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In this work, 2099 experimental data of binary systems composed of CO2 and ionic liquids are studied to predict solubility using a multilayer perceptron. The dataset includes 33 different types of ionic liquids over a wide range of temperatures, pressures, and solubilities. The main objective of this work is to propose a procedure for the prediction of CO2 solubility in ionic liquids by establishing four stages to determine the model parameters: (1) selection of the learning algorithm, (2) optimization of the first hidden layer, (3) optimization of the second hidden layer, and (4) selection of the input combination. In this study, a bound is set on the number of model parameters: the number of model parameters must be less than the amount of predicted data. Eight different learning algorithms with (4,m,n,1)-type hidden two-layer architectures (m = 2, 4, …, 10 and n = 2, 3, …, 10) are studied, and the artificial neural network is trained with three input combinations with three combinations of thermodynamic variables such as temperature (T), pressure (P), critical temperature (Tc), critical pressure, the critical compressibility factor (Zc), and the acentric factor (ω). The results show that the 4-6-8-1 architecture with the input combination T-P-Tc-Pc and the Levenberg–Marquard learning algorithm is a very acceptable and simple model (95 parameters) with the best prediction and a maximum absolute deviation close to 10%.

We discuss the tomography of N-qubit states using collective measurements. The method is exact for symmetric states, whereas for not completely symmetric states the information accessible can be arranged as a mixture of irreducible SU(2) blocks. For the fully symmetric sector, the reconstruction protocol can be reduced to projections onto a canonically chosen set of pure states.