Future research directions (Quantum Computing)

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Future research directions (Quantum Computing)

Tim Daly
Axiom is reaching a stable point where it can support research
in new areas. There is current work on Gustafson's Universal
Numbers (UNUMS) which promises to simplify the numeric
libraries. It seems to also promise some symbolic/numeric
computation. Time will tell.

Another area, still at the read-the-literature stage is quantum
computing. IBM has made a 5-qubit machine available on the
web. Some effort was devoted to implementing known algorithms.

Quantum computing had come a long way in the last few years.
There are several attempts to create a high level language for
expressing algorithms.

Quipper is an interesting effort:
www.mathstat.dal.ca/~selinger/quipper
It is currently implemented on top of Haskell but it looks like
it could be implemented in Axiom. It uses Knill's QRAM model.
Some papers:
https://arxiv.org/pdf/1304.3390v1.pdf (Overview of the language)
https://arxiv.org/pdf/1304.5485v1.pdf (Introductory examples)

My particular interest is twofold: Given my crypto background I'm
interested in the post-crypto quantum work. I'm also interested in
my observation that Hadamard gates are the basis for both unitary
quantum operations and shared-channel telecommunications. By
combining quantum crypto and shared-channel communication it
seems that there is a potential for ultra-secure communication.

There are quantum computer simulators which could be embedded
into Axiom to support simulated quantum development. Since the
quantum operations are simple (unitary matrix operators) we could
create a syntax and language front end to express them. For instance,
being able to write a|Y> using the bra and ket notation.

This is a NIST-supported exploding area of research with many dozens
of algorithms already available in the literature:
http://math.nist.gov/quantum/zoo/

Tim


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