DONE!! A few weeks late, as expected 🫠 This should hopefully be out on the arXiv soon and if it gets stuck in the waiting list, I am hosting it on my website either way. Please leave comments/questions if you're interested and have something to discuss!
So if all goes well, I plan to put my corrected and perfected ✨ thesis up on the arxiv in the next week or two.
If anyone would find it useful to learn a bit more about Counterdiabatic Driving or optimal control of quantum systems, keep an eye out!
"Geometric anatomy of theoretical physics" by Frederic Schuller
already looking like my favourite online resource for mathematical physics ever! 😮 It's both rigorous and incredibly clear!
After you defend your quantum physics PhD they take you into a dark room and tell you the truth. "Actually some russian already solved this in the 60s. We just made this all up for grant money"
Ah! Okay! Oh my, oh goodness, this blog post is a very good way to get excited about geometry, symmetry, scale-invariance and deep learning all at once!
My thanks to
@mmbronstein
,
@joanbruna
,
@TacoCohen
and
@PetarV_93
The Scottish Highlands make me exceptionally happy and deserve to be appreciated so here's a picture thread I will add to sporadically for reasons of joy. First is Liathach ridge near Torridon, May 2019
Spending more and more time around extremely intelligent and accomplished researchers has lead to a massive increase in hearing the words:
"This may be a really stupid question, sorry, but..."
I love it
I still can’t get over how much information can be effectively stored and transmitted in a well-designed diagram. Same with certain equations tbf. Visualisation is a big part of my learning process.
Learning *anything* without the pressure of an exam is just so much better.
I genuinely missed out on reading about stuff I was interested in because I had to cram for the stuff I would be examined on.
Every time I revisit this paper it is a treat.
"Physical entropy measures amount of information; here I'll argue that physical action measures amount of computation."
Ah! Found this paper ():
"A micro Lie theory for state estimation in robotics"
which not only works to answer my original quoted tweet but also informed me that Lie algebras are a big thing in robotics (unsurprisingly)!
Okay this sounds v cool:
Lie group is a manifold w group structure and Lie algebra is its tangent space -> a direction on the manifold is a "generator" of the one-element(parameter?) subgroup.
I'm struggling to intuit this, does anyone have resources/wisdom to help?
Accidentally started reading "Monoidal categories in, and linking, geometry and algebra" by Ross Street and it has so many immediate insights for a noob like me
I've started to really warm up to pure maths for reasons that aren't as immediately obvious. I've realised that concepts I previously thought were self-evident and precise were not actually so irl. Conversations with people keep getting more difficult as I grow older. 1/3
Just got my code to solve Maximal Independent Sets by encoding them into Hamiltonians (), turning those into classical shadows () and then using neural tangent kernels () to train an ML model!
So I just found this image on wikipedia and it is possibly one of the more useful diagrams I've ever seen for explaining science. There is an interplay between experiment and modelling and their implementations which is captured pretty nicely here.
Why is 'minimisation' rather than 'maximisation' more common in general optimisation problems? They're equivalent as far as I can tell, so what's the reason?
My hunch is it's historic and maybe something to do w/ energy minimisation in Physics?
I've realised now that I have somewhat of a platform, it might be good to share a little something of my past experience with eating disorders. I remember making myself a promise that I'd try to be open about it and help others as much as I can once I can. 1/n
What is Counterdiabatic Driving?
A thread for the Physicist, the Non-Physicist and every superposition of the above. I'll start with the simple and go progressively towards more quantum physics-y, but I hope this is interesting to most.
1/n
Just reading this brilliant post by
@johncarlosbaez
(sent to me by
@bgavran3
<3) and it's absolutely fascinating.
CT is giving me deeper intuitions about tensor products and their relationship to information flow in quantum vs classical systems
I think the joke about how physicists approximate everything is actually a very cool observation about mathematical modelling:
In math, you define the model and the structures you're working with: these tend to be precise/exact because you "define" them to begin with... 1/3
Okay so I only know dual spaces in the context of Hilbert spaces and complex numbers etc.
Are there any other contexts in which dual spaces are obviously key? Why? Basically I just want to understand *why* dual spaces.
Thinking of actually writing this up as a blogpost(/arxiv?), largely because it's a fun thing that might inspire others :))
Would anyone be interested? Would include my own brief take on classical shadows, Maximal Independent Sets and maybe a bit on neural tangent kernels
Just got my code to solve Maximal Independent Sets by encoding them into Hamiltonians (), turning those into classical shadows () and then using neural tangent kernels () to train an ML model!
I really like this definition and it seems necessary to have one given how often an argument in physics is based on 'physicality'.
From the very recent "The unphysicality of Hilbert spaces"
Proof by process: I realised computer science allowed me to understand math and abstraction better than pure math ever did. Something about the act of computation makes things clearer.
In the midst of all this, I’m finally getting a first-author paper published and another submitted to a journal. This PhD hasn’t been going quite as planned (global/personal crises and all), but I feel a bit reinvigorated 🥳
I almost didn't get a PhD after my undergrad/masters and now people are actively offering me jobs and postdocs
Wish I could go back to baby undergrad Ieva and tell her it would all be okay 😊
This is a really cool essay about viewing time and temperature as quantum entanglement by Vlatko Vedral (from "Time in Physics", 2010).
Does anyone know the current state of our understanding of time in the quantum sense?
I obsess over this fact occasionally, largely because I deeply enjoy finding and exploring links between finite Hilbert spaces (ie quantum states/operators) and graph problems.
The single most undervalued fact of linear algebra: matrices are graphs, and graphs are matrices.
Encoding matrices as graphs is a cheat code, making complex behavior simple to study.
Let me show you how!
This is the best cheat-sheet paper I've found in a LONG time.
EVERY 'introduction' paper should have a glossary this basic and clear (and simple, obvious figures to boot). People seeking these sorts of papers out often find obvious things non-obvious.
Is there anyone on here who still wants to engage with interesting/practical quantum tech/info questions? Asking genuinely.
I am increasingly (exponentially) growing disenchanted with twitter and don’t feel like posting or responding. I don’t know whether a community is there
My late grandad worked on laser physics in Soviet Lithuania in the early 70s and when I told him about quantum computing/tech back in 2017, he genuinely thought I was making it up because he couldn’t believe we could have this much control of quantum phenomena
When I was little I thought science was about making things complicated with math and now I see that science is about making things as uncomplicated as possible with math
So transistors were proposed in 1925, built in 1947 and integrated into digital computers in 1955. Then MOSFET came along in 1959 and (I'd say) changed computing forever. That's 30+ years of development. We forget technology needs time (RE: quantum computing hardware)
For me, personally, becoming a good (great?) researcher began when I began having enough confidence to actually ask the questions I needed to ask and to very calmly accept my own misunderstandings and ignorance
I'm not a type theorist so most of this flies completely over my head, but I still maintain that one day I will understand this paper because it just seems *so cool*
Okay this sounds v cool:
Lie group is a manifold w group structure and Lie algebra is its tangent space -> a direction on the manifold is a "generator" of the one-element(parameter?) subgroup.
I'm struggling to intuit this, does anyone have resources/wisdom to help?
I didn’t even know about this but what a brilliant way to find inspiring people! It’s
#WomenScienceDay
and
#IAmAPhysicist
who plays around with quantum algorithms and quantum many-body systems and mostly just fixes code bugs