The Square Kilometre Array (SKA) will be the most sensitive radio telescope in the world. This unprecedented sensitivity will be achieved by combining and analyzing signals from 262,144 antennas and 350 dishes at a raw datarate of petabits per second. The processing pipeline to create useful astronomical data will require hundreds of peta-operations per second, at a very limited power budget. We analyze the compute, memory and bandwidth requirements for the key algorithms used in the SKA. By studying their implementation on existing platforms, we show that most algorithms have properties that map inefficiently on current hardware, such as a low compute-bandwidth ratio and complex arithmetic. In addition, we estimate the power breakdown on CPUs and GPUs, analyze the cache behavior on CPUs, and discuss possible improvements. This work is complemented with an analysis of supercomputer trends, which demonstrates that current efforts to use commercial off-the-shelf accelerators results in a two to three times smaller improvement in compute capabilities and power efficiency than custom built machines. We conclude that waiting for new technology to arrive will not give us the instruments currently planned in 2018: one or two orders of magnitude better power efficiency and compute capabilities are required. Novel hardware and system architectures, to match the needs and features of this unique project, must be developed.