Variational method for learning Quantum Channels via Stinespring Dilation on neutral atom systems

The state $|\psi(t)\rangle$ of a closed quantum system evolves under the Schr\"{o}dinger equation, where the reversible evolution of the state is described by the action of a unitary operator $U(t)$ on the initial state $|\psi_0\rangle$, i.e.\ $|\psi(t)\rangle=U(t)|\psi_0\rangle$. However, realistic quantum systems interact with their environment, resulting in non-reversible evolutions, described by Lindblad equations. The solution of these equations give rise to quantum channels $\Phi_t$ that describe the evolution of density matrices according to $\rho(t)=\Phi_t(\rho_0)$, which often results in decoherence and dephasing of the state. For many quantum experiments, the time until which measurements can be done might be limited, e.g. by experimental instability or technological constraints. However, further evolution of the state may be of interest. For instance, to determine the source of the decoherence and dephasing, or to identify the steady state of the evolution. In this work, we introduce a method to approximate a given target quantum channel by means of variationally approximating equivalent unitaries on an extended system, invoking the Stinespring dilation theorem. We report on an experimentally feasible method to extrapolate the quantum channel on discrete time steps using only data on the first time steps. Our approach heavily relies on the ability to spatially transport entangled qubits, which is unique to the neutral atom quantum computing architecture. Furthermore, the method shows promising predictive power for various non-trivial quantum channels. Lastly, a quantitative analysis is performed between gate-based and pulse-based variational quantum algorithms.Comment: 11 pages, 7 figure

On the Efficiency of All-Pay Mechanisms

We study the inefficiency of mixed equilibria, expressed as the price of anarchy, of all-pay auctions in three different environments: combinatorial, multi-unit and single-item auctions. First, we consider item-bidding combinatorial auctions where m all-pay auctions run in parallel, one for each good. For fractionally subadditive valuations, we strengthen the upper bound from 2 [Syrgkanis and Tardos STOC'13] to 1.82 by proving some structural properties that characterize the mixed Nash equilibria of the game. Next, we design an all-pay mechanism with a randomized allocation rule for the multi- unit auction. We show that, for bidders with submodular valuations, the mechanism admits a unique, 75% efficient, pure Nash equilibrium. The efficiency of this mechanism outperforms all the known bounds on the price of anarchy of mechanisms used for multi-unit auctions. Finally, we analyze single-item all-pay auctions motivated by their connection to contests and show tight bounds on the price of anarchy of social welfare, revenue and maximum bid.Comment: 26 pages, 2 figures, European Symposium on Algorithms(ESA) 201

Evolution of Scikit-Learn Pipelines with Dynamic Structured Grammatical Evolution

The deployment of Machine Learning (ML) models is a difficult and time-consuming job that comprises a series of sequential and correlated tasks that go from the data pre-processing, and the design and extraction of features, to the choice of the ML algorithm and its parameterisation. The task is even more challenging considering that the design of features is in many cases problem specific, and thus requires domain-expertise. To overcome these limitations Automated Machine Learning (AutoML) methods seek to automate, with few or no human-intervention, the design of pipelines, i.e., automate the selection of the sequence of methods that have to be applied to the raw data. These methods have the potential to enable non-expert users to use ML, and provide expert users with solutions that they would unlikely consider. In particular, this paper describes AutoML-DSGE - a novel grammar-based framework that adapts Dynamic Structured Grammatical Evolution (DSGE) to the evolution of Scikit-Learn classification pipelines. The experimental results include comparing AutoML-DSGE to another grammar-based AutoML framework, Resilient ClassificationPipeline Evolution (RECIPE), and show that the average performance of the classification pipelines generated by AutoML-DSGE is always superior to the average performance of RECIPE; the differences are statistically significant in 3 out of the 10 used datasets.Comment: EvoApps 202

HPLC-DAD and HPLC-ESI-Q-ToF characterisation of early 20th century lake and organic pigments from Lefranc archives

The characterisation of atelier materials and of the historical commercial formulation of paint materials has recently gained new interest in the field of conservation science applied to modern and contemporary art, since modern paint materials are subjected to peculiar and often unpredictable degradation and fading processes. Assessing the composition of the original materials purchased by artists can guide not only their identification in works of art, but also their restoration and conservation. Advances in characterisation methods and models for data interpretation are particularly important in studying organic coloring materials in the transition period corresponding to the late 19th-early 20th century, when many such variants or combinations were hypothetically possible in their formulations. There is thus a need for reliable databases of materials introduced in that period and for gaining chemical knowledge at a molecular level related to modern organic pigments, by state-of-the-art protocols. This paper reports on the results of a study on 44 samples of historical colorants in powder and paint tubes, containing both lake pigments and synthetic organic pigments dating from 1890 to 1926. The samples were collected at the Lefranc Archive in Le Mans (France) as a part of Project Futurahma "From Futurism to Classicism (1910-1922). Research, Art History and Material Analysis", (FIRB2012, Italian Ministry of University and Research), and were investigated using an analytical approach based on chromatographic and mass spectrometric techniques. The focus of the chemical analyses was to reveal the composition of the historical organic lake pigments including minor components, to discriminate between different recipes for the extraction of chromophore-containing molecules from the raw materials, and ultimately to distinguish between different formulations and recipes. High performance liquid chromatography (HPLC) with diode array detector (DAD) or electrospray-Quadrupole-Time of Flight tandem mass spectrometry detector (ESI-Q-ToF) were chosen given their considerable capacity to identify such complex and widespread organic materials. Although the inorganic components of the pigments were not taken into account in this survey, the specific molecular profiles provided invaluable information on the extraction procedures or synthetic strategy followed by the different producers, at different times. For instance, the use of Kopp's purpurin and garancine was highlighted, and synthetic by-products were identified. The results provided evidence that the addition of synthetic organic pigments to paint mixtures started from 1910 onwards, but they also suggest that in the formulation of high quality (surfin) colorants, natural products were still preferred. Moreover, in one of the samples the use of murexide as the colouring material was confirmed. This paper presents the first systematic and comprehensive survey on organic lakes and pigments belonging to an historical archive, by both HPLC-DAD and HPLC-ESI-Q-ToF. Specific by-products of synthetic production of pigments, which can act as specific molecular markers for dating or locating a work of art, were also identified for the first time