From storing charged atoms, via Shor's algorithm, to a stand-alone quantum computer

Quantum computers are the holy grail of quantum technologies. They promise to disrupt and revolutionize communication, optimisation problems, machine learning, and influence areas that physicists tend to ignore - such as high-frequency trading. Here, ion-trap based systems have been at the forefront of quantum technologies for decades: be that coupling remote ions for secure communications, quantum simulations with fully tunable interactions, to operating the most complex quantum algorithms. In this presentation, I will outline the capabilities of the Innsbruck ion-trap quantum computer and illustrate their combination to implement Shor's algorithm. The talk will conclude with considerations towards a maintenance-free scalable quantum computer.