This paper investigates the application of Simulated Bifurcation algorithms to approximate optimal asset allocations. It will provide the reader with an explanation of the physical principles underlying the method and a Python implementation of the latter applied to 441 assets belonging to the S&P500 index. In addition, the paper tackles the problem of the selection of an optimal sub-allocation; in this particular case, we find an adequate solution within an unrivaled timescale.We would like to thank Damien Challet (Full professor HDR; Associate editor for Quantitative Finance, Journal of Economic Interaction and Coordination, Journal of Statistical Mechanics: theory and experiments; Co-chief editor of Market Microstructure and Liquidity) for his many useful pieces of advice and his guidance throughout the year. All remaining errors are ours.We also thank Romain Perchet (Head of Multi-Asset Team for Quant Research Group at BNP Paribas Asset Management) for introducing us to the field of portfolio optimization theory and for providing us with resourceful data. Finally, we thank the members of the MICS (Research laboratory in Mathematics and Computer Science at CentraleSupélec) and CentraleSupélec (Graduate School of Engineering of the Paris-Saclay University) for giving us the opportunity of undertaking research which falls under the scope of our general engineering curriculum.