Can somebody point to publications describing essential logic gates (e.g. AND and NOT) implemented in the most basic model of classical mechanics - bistable systems consisting of point masses (point charges) in external potential fields, manipulated by other external potential fields.
E.g., a single bit can be implemented in this classical mechanics framework as a bistable system consisting of a single charged particle trapped in one of two nearby potential wells of the field interacting with the charge of the particle. The time-dependent external field can be applied to move the particle between these two wells, thus implementing flipping the bit between 0 and 1. Perhaps, other time-dependent fields can be suggested, acting on a single and multiple bits, thus implementing the logic gates? See below.
The question is motivated by the physics of quantum computing (QC), where QC practitioners use external fields to manipulate qubits, thus implementing quantum gates, claiming that many/most/all quantum gates can be implemented by properly modulated external fields.
Thank you!
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Here is some information on mechanical logic gates and some thoughts on potential approaches to the implementation of such logic gates in simple classical mechanics model.
Mechanical logic gates exist - see, for instance:
https://en.wikipedia.org/wiki/Billiard-ball_computer
https://en.wikipedia.org/wiki/Domino_computer
https://www.google.com/search?q=mechanical+logic+gate
However, these mechanical logic gates are more complex than just point charges in external fields - they involve solid bodies (of certain dimensions and shapes), interacting with each other.
For the bit implemented as a single charged particle trapped in one of two adjacent potential wells, as described above, perhaps the following approaches can be used to implement the NOT and AND logic gates.
To implement the NOT logic gate, consider the field that would drag the particle from the well 0 to the well 1, combined with the simultaneously applied field, dragging the particle from the well 1 to the well 0, along the non-intersecting paths. Regardless of the original position of the particle (well 0 or well 1), such time-varying field will flip the value of the bit from 0 to 1 or from 1 to 0. This time-varying field implements the NOT gate.
The AND gate can be constructed using the fact that the field from the charged particle trapped in the well compensates, in part, the field of this well. So, if the "depth" of the well is properly chosen, and the second particle is dragged through the well with another particle already trapped there, this second particle will not be trapped in this well, which can be used to implement the AND gate.
It is possible to build logic gates with cellular automata, even 2D ones.
https://www.stephenwolfram.com/media/computer-recreations/
Here are other approaches
https://physicsworld.com/a/trapped-ions-make-logic-gates/
https://phys.org/news/2014-08-3d-magnetic-logic-gate.html
Article Majority Logic Gate for Magnetic Quantum-Dot Cellular Automata
https://physicsworld.com/a/silver-nanoclusters-make-logic-gates/
Article Massively parallel computing on an organic molecular layer
https://physicsworld.com/a/magnets-open-the-gate-to-nanoscale-logic/
Regards,
Joachim
Joachim Pimiskern : thank you for providing the links.
After looking through the list, I can see that the systems used to implement the logic gates in them are either (1) formal systems, not immediately realized as mechanical systems (cellular automata); or (2) essentially quantum mechanical systems, not immediately reducible to classical mechanical systems (trapped ions, magnetic quantum dots); or (3) the systems which are not obviously (to me) reducible to simple classical mechanics system (the rest of the examples).
Which of the example(s) provided by you are the systems evolving according to the laws of classical mechanics, in the most obvious way?
Thank you!
I think the last one where domain walls are moved is the most mechanical logic gate. Here's a more macroscopic one: have you ever heard of Konrad Zuse's first computer, the Z1?
https://www.printables.com/de/model/42012-zuse-inspired-z1-logic-gate-demonstration-set
https://www.youtube.com/watch?v=W0b7DHDp7QA
https://www2.hs-fulda.de/~grams/mathehilft/Zuse/AnmerkungenAddierer.pdf
The energy used comes from the clock metal sheets, which were operated in a scheme north-east-south-west-north...
Regards,
Joachim
Joachim Pimiskern : Thank you for the clarification pointing to moving domain walls in the example at the end of the list you provided earlier, and for pointing to the work of Konrad Zuse, his Z1 and the examples of Zuse's Z1 mechanical logic gates implemented using flat sliding rods!
I am particularly intrigued by Zuse's concept of Rechnender Raum (Calculating Cosmos / Calculating Space), which seems to involve the particles interacting with each other (and external fields?) and performing Boolean(?) calculations!
https://en.wikipedia.org/wiki/Konrad_Zuse
https://en.wikipedia.org/wiki/Z1_(computer)
Rechnender Raum (Calculating Cosmos/ Calculating Space) :
https://en.wikipedia.org/wiki/Calculating_Space
https://philpapers.org/archive/ZUSRR.pdf
https://web.archive.org/web/20200325103231/ftp://ftp.idsia.ch/pub/juergen/zuserechnenderraum.pdf
It might be interesting to study latest research results on emergent information processing, which is basically finding computational methods that are capable to perform complicated computations by using self-organization and emergent computations without using their manual design.
The review with incorporated research results is here:
https://www.researchgate.net/publication/378750463_Emergent_Information_Processing_Observations_Experiments_and_Future_Directions
There is existing a database of videos depicting animatuins of simulations, see the link in the review. The software used to create those animations is open souce.
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