1st IEE Seminar on Quantum Information Processing 

Quantum Information Processing within the Quantum Processing of Information.
The Theory and Practice Compared.

B Nick Rossiter, Informatics, Northumbria University NE1 8ST, UK,nick.rossiter@unn.ac.uk
M A Heather, Sutherland Building, Northumbria University NE1 8ST,
 m.heather@unn.ac.uk
http://computing.unn.ac.uk/staff/CGNR1/

Information processing is concerned today with very large quantities of very complex data. The complexity arises from the diversity of the type of data and the relationships between data and the different types of relationships. At present semantic complexity can only be processed at the surface level, for instance with keyword searching or citation networks. The power is needed for this semantic processing. The present state of the art is represented on classical computers by the semi-automatic methods in Berners-Lee’s semantic web. In quantum information processing there is the database lookup using Grover’s extension to Shor’s algorithm [Grover 1996, 2000]. This is only the beginning and in terms of information processing at a comparable stage to that of classical algorithms of the 1950s. We need to distinguish between quantum information processing (QIP) and the quantum processing of information (QPI). QIP is at the more glamorous end with topics like teleportation and crypto-code-breaking but these are just exotic examples within the wider QPI most of which is concerned with run-of-the-mill data. QPI includes QIP. 

There are three challenging issues for QPI: the theory, the logic and the materials needed. Quantum information is usually thought of for QIP in terms of discrete qubits roughly corresponding to the level of Shannon’s atomistic bits in classical theory. However while it may be possible to deconstruct complex data discretely, an atomistic approach is too reductionist. As classical data processing found a theoretical underpinning early in terms of the ANSI/SPARC architecture so comparable theory is now needed for QPI within an appropriate philosophical context. The ANSI/SPARC provides a model for classical computation whereas to construct a quantum computer cannot be limited to a model of a quantum computer. Quantum information cannot be copied. Therefore neither can it truly be modelled. For a classical model is a form of copying.  Fortunately category theory allows specifications which are not subject to the reductionism of ZFC set theory because sets are limited for example in locality. Categories on the other hand are not so constrained and can retain non-locality in both time and space if the right path is chosen. There are presently two ways to apply category theory. One is to upgrade existing set theoretic concepts by categorification for instance to define the category of Hilbert spaces but this is a model of a model and subject to the ban on the copying principle. The alternative is the direct use of category theory per se which is the subject of current work in applied categories. [Heather 2003]

An important distinction between theory and practice is in the use of logic for instance to construct logical gates. Quantum mechanics has been historically developed and is an enriched form of wave mechanics and probability theory expressed in the Boolean world of the differential calculus often described in terms of output from a black box oracle. This assumes the use of the axiom of choice. Practice however needs to fall back on an assumptionless universal logic [Heather & Rossiter 2005]. Of course it is already possible approximately to model in software quantum processing on a classical computer using statistics. A hardware model of a quantum compute is not a quantum computer and therefore unlikely to give any better results than quantum software modelling on the classical computer. 

A remaining big question is the nature of the materials to be used in building quantum computing devices. Paradoxically we are surrounded by quantum materials because quantum mechanics is the basic mechanism in the universe. Everything happens that way at the fundamental level. The most promising sources of physical materials appear to be derived from biology. DNA for instance is presumably quantum material which combines both hardware and software in genetic processing very robustly over long scales of both length and time. The materials for quantum processing need to be of this kind, natural and self-organising. The devices for quantum processing of data may then be considered as evolvable databases [Rossiter & Heather 2004]. The bottom line is then to recognise the difference between engineering and mathematical theory. There are at present several gaps along the implementation route which need to be bridged. 

References

Grover L K, A fast quantum mechanical algorithm for database search, 
Proc 28th Annual ACM symposium Theory of Computing 212-219 (1996).

Grover, L K, Rapid sampling through quantum computing. 
Proc 32nd Annual ACM Symposium Theory of Computing 618-626 (2000).

Heather, M, Quantum logic and applied categories Archive, Categories List
ftp://tac.mta.ca/pub/categories/, 4/11/03 (2003).

Heather, Michael, & Rossiter, Nick, Logical Monism: The Global Identity of Applicable Logic, 1st World Congress and School on Universal Logic, Montreux, March (2005). 

Rossiter, Nick, & Heather, Michael, Evolvable Databases, MRC Meeting on Self–Organising Systems, Edinburgh University, 24-25 May 2pp (2004).