The Secret to Automatski’s Quantum Computer is the O(N) implementation of the Quantum Physics (Model) of the Transmon Qubit.
Once you have the Quantum Physical Model of the Qubit successfully implemented. You have to extend the Mathematical Perspective of Quantum Gates in terms of Quantum Physics Evolution Quantum Systemc of ‘N’ Qubits where N= 100,000 .. 1000,000 etc.
Basically please stop thinking in terms of Computations and Mathematics. Think only in terms of Quantum Physics. The underlying Quantum Many Body Simulation aka The Algorithm of The Universe is plenty solvable in O(N).
Trust me, if you have a model of a spinning electron and a physical model of a Schrödinger’s evolution. Thats all you need to implement a perfect Quantum Computer.
And thats exactly what we have done in 2014.