Prof. Ignacio Cirac from the Max-Planck Institut für Quantenoptik, Germany, will give an inaugural lecture on "Quantum Simulations and the difficulty of solving Quantum many-body systems" within the ceremony for the launch of the new Trieste Institute for the Theory of Quantum Technologies (TQT), a new initiative between ICTP, SISSA and the University of Trieste. The ceremony starts at 11.00 on Monday 25 March 2019 in the Budinich Lecture Hall and will include the signing of the Memorandum of Understanding by the Directors of the three institutes. The new Institute for the Theory of Quantum Technologies has been established as a joint venture to address the significant and growing number of researchers working in the field of the so-called "Quantum Technologies" in universities and research institutions in the region, taking into account the high quality of scientific production in this field and the need to unite and coordinate activities and skills into an Inter- organizational Institute. "TQT" will be an international centre of excellence promoting theoretical research in the field of Quantum Technologies, serving as a catalyst for theoretical activities not only in Italy, but also in the neighbouring regions of the former Eastern Europe reaching out to also engage developing countries. The talk will be livestreamed from the ICTP website. ABSTRACT: Quantum many-body systems are very hard to simulate, as computational resources (time and memory) typically grow exponentially with system size. However, quantum computers or analog quantum simulators may perform that task in a much more efficient way. In this talk, I will first review some of the quantum algorithms that have been proposed for this task and then explain the advantages and disadvantages of analog quantum simulators. I will also describe the development of tensor network methods for that task, as well as a theoretical proposal to solve quantum chemistry problems with an analog simulator based on atoms in optical lattices. Light refreshments will follow the event. All are welcome to participate.