[Article] Quantum Walks with Gremlin
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Marko Rodriguez
Nov 20, 2015, 2:21:47 PM11/20/15
to gremli...@googlegroups.com, d...@tinkerpop.incubator.apache.org, Lynn Bender
Hello,
At the beginning of summer I started studying quantum mechanics in my spare time. I realized that many of the concepts in quantum mechanics are similar to "Gremlin mechanics." In particular, both systems exploit particle/traverser superposition. However, what Gremlin doesn't have is an explicit notion of wave dynamics -- a fundamental component of quantum systems. That is, the traversers in Gremlin only constructively interfere (called "bulking"), they never destructively interfere. Upon further exploration, I realized that there are very few articles that discuss the use of waves in graph/network theory. Thus, either there is a rich vein of untapped ideas or the endeavor is a dead end with little to be leveraged. I leaned towards the prior assumption given that discrete quantum mechanics is conveniently modeled as a wave on a graph. This wave is known as the famous "wavefunction" of quantum mechanics' wave-particle duality thesis.
In order to learn, I teach. Thus, for GraphDay in January, I decided to present a talk called "Quantum Processes in Graphs." [http://graphday.com/sessions/#rodriguez] However, to ensure that my knowledge is sound, I thought it prudent to first write an article on the topic. This article is entitled "Quantum Walks with Gremlin" and you can find it referenced in the tweet below.
https://twitter.com/twarko/status/667784364210569216
Interestingly, there is little difference between classical wave mechanics and quantum mechanics. I suppose the difference can be naively stated as: "quantum mechanics ultimately 'does something' with the wave." In particular, the quantum wavefunction "collapses" to form a particle upon observation/measurement (in the lexicon of the Copenhagen interpretation). While in classical wave mechanics, the wave itself is the ultimate object of concern. Hopefully, the aforementioned article (and future presentation in January) will allow us to kill two birds with one stone -- we learn how to model waves in graphs and, as a nice amendment, we will also learn about quantum computing. We gain all of this from the familiar perspective of the Gremlin graph traversal machine and language.
Enjoy,
Marko.
http://markorodriguez.com
At the beginning of summer I started studying quantum mechanics in my spare time. I realized that many of the concepts in quantum mechanics are similar to "Gremlin mechanics." In particular, both systems exploit particle/traverser superposition. However, what Gremlin doesn't have is an explicit notion of wave dynamics -- a fundamental component of quantum systems. That is, the traversers in Gremlin only constructively interfere (called "bulking"), they never destructively interfere. Upon further exploration, I realized that there are very few articles that discuss the use of waves in graph/network theory. Thus, either there is a rich vein of untapped ideas or the endeavor is a dead end with little to be leveraged. I leaned towards the prior assumption given that discrete quantum mechanics is conveniently modeled as a wave on a graph. This wave is known as the famous "wavefunction" of quantum mechanics' wave-particle duality thesis.
In order to learn, I teach. Thus, for GraphDay in January, I decided to present a talk called "Quantum Processes in Graphs." [http://graphday.com/sessions/#rodriguez] However, to ensure that my knowledge is sound, I thought it prudent to first write an article on the topic. This article is entitled "Quantum Walks with Gremlin" and you can find it referenced in the tweet below.
https://twitter.com/twarko/status/667784364210569216
Interestingly, there is little difference between classical wave mechanics and quantum mechanics. I suppose the difference can be naively stated as: "quantum mechanics ultimately 'does something' with the wave." In particular, the quantum wavefunction "collapses" to form a particle upon observation/measurement (in the lexicon of the Copenhagen interpretation). While in classical wave mechanics, the wave itself is the ultimate object of concern. Hopefully, the aforementioned article (and future presentation in January) will allow us to kill two birds with one stone -- we learn how to model waves in graphs and, as a nice amendment, we will also learn about quantum computing. We gain all of this from the familiar perspective of the Gremlin graph traversal machine and language.
Enjoy,
Marko.
http://markorodriguez.com
Sebastian Good
Nov 24, 2015, 5:28:54 PM11/24/15
to Gremlin-users, d...@tinkerpop.incubator.apache.org, ly...@lynnbender.com
Groovy.
Marko Rodriguez
Nov 24, 2015, 5:31:25 PM11/24/15
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How do you like TinkerPop3, Sebastian? I see you on Twitter all the time with nice posts about TinkerPop.
You diggin' it?
Marko.
On Nov 24, 2015, at 3:26 PM, Sebastian Good <seba...@palladiumconsulting.com> wrote:
Groovy.--
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Sebastian Good
Nov 24, 2015, 5:38:16 PM11/24/15
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TP3 has collected lots of things together and just makes things plain easier to think about. Gremlin has moved from a naked query plan to a higher level query language, which is the part I like best. For me the progress I’ve seen in a year has been impressive.
Denise Gosnell
Jan 15, 2016, 9:58:21 AM1/15/16
to Gremlin-users
I am looking forward to gaining a fuller perspective from your talk at GraphDay. From what I have read here, the notion of "destructive interference" in graphs is synonymous to the study of edge/vertex lifting or graph modifications in topological graph theory. Some of the current work in this area examines the stability of graphs as vertices/edges are deleted randomly, directly, or via graph walks. Most of the work in this realm which I can recommend is by Wyatt Desormeaux, Teresa Haynes, and/or Michael Henning.
I would be interested in hearing your thoughts on the relatedness of this work to modeling the destructive component of the wave function of quantum mechanics.
Great work, thanks!
Marko Rodriguez
Jan 15, 2016, 11:54:22 AM1/15/16
to gremli...@googlegroups.com
Hello Denise,
> I am looking forward to gaining a fuller perspective from your talk at GraphDay. From what I have read here, the notion of "destructive interference" in graphs is synonymous to the study of edge/vertex lifting or graph modifications in topological graph theory. Some of the current work in this area examines the stability of graphs as vertices/edges are deleted randomly, directly, or via graph walks. Most of the work in this realm which I can recommend is by Wyatt Desormeaux, Teresa Haynes, and/or Michael Henning.
Destructive interference, as its modeled for quantum walks, does not effect the topology of the graph. It effects the merging/splitting of the traversers containing the wave energy.
I suppose you could alter the graph structure, but I don't know (off the top of my head right now answering this email) the benefit of that would be.
> I would be interested in hearing your thoughts on the relatedness of this work to modeling the destructive component of the wave function of quantum mechanics.
If you will be at GraphDay, I will be there, so please feel free to pull me aside and we can discuss.
Take care,
Marko.
http://markorodriguez.com
> I am looking forward to gaining a fuller perspective from your talk at GraphDay. From what I have read here, the notion of "destructive interference" in graphs is synonymous to the study of edge/vertex lifting or graph modifications in topological graph theory. Some of the current work in this area examines the stability of graphs as vertices/edges are deleted randomly, directly, or via graph walks. Most of the work in this realm which I can recommend is by Wyatt Desormeaux, Teresa Haynes, and/or Michael Henning.
I suppose you could alter the graph structure, but I don't know (off the top of my head right now answering this email) the benefit of that would be.
> I would be interested in hearing your thoughts on the relatedness of this work to modeling the destructive component of the wave function of quantum mechanics.
Take care,
Marko.
http://markorodriguez.com
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