Variational techniques have long been at the heart of atomic, solid-state, and many-body physics. They have recently extended to quantum and classical machine learning, providing a basis for representing quantum states via neural networks. These methods generally aim to minimize the energy of a given ansatz, though open questions remain about the expressivity of quantum and classical variational ansätze. The connection between variational techniques and quantum computing, through variational quantum algorithms, offers opportunities to explore the quantum complexity of classical methods. We demonstrate how the concept of non-stabilizerness, or magic, can create a bridge between quantum information and variational techniques and we show that energy accuracy is a necessary but not always sufficient condition for accuracy in non-stabilizerness. Through systematic benchmarking of neural network quantum states, matrix product states, and variational quantum methods, we show that while classical techniques are more accurate in non-stabilizerness, not accounting for the symmetries of the system can have a severe impact on this accuracy. Our findings form a basis for a universal expressivity characterization of both quantum and classical variational methods.

This paper provides an overview of the JointContest on Multimedia Challenges Beyond Visual Analysis.We organized an academic competition that focused on fourproblems that require e‚ective processing of multimodalinformation in order to be solved. Two tracks were devoted togesture spotting and recognition from RGB-D video, two fundamentalproblems for human computer interaction. Anothertrack was devoted to a second round of the €rst impressionschallenge of which the goal was to develop methods torecognize personality traits from short video clips. For thissecond round we adopted a novel collaborative-competitive(i.e., coopetition) setting. ‡e fourth track was dedicated tothe problem of video recommendation for improving userexperience. ‡e challenge was open for about 45 days, andreceived outstanding participation: almost 200 participantsregistered to the contest, and 20 teams sent predictions inthe €nal stage. ‡e main goals of the challenge were ful€lled:the state of the art was advanced considerably in the fourtracks, with novel solutions to the proposed problems (mostlyrelying on deep learning). However, further research is stillrequired. ‡e data of the four tracks will be available to allowresearchers to keep making progress in the four tracks

We consider a technique to estimate an approximate gradient using an ensemble of randomly chosen control vectors, known as Ensemble Optimization (EnOpt) in the oil and gas reservoir simulation community. In particular, we address how to obtain accurate approximate gradients when the underlying numerical mod- els contain uncertain parameters because of geological uncertainties. In that case, ‘robust optimization’ is performed by optimizing the expected value of the objective function over an ensemble of geological mod- els. In earlier publications, based on the pioneering work of Chen et al. (2009), it has been suggested that a straightforward one-to-one combination of random control vectors and random geological models is capa- ble of generating sufficiently accurate approximate gradients. However, this form of EnOpt does not always yield satisfactory results. In a recent article, Fonseca et al. (2015) formulate a modified EnOpt algorithm, referred to here as a Stochastic Simplex Approximate Gradient (StoSAG; in earlier publications referred to as ‘modified robust EnOpt’) and show, via computational experiments, that StoSAG generally yields significantly better gradient approximations than the standard EnOpt algorithm. Here, we provide theoreti- cal arguments to show why StoSAG is superior to EnOpt