This project proposes a deep reconsideration of the very foundations of Quantum Field Theory, arguably the most profound theory in science. It explores the power of the paradigm of a Universe as a huge quantum computer, namely, with physics as emergent from pure quantum information processing. In addition to the principles that identify Quantum Theory as a theory of information, the project establishes new informational principles, corresponding to minimizing the algorithmic complexity of the physical process, and resulting in a Quantum Cellular Automaton description of physics at the Planck scale. This new theory recovers physics at the usual scale of particle physics, but also predicts new phenomenology that can be experimentally tested in an ultra-relativistic domain. The new theoretical formulation naturally resolves the tension between Quantum Theory and relativity, by reducing the latter to a theory emergent from the former, and opens a new and promising perspective on a quantum theory of gravity.