You introduced the term "quantum supremacy" to our discussion. I don't usually think in such hype-y / marketing terminology, but I assented because I take it to be synonymous with there being a classical realization of quantum superposition. There is. Sparsey is an example. But you haven't taken the time, again by your own admission, to study or understand that.
For the (apparently hundreds, based on hits on my website) of others watching this thread, my short 2012 paper, "Quantum Computation via Sparse Distributed Representation", clearly describes how the probabilities of multiple states can simultaneously, physically be active, in superposition if those states are represented as sparse distributed representations (SDRs). And, contrary Ron Garret's claim, my 2017 paper, "A Radically New Theory of how the Brain Represents and Computes with Probabilities", provides empirical evidence that the probabilities of all states (hypotheses) represented (stored) in an SDR coding field are updated (in a way that is semantically consistent with the learned dynamics of the input space) with a number of steps that remains constant as the number of stored states increases. That capability is minimally necessary for any quantum algorithm. I don't know of any other model that has shown this ability.
I think the mental block that has existed thus far in quantum computing (QC), and in quantum theory (QT) more generally, is that theorists have been thinking in terms of the probability amplitudes of states as being represented in localist fashion A localist representation is one in which any single entity is represented by a single representational unit and that unit represents only that entity. Any localist simulation of QC on a classical machine will require exponential memory. But, an SDR coding space has a storage capacity of combinatorial order. This opens the possibility that an exponential order number of states can be represented in the polynomial number of units comprising the SDR coding field.