We are not up to the advancement of Quantum Computing (QC) as a scientific Math/Phys field or discipline. Rather, we want to explore possibilities to use it as a mean to solve challenging classical problems – to handle large-scale optimization tasks, to sort Big Data, and to do quantum modeling (in Feynman’s sense, the next stage in the evolution of computational quantum physics). This direction can be called applied QC. To put it short, it is about advancement of classical IT fields and computational quantum physics by implementing QC.

There is analogy in the computational physics which, as a research field, has two ‘lawns’: on one researchers develop new computational methods and algorithms while on the another one their colleagues implements these developments to model & investigate physical phenomena. F.e., one community develops symplectic methods to propagate quantum systems (on classical computers!), while another community uses them to study ionization of atoms by strong EM pulses.

Note added: Another example is complex analysis. It is a branch of mathematics but it provides the best tool to analyze AC circuits in electric engineering.

Finally, in Norwegian IT industry and commercial R&D enterprises they are least interested in the advancement of the QC as a scientific field. What they expect from QC are new computational tools to solve their practical problems.

Alice collected all  bills (banknotes) of a certain series, i.e., all bills marked XYZ (series) + numbers, from 00…000 to 11…111 (in binary basis), so altogether she has collected 2^n bills. She knows that in any series (i) either all banknotes are fine or (ii) exactly half of them are counterfeited.

Bob has a quantum checking device: when the series* is introduced on its pad for any binary string x_1x_2x_3…x_n (number on the bill) it calculates f(x_1x_2x_3…x_n), a function which takes two values – 0 [“the bill is fine”] or 1 [“the bill is false (counterfeited)”]. Now Alice wants to know what did she get.

*communicated to Bob by Alice through a standard classical channel