Data and Algorithm Part-1 (Continued): Quantum Inspired System Semantics (QUISS) - Overview

Quantum Inspired Computing (QUIC)

There is a lot of information available on the Internet for the definitions of Qubits, Qutrits and Qudits so there is no need to repeat those here.

What is not discussed is that these objects are all geometric in nature and have more than one dimensionality to them.

There are many options for quantum-inspired computing (QUIC) and for a QUIC list of options, we can choose to represent the properties of data using one or some combination or all of our own short selection of ten such options:

1. Bloch-Hyperspheres in the sense of extensions of the Bloch-Sphere;
2. Amplituhedral structures and Grassmanians in the sense of Trnka, Postnikov, Bourjaily et.al in which volumes produce probabilities
3. Polyhedral and Combinatohedral structures (e.g. Permutohedron) in which directional probabilities are represented by permutation polyhedra where each vertex represents a permutation (there are N! vertices for an N-element permutation);
4. Topological structures such as Topoi, simplices and generalized maps in which involutions and functions with higher order symmetries (complex involutions) define the skeletal structures.
5. Non-Binary Base Numbers (Complex, Figural, Tree, Functional and Mixed Radix) in which properties of big numbers that can represent the Goedel numberings of various structures are combined with probabilities (for example, the real parts and the imaginary parts treated as on single whole but entwining different conceptual bases);
6. Quantum random walk and quasi-quantum like stochastic walks on classical structures like graphs or lattices represent properties of the data of interest.
7. Field Structured Representations and quasi-quantum/analog representations such as particle swarms which are represented in the complex plane as well as the real plane.
8. Quantum-like entanglement defined as any correlation in complementary bases of representation of information.  For example, measures of discord or mutual ignorance may co-correlate with measures of informativeness and these may produce some quantum-like effects (though not true quantum entanglement ... we are, after all, working on QUIC).
9. Virtual machine designs and architectures that represent quantum like properties such as variables that entangle (as high-order "sharing")  or produce uncertainty between clause definitions or reflective, simulations of quantum particles as computational analogs of quantum processes (such as treating text in terms of Bose-Einstein condensates)
10. Genetic, parallel, distributed systems as quantum analogs or real quantum systems.

These are just some ideas for some top level concepts for representing quantum inspired data structures that encapsulate the desirable properties of being able to quantize, superpose and correlate at higher dimensions (i.e. entangle) information in a possibly useful way.

For other sources of data structures and examples the following sources are also very useful and inspiring:

Quantum Computing since Democritus  and its companion website online course.
Quantum Machine Learning: What Quantum Computing Means to Data Mining
Principles of Quantum Artificial Intelligence

There are, of course many sources around but we shall attempt to look into a few algorithms and reprsentations in the coming months to see what the possibilities can be.