Connectionists: new paper proposing that sparse distributed codes instantiates quantum computing

[Rod Rinkus]

Dear Connectionists,

I have a new paper, "Quantum Computing via Sparse Distributed
Representation", in the journal, NeuroQuantology, which may be of
interest to many of you.

The link is:  http://www.neuroquantology.com/index.php/journal/article/view/507

Abstract:
Quantum superposition states that any physical system simultaneously
exists in all of its possible states, the number of which is
exponential in the number of entities composing the system. The
strength of presence of each possible state in the superposition—i.e.,
the probability with which it would be observed if measured—is
represented by its probability amplitude coefficient. The assumption
that these coefficients must be represented physically disjointly from
each other, i.e., localistically, is nearly universal in the quantum
theory/computing literature. Alternatively, these coefficients can be
represented using sparse distributed representations (SDR), wherein
each coefficient is represented by a small subset of an overall
population of representational units and the subsets can overlap.
Specifically, I consider an SDR model in which the overall population
consists of Q clusters, each having K binary units, so that each
coefficient is represented by a set of Q units, one per cluster. Thus,
K^Q coefficients can be represented with KQ units. We can then
consider the particular world state, X, whose coefficient’s
representation, R(X), is the set of Q units active at time t to have
the maximal probability and the probabilities of all other states, Y,
to correspond to the size of the intersection of R(Y) and R(X). Thus,
R(X) simultaneously serves both as the representation of the
particular state, X, and as a probability distribution over all
states. Thus, set intersection may be used to classically implement
quantum superposition. If algorithms exist for which the time it takes
to store (learn) new representations and to find the closest-matching
stored representation (probabilistic inference) remains constant as
additional representations are stored, this would meet the criterion
of quantum computing. Such algorithms, based on SDR, have already been
described. They achieve this "quantum speed-up" with no new esoteric
technology, and in fact, on a single-processor, classical (Von
Neumann) computer.

Sincerely,
Rod Rinkus


--

Gerard (Rod) Rinkus, PhD
President,
Neurithmic Systems
468 Waltham St
Newton, MA 02468
617-997-6272

Visiting Scientist, Lisman Lab
Volen Center for Complex Systems
Brandeis University, Waltham, MA
grinkus at brandeis dot edu
http://people.brandeis.edu/~grinkus/