivities. Further examples show that arbitrarily high order logical terms can be efficiently realised, even in a strictly 2D layout. Our stabilisers can correspond to either even-parity constraints, as in the LHZ proposal, or as odd-parity constraints. Considering the latter option applied to the original LHZ layout, we note it may simplify the physical realisation since the required ancillas are only spin-$\frac{1}{2}$ systems (i.e. qubits, rather than qutrits) and moreover the interactions are very simple. We make a preliminary assessment of the impact of this design choices by simulating small (few-qubit) systems; we find some indications that the new variant may maintain a larger minimum energy gap during the annealing process.Comment: A dramatically expanded revision: we now show how to use our stabiliser formulation to construct a wide variety of new physical layouts, including ones with fewer than Order N^2 spins but custom connectivities, and a means to achieve higher order coupling even in 2

Signs of a faint disc population at polluted white dwarfs

Observations of atmospheric metals and dust discs around white dwarfs provide important clues to the fate of terrestrial planetary systems around intermediate mass stars. We present Spitzer IRAC observations of 15 metal polluted white dwarfs to investigate the occurrence and physical properties of circumstellar dust created by the disruption of planetary bodies. We find subtle infrared excess emission consistent with warm dust around KUV 15519+1730 and HS 2132+0941, and weaker excess around the DZ white dwarf G245-58, which, if real, makes it the coolest white dwarf known to exhibit a 3.6 micron excess and the first DZ star with a bright disc. All together our data corroborate a picture where 1) discs at metal-enriched white dwarfs are commonplace and most escape detection in the infrared (possibly as narrow rings), 2) the discs are long lived, having lifetimes on the order of 10^6 yr or longer, and 3) the frequency of bright, infrared detectable discs decreases with age, on a timescale of roughly 500 Myr, suggesting large planetesimal disruptions decline on this same timescale.Comment: 11 pages, 6 figures, 5 tables, MNRAS accepted. Minor changes to match published versio

Formal Analysis of Vulnerabilities of Web Applications Based on SQL Injection (Extended Version)

We present a formal approach that exploits attacks related to SQL Injection (SQLi) searching for security flaws in a web application. We give a formal representation of web applications and databases, and show that our formalization effectively exploits SQLi attacks. We implemented our approach in a prototype tool called SQLfast and we show its efficiency on real-world case studies, including the discovery of an attack on Joomla! that no other tool can find

Modelling Non-Markovian Quantum Processes with Recurrent Neural Networks

Quantum systems interacting with an unknown environment are notoriously difficult to model, especially in presence of non-Markovian and non-perturbative effects. Here we introduce a neural network based approach, which has the mathematical simplicity of the Gorini-Kossakowski-Sudarshan-Lindblad master equation, but is able to model non-Markovian effects in different regimes. This is achieved by using recurrent neural networks for defining Lindblad operators that can keep track of memory effects. Building upon this framework, we also introduce a neural network architecture that is able to reproduce the entire quantum evolution, given an initial state. As an application we study how to train these models for quantum process tomography, showing that recurrent neural networks are accurate over different times and regimes.Comment: 10 pages, 8 figure

Learning hard quantum distributions with variational autoencoders

Studying general quantum many-body systems is one of the major challenges in modern physics because it requires an amount of computational resources that scales exponentially with the size of the system.Simulating the evolution of a state, or even storing its description, rapidly becomes intractable for exact classical algorithms. Recently, machine learning techniques, in the form of restricted Boltzmann machines, have been proposed as a way to efficiently represent certain quantum states with applications in state tomography and ground state estimation. Here, we introduce a new representation of states based on variational autoencoders. Variational autoencoders are a type of generative model in the form of a neural network. We probe the power of this representation by encoding probability distributions associated with states from different classes. Our simulations show that deep networks give a better representation for states that are hard to sample from, while providing no benefit for random states. This suggests that the probability distributions associated to hard quantum states might have a compositional structure that can be exploited by layered neural networks. Specifically, we consider the learnability of a class of quantum states introduced by Fefferman and Umans. Such states are provably hard to sample for classical computers, but not for quantum ones, under plausible computational complexity assumptions. The good level of compression achieved for hard states suggests these methods can be suitable for characterising states of the size expected in first generation quantum hardware.Comment: v2: 9 pages, 3 figures, journal version with major edits with respect to v1 (rewriting of section "hard and easy quantum states", extended discussion on comparison with tensor networks

A Formal Approach to Exploiting Multi-Stage Attacks based on File-System Vulnerabilities of Web Applications (Extended Version)

Web applications require access to the file-system for many different tasks. When analyzing the security of a web application, secu- rity analysts should thus consider the impact that file-system operations have on the security of the whole application. Moreover, the analysis should take into consideration how file-system vulnerabilities might in- teract with other vulnerabilities leading an attacker to breach into the web application. In this paper, we first propose a classification of file- system vulnerabilities, and then, based on this classification, we present a formal approach that allows one to exploit file-system vulnerabilities. We give a formal representation of web applications, databases and file- systems, and show how to reason about file-system vulnerabilities. We also show how to combine file-system vulnerabilities and SQL-Injection vulnerabilities for the identification of complex, multi-stage attacks. We have developed an automatic tool that implements our approach and we show its efficiency by discussing several real-world case studies, which are witness to the fact that our tool can generate, and exploit, complex attacks that, to the best of our knowledge, no other state-of-the-art-tool for the security of web applications can find