Final Report Summary - UQSI (Universal Quantum Simulation With Trapped Ions) Executive Summary: Scientists are beginning to achieve an unprecedented level of control over quantum systems in the laboratory. These systems include photons, superconductors and arrays of single atoms or ions. Very recently it has been realized that these systems can be applied to address one of the fundamental problems in science and engineering: that of predicting how other quantum systems should behave. This emerging field of science called quantum simulation has the potential to solve problems of fundamental importance in many fields of research and technology.Arrays of cold trapped ions represent one of the most advanced and promising systems to realise quantum simulators. At the beginning of this research project a few impressive proof-of-principle quantum simulations had been carried out using ions, including two at the host institution in Innsbruck. An important goal in the field is to scale up the size of trapped ion quantum simulators and this was the central goal of this project.The first research objective of this project was to build a new trapped ion quantum simulator capable of stably trapping and allowing for coherent manipulation of the quantum state of 10 or more ions. The second group of objectives were to demonstrate the techniques necessary to obtain a universal quantum simulator and use them to implement new quantum simulations. A universal quantum simulator is one that is capable of simulating almost any other quantum system using a ‘Trotterisation’ technique.Over the course of this project all of these objectives were met. First, a new trapped ion quantum simulator was built that is capable of stably trapping and coherently manipulating the quantum states of strings of more than 10 ions. This device can be found in the host institution today and is currently being used to implement the next generation of quantum simulations using strings of more than ten ions. Second, the techniques and principles of universal quantum simulation were demonstrated and used to realize simulations of a range of quantum systems with interactions not present in our system. This work was published in the journal Science and presented a several international conferences. The project outcomes have helped establish systems of trapped ions as one of the leading platforms for realizing an experimental quantum simulator. The construction of a quantum simulator capable of outperforming classical numerical simulation techniques for the purpose of understanding quantum-many body systems requires the number of ions to be scaled up beyond what is currently possible in expeirments in this domain. The work performed within this project has enabled us to start carrying out simulations of quantum-many-body physics with up to 11 ions. The insights gained from the project are at the time of writing this report being implemented in a new series of experiments targeting to use about twenty ions. If this number can be further scaled up to about 50 ions, numerical simulation techniques, numerical techniques will no longer be able to predict the outcomes produced by a trapped-ion quantum simulator, establishing the latter as a new tool for analyzing and understanding quantum many body physics of interacting spin systems with long-range interactions.