Of course, because what we know about the halting problem, there cannot exist a single decider that decides all Turing machines.
E.g. The Busy Beaver Challenge has a set of deciders clearly published, which decide a large part of BB(5). Their proposed deciders are listed at: discuss.bbchallenge.org/c/deciders/5 and actually applied ones at: bbchallenge.org.
But there are deciders that can decide large classes of turing machines.
Many (all/most?) deciders are based on simulation of machines with arbitrary cutoff hyperparameters, e.g. the cutoff space/time of a Turing machine cycler decider.
The simplest and most obvious example is the Turing machine cycler decider
Some further comments at: Section "Cataclysm: Dark Days Ahead".
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. Added font awesome icons. github.com/ourbigbook/ourbigbook/issues/151
Didn't manage to subset, but so be it for now: stackoverflow.com/questions/62395038/how-can-i-export-only-one-character-from-ttf-woff-file-to-avoid-load-unnecessa/71197892#71197892
TODO understand.
Trapping Ions for Quantum Computing by Diana Craik (2019)
Source. A basic introduction, but very concrete, with only a bit of math it might be amazing:Sounds complicated, several technologies need to work together for that to work! Videos of ions moving are from www.physics.ox.ac.uk/research/group/ion-trap-quantum-computing.
- youtu.be/j1SKprQIkyE?t=217 you need ultra-high vacuum
- youtu.be/j1SKprQIkyE?t=257 you put the Calcium on a "calcium oven", heat it up, and make it evaporates a little bit
- youtu.be/j1SKprQIkyE?t=289 you need lasers. You shine the laser on the calcium atom to eject one of the two valence electrons from it. Though e.g. Universal Quantum is trying to do away with them, because alignment for thousands or millions of particles would be difficult.
- youtu.be/j1SKprQIkyE?t=518 keeping all surrounding electrodes positive would be unstable. So they instead alternate electrode quickly between plus and minus
- youtu.be/j1SKprQIkyE?t=643 talks about the alternative, of doing it just with electrodes on a chip, which is easier to manufacture. They fly at about 100 microns above the trap. And you can have multiple ions per chip.
- youtu.be/j1SKprQIkyE?t=1165 using microwaves you can flip the spin of the electron, or put it into a superposition. From more reading, we understand that she is talking about a hyperfine transition, which often happen in the microwave area.
- youtu.be/j1SKprQIkyE?t=1210 talks about making quantum gates. You have to put the ions into a magnetic field at one of the two resonance frequencies of the system. Presumably what is meant is an inhomogenous magnetic field as in the Stern-Gerlach experiment.This is the hard and interesting part. It is not clear why the atoms become coupled in any way. Is it due to electric repulsion?She is presumably describing the Cirac–Zoller CNOT gate.
How To Trap Particles in a Particle Accelerator by the Royal Institution (2016)
Source. Demonstrates trapping pollen particles in an alternating field.- youtu.be/lJOuPmI--5c?t=1601 Cirac–Zoller CNOT gate was the first 2 qubit gate. Explains it more or less.
Introduction to quantum optics by Peter Zoller (2018)
Source. THE Zoller from Cirac–Zoller CNOT gate talks about his gate.- www.youtube.com/watch?v=W3l0QPEnaq0&t=427s shows that the state is split between two options: center of mass mode (ions move in same direction), and strechmode (atoms move in opposite directions)
- youtu.be/W3l0QPEnaq0?t=658 shows a schematic of the experiment
After something broke on the website due to SQLite vs PostgreSQL inconsistencies and took me a day to figure it out, I finally decided to update the test system so that
OURBIGBOOK_POSTGRES=true npm test will run the tests on PostgreSQL.Originally, these were being run only on SQLite, which is the major use case for OurBigBook CLI, which came before the website.
We know that superfluidity happens more easily in bosons, and so electrons joins in Cooper pairs to form bosons, making a superfluid of Cooper pairs!
Isn't that awesome!
Theories of Quantum Matter by Austen Lamacraft The Elastic Chain Discrete Fourier Transform Updated 2025-07-11 +Created 1970-01-01
Transmission Electron Microscope by LD SEF (2019)
Source. Images some gold nanopraticles 5-10 nm. You can also get crystallographic information directly on the same machine. Stack Overflow policy that you cannot harshly criticize the character of a politician Updated 2025-07-11 +Created 1970-01-01
Advantages over Riemann:
- Lebesgue integral of is complete but Riemann isn't.
- youtu.be/PGPZ0P1PJfw?t=710 you are able to switch the order of integrals and limits of function sequences on non-uniform convergence. TODO why do we care? This is linked to the Fourier series of course, but concrete example?
youtube.com/watch?v=PGPZ0P1PJfw&t=808 shows how Lebesgue can be visualized as a partition of the function range instead of domain, and then you just have to be able to measure the size of pre-images.
One advantage of that is that the range is always one dimensional.
But the main advantage is that having infinitely many discontinuities does not matter.
Infinitely many discontinuities can make the Riemann partitioning diverge.
But in Lebesgue, you are instead measuring the size of preimage, and to fit infinitely many discontinuities in a finite domain, the size of this preimage is going to be zero.
Which is why we then fall into measure theory!
The inaugural that predicted the Josephson effect.
Published on Physics Letters, then a new journal, before they split into Physics Letters A and Physics Letters B. True Genius: The Life and Science of John Bardeen mentions that this choice was made rather than the more prestigious Physical Review Letters because they were not yet so confident about the results.
Correspond to the angular part of Laplace's equation in spherical coordinates after using separation of variables as shown at: en.wikipedia.org/wiki/Spherical_harmonics#Laplace's_spherical_harmonics
This theorem roughly states that states that for every quantum algorithm, once we reach a certain level of physical error rate small enough (where small enough is algorithm dependant), then we can perfectly error correct.
This algorithm provides the conceptual division between noisy intermediate-scale quantum era and post-NISQ.
One is reminded of Nick Leeson.
One things must be said: the root cause of all of this is the replication crisis.
This is why he managed to go on for so long.
There are unlisted articles, also show them or only show them.