Computers have become vastly more powerful over the years. This rapid progress, expressed as Moore's law, is now coming to an end, so there is world-wide interest in a fundamentally new paradigm: quantum computation. A quantum computer can help solve many practical problems: from the creation of super-strong and superconducting materials to a revolution in the field of artificial intelligence. The challenge in building such a computer is that quantum states are extremely fragile, such that small interactions with the outside world destroys its memory. In my lecture, I will explain how my laboratory has overcome this problem to enable building large quantum systems. We are currently building a device with 49 superconducting quantum bits that can compute over a huge state space of 2⁴⁹ = 560 trillion, such that the computation can only be checked by the world's largest supercomputers. Our goal is to demonstrate this "supremacy" of quantum technologies by the end of 2017.