Introduction
The next set of posts will introduce several elements that will build a mindset, or mental model and a point of view about quantum inspired system semantics that will focus on the actual path to building operational quantum-like data representations, processing and algorithms.
Quantum Inspired System Semantics or QUISS for short follows the KISS principle. That is, I will do my best to get to the point quickly and efficiently. However, let's not forget what Feynman and Nielsen said about trying to explain quantum computing or other challenging emerging science. If it could be written and explained to everyone or anyone, then it would not be new but commonplace and old-hat.
In terms of the approach, we will take things starting at the beginning and provide some concretely usable concepts, in several cases, implementations as well, and example data input/outputs and value.
Bits, Bytes and the Qubit
Traditional computing uses the familiar abstraction of the Bit over its implementation as an electrical circuit, or even a mechanical circuit (like Turing's original designs) whose voltage or mechanical lever is either above or below a certain threshold.
The concept of aggregating a number of bits, in order, using the binary base numbering system was all that was needed to complete the most basic and fundamental data structure: the byte. It is on bits and bytes that all of modern computing rests.
From a linguistic perspective it was natural, therefore, that a name that had as its past, the word "bit" in it would be chosen as the simplest term for a Quantum datum. But unlike the word "Bit", which is crisp clear and simple, with an underlying abstraction built on electrical or mechanical circuits, adding the word "Quantum" changes everything so much to the point that the word "QuBit" leads one into a morass.
The best explanation is not the Wiki Qubit, but the David Deutch article on "It from Bit".
A Qubit is neither crisp, clear nor simple: it is a superposition of states of objects representing states, such as state vectors whose elements are some other sorts of mathematical objects that have nothing to do with voltage thresholds or the positions of mechanical levers.
In fact, the Qubit concept as you find it online incorporates two notions: the first is that there is a probability scale between the elements that make up a qubit and second that knowledge of the first element automatically implies knowledge of a second. So, as an example, consider the question whether if it will rain tonight: instead of a classical "yes" / "no" stated as binary {1} or {0}, you have some range from [0, 1] representing the probability of the outcome that it will rain and not rain. In other words, the underlying elements are not probabilities but wavefunctions whose amplitudes when subjected to squaring eliminate the complex plane to produce a real value that is then interpreted as the probability.
The issue is that the underlying abstraction for a qubit is not a circuit but a complex vector space, and then, the underlying abstraction of that complex vector space is the mental model of a quantum entity as inferred from field theory and other branches of physics.
A quantum observable is neither a real variable, like a classical degree of freedom, or probability measurement nor a discrete variable like a classical bit, or a random choice, but a much more fascinating, and deeply significant object that entangles and integrates all the discrete and continuous aspects in all the dimensional as well as non-dimensional but measurable phenomena.
The implication is actually staggering: how does a quantum entity make the transition from one state to another? Does it just "jump" between states? The answer is incredible and given by quantum theory is that it makes it
continuously but is only observable discretely!
The point here is that the Qubit is nothing like the Bit and not even remotely so. It would have, in my opinion, been better to chose some other completely different name to avoid the confusion that this now produces.
Qubits, Qutrits, Qudits
The key goal in representation is to figure what data structures are most useful and enable suporpositioning, quantization and entanglement. If we take a step back to see the forest from the trees, we realize the combinatorial structures and geometries have a utility all their own: Alexander Grothedieck developed a theory of "places", formally called Topose Theory, as a replacement and as an advancement of the theory of categories where the intuitive patterns of geometry could be localized and captured in model for reuse.The major idea we are presenting here is that geometry is intimately tied into combinatorics which is the key to the quantum probabilistic description of information structure.
I enjoyed this post Arun, the notion "that geometry is intimately tied into combinatorics which is the key to the quantum probabilistic description of information structure" is something that we modelled early on in our virtual particle. A foundation function of Toridion Byte mathematics libraries is the use of what we call "BQR" a kind of approximation that allows the model to make closer approximations of a "almost" infinite set of probabilities. In fact Toridion operates in a finite phase space... What we have succeed in achieving is the ability to scatter particles in such a way as to make probabilities fall into extremely selectable and discrete steps.
ReplyDeleteSounds we are on related parallel tracks on some things - convergence is a natural feature of discovery :)
ReplyDeleteI have been looking at Nima's, Trnka's and Bourjailly's work on the Amplithedron and realize it has a lot of other applications - it's a pretty good example of the quantum nature of geometry.
Cheers!