In view of the above, how much of a stretch is it to say that back in 1980, before Feynman's famous lecture, even the NMR scientists were discussing how to perform a 'quantum computation' using phase-cycling/Trotterization?
To some extent, "how much of a stretch" seems to be a matter of opinion (and semantics). But in my opinion it is probably too much of a stretch.
The picture from Fig. 4 of the cited paper shows the evolution of a system broken down into time steps, and the authors state that they are approximating each time step $i$ as evolving via a separate propagator
$$
U_i = e^{-i \hat H_i \Delta\tau}\;.\tag{1}
$$
Eq. (1) looks nice if it could somehow be considered as a "gate" acting on "qubits," but I do not see any such explanation in this direction in the paper.
The use of a sequence of operators from Eq. (1) as representing the entire unitary evolution is an approximation. In general, unless the Hamiltonian is time-independent, no such separation into distinct exponentials of the form of Eq. (1) can be made. (The issue is that the exponential of a sum of operators $e^{A+B}$ is not generally equal to the product of the exponential of the individual operators $e^{A}e^{B}$, unless the operators commute, which they won't necessarily do if the Hamiltonian is time-dependent.)
Further, there is no clear indication as to what the local "qubits" would be. Presumably, they would be something to do with the nuclear spins undergoing resonance, but the link is too vague for my taste.
Further, if we are to allow any system whose evolution can be approximated by a set of unitary transformation like Eq. (1) to be called a "quantum computer," then really just about anything could be called a quantum computer... To be a realistic quantum computer, it seems to me that we need to have some kind of reasonable justification that we can isolate and differentiate this "qubit" from that "qubit" and thereby treat the "qubits" as different and thereby have "one-qubit" gates (where the qubits don't interact) and "two-qubit" gates (when the qubits interact) versus just general time evolution of any old system.
On the other hand, I feel like it is safer (if not somewhat glib) to say that the original Stern-Gerlach experiment is akin to first instance of a "one-qubit quantum computer," since that "computer" actually produces "output" (the measurement of the spin value).
If one agrees with the above characterization then one might say that the "one qubit quantum computer" was invented in the 1920s. But, one would not say that the one-qubit quantum computer was invented at the time silver was discovered even though the Stern-Gerlach experiment used silver atoms.
Similarly, to get to the first realistic multi-qubit quantum computers based on NMR, it seems like you have to go further into the future, say around 2001.
