For those who want to work at the research front I'm going to post links to sites that provide quantum computing ideas. These posts will have the [quantum] label. Axiom can support qubits as a type. It can implement Knill's architecture (i.e. using a classical computer to control a quantum computer).
For those who need things to seem "useful" it appears that quantum computers can find the group underlying the algorithms at the heart of public key encryption. That implies that the whole internet falls since things like site certificates depend on it. Axiom has added a chapter on finite fields written by Grabmeier (Chapter 8) http://axiom-developer.org/axiom-website/bookvol10.1.pdf (the author of Axiom's FF types) as well as links to background courses embedded in Axiom's PDFs (e.g. http://axiom-developer.org/axiom-website/GroupTheoryII/Salomone.html There are implementations of quantum computing simulations making it possible to run quantum programs on stock hardware. An online example is the Quantum Computing Playground http://www.quantumplayground.net/#/home which provides simulation of up to 22 qubits. Axiom could implement such a simulation engine. IBM provides a real online 5-qubit quantum computer http://www.research.ibm.com/quantum/ I've tried to implement some trivial algorithms there. The Quipper language http://www.mathstat.dal.ca/~selinger/quipper/ is a Haskell-based language. Axiom actually provides more features than the Haskell platform, such as dependent types, which the Haskell implementation has to check at runtime. Quipper is supported by DARPA. They have implemented 7 non-trivial quantum algorithms required by DARPA. A good introduction is provided by Siddiqui, et al. "Five Quantum Algorithms Using Quipper" https://arxiv.org/pdf/1406.4481v2.pdf For a solid background, Susskind's lectures are golden: http://newpackettech.com/Resources/Susskind/ For a computer science background see Mermin, David "Quantum Computer Science" 978-0-521-87658-2 This is research so there will be blind paths, speculation, confusion, and all the usual fun without the unusual riches. But that's what we "research rats" love. Tim "research rat" Daly
_______________________________________________ Axiom-developer mailing list Axiom-developer@nongnu.org https://lists.nongnu.org/mailman/listinfo/axiom-developer