"We simulated 2 trillion such dark matter "pieces", the largest calculation of this type that has ever been performed. To do this we had to use a computation technique known as the "fast multipole method" and use one of the fastest computers in the world, "Piz Daint" at the Swiss National Supercomputing Centre, which among other things has very fast graphics processing units (GPUs) which allow an enormous speed-up of the floating point calculations needed in the simulation. The dark matter clusters into dark matter "halos" which in turn harbor the galaxies. Our calculation accurately produces the distribution and properties of the dark matter, including the halos, but the galaxies, with all of their properties, must be placed within these halos using a model. This part of the task was performed by our colleagues at Barcelona under the direction of Pablo Fossalba and Francisco Castander. These galaxies then have the expected colors, spatial distribution and the emission lines (important for the spectra observed by Euclid) and can be used to test and calibrate various systematics and random errors within the entire instrument pipeline of Euclid."