Ciro Santilli @cirosantilli 35

The knowledge that light is polarized precedes the knowledge of the existence of the photon, see polarization of light for the classical point of view.

The polarization state and how it can be decomposed into different modes can be well visualized with the Poincaré sphere.

One key idea about photon polarization is that it carries angular momentum. Therefore, when an electron changes orbitals in the Schrödinger equation solution for the hydrogen atom, the angular momentum (as well as energy) change is carried out by the polarization of the photon!

Video 1.

Quantum Mechanics 9b - Photon Spin and Schrodinger's Cat II by ViaScience (2013)

Source.

clear animations showing how two circular polarizations can make a vertical polarization
a polarizer can be modelled bra operator.
light polarization experiments are extremely direct evidence of quantum superposition. Individual photons must be on both L and R states at the same time because a V filter passes half of either L or R single photons, but it passes all L + R photons

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Ladner's Theorem by

Ciro Santilli 35  Updated 2025-03-28  +Created 1970-01-01

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Night climbing by

Ciro Santilli 35  Updated 2025-03-28  +Created 1970-01-01

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www.varsity.co.uk/features/24648 ‘It felt impossibly romantic’: the nightclimbers of Cambridge by Varsity (2022)

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Quantinuum by

Ciro Santilli 35  Updated 2025-03-28  +Created 1970-01-01

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Merger between Cambridge Quantum Computing, which does quantum software, and Honeywell Quantum Solutions, which does the hardware.

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IBM Quantum Computing by

Ciro Santilli 35  Updated 2025-03-28  +Created 1970-01-01

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The term "IBM Q" has been used in some promotional material as of 2020, e.g.: www.ibm.com/mysupport/s/topic/0TO50000000227pGAA/ibm-q-quantum-computing?language=en_US though the fuller form "IBM Quantum Computing" is somewhat more widely used.

They also internally named an division as "IBM Q": sg.news.yahoo.com/ibm-thinks-ready-turn-quantum-050100574.html

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PsiQuantum by

Ciro Santilli 35  Updated 2025-03-28  +Created 1970-01-01

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CEO: Jeremy O'Brien

Raised 215M in 2020: www.bloomberg.com/news/articles/2020-04-06/quantum-computing-startup-raises-215-million-for-faster-device

Good talk by CEO before starting the company which gives insight on what they are very likely doing: Video "Jeremy O'Brien: "Quantum Technologies" by GoogleTechTalks (2014)"

PsiQuantum appears to be particularly secretive, even more than other startups in the field.

They want to reuse classical semiconductor fabrication technologies, notably they have close ties to GlobalFoundries.

So he went to the US and raised N times more from the American military-industrial complex.

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EeroQ by

Ciro Santilli 35  Updated 2025-03-28  +Created 1970-01-01

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eeroq.com/

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shred (UNIX) by

Ciro Santilli 35  Updated 2025-03-28  +Created 1970-01-01

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Nest.js by

Ciro Santilli 35  Updated 2025-03-28  +Created 1970-01-01

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JavaScript memory usage benchmark by

Ciro Santilli 35  Updated 2025-03-28  +Created 1970-01-01

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In this section we will use the file nodejs/bench_mem.js, tests are run on Node.js v16.14.2 from NVM, Ubuntu 21.10, on Lenovo ThinkPad P51 (2017) which has 32 GB RAM.

First using topp from stackoverflow.com/questions/1221555/retrieve-cpu-usage-and-memory-usage-of-a-single-process-on-linux/40576129#40576129 let's observe the memory usage of some baseline cases.

A C hello world with an infinite loop at the end has:

2.7 MB
770 KB

For a Node.js infinite loop nodejs/infinite_loop.js

topp infinite_loop.js

This gives approximately:

RSS: 20 MB
VSZ: 230 MB

Adding a single hello world to it as in nodejs/infinite_hello.js and running:

topp infinite_hello.js

leads to:

RSS: 26 MB
VSZ: 580 MB

We understand that Node.js preallocates VSZ wildly. No big deal, but it does mean that VSZ is a useless measure for Node.js.

Forcing garbage collection as in nodejs/infinite_hello.js brings it down to 20 MB however:

topp node --expose-gc infinite_hello_gc.js

Finally let's see a baseline for process.memoryUsage nodejs/infinite_memoryusage.js:

node --expose-gc infinite_memoryusage.js

which gives initially:

{
  rss: 23851008,
  heapTotal: 6987776,
  heapUsed: 3674696,
  external: 285296,
  arrayBuffers: 10422
}

but after a few seconds randomly jumps to:

{
  rss: 26005504,
  heapTotal: 9084928,
  heapUsed: 3761240,
  external: 285296,
  arrayBuffers: 10422
}

so we understand that

heapUsed seems constant at 3.7 MB
heapTotal is a very noisy, as it starts at 7 MB, but randomly jumps to 9 MB at one point without apparent reason

Now let's run our main test program.

First a baseline case with an array of length 1:

node --expose-gc bench_mem.js n 1

This gives the same results as node --expose-gc infinite_memoryusage.js. The same result is obtained by doing:

a = undefined

with:

node --expose-gc bench_mem.js dealloc

Not let's vary the size of n a bit with:

node --expose-gc bench_mem.js n N

which gives:

N	`heapUsed`	`heapTotal`	`rss`	`heapUsed` per elem	`rss` per elem
1 M	14 MB	48 MB	56 MB	10	30
10 M	122 MB	157 MB	176 MB	18	15
100 M	906 MB	940 MB	960 MB	9	9.3

"rss per elem" is calculated as: rss - 26 MB, where 26 MB is the baseline RSS seen on n 1.

Similarly "heapUsed per elem" deduces the 4 MB (approximation of the above 3.7 MB) seen on n 1.

Note that to reach MAX_SAFE_INTEGER we would need 8 bytes per elem worst case.

Everything below 100 million (8) is therefore very memory wasteful in terms of RSS.

If we use Int32Array typed array buffers instead of a simple Array:

node --expose-gc bench_mem.js array-buffer n N

we see that the memory is now, unsurprisingly, accounted for under arrayBuffers, e.g. for N 1 million:

{
  rss: 31776768,
  heapTotal: 6463488,
  heapUsed: 3674520,
  external: 4285296,
  arrayBuffers: 4010422
}

Results for different N:

|| N
|| `arrayBuffers`
|| `rss`
|| `rss` per elem

| 1 M
| 4 MB
| 31 MB
| 5

| 10 M
| 40 MB
| 67 MB
| 4.6

| 100 M
| 40 MB
| 427 MB
| 4

We see therefore that typed arrays are much closer to what they advertise (4 bytes per element), even for smaller element counts, as expected.

Now let's try one million objects of type { a: 1, b: -1 }:

node --expose-gc bench_mem.js obj

gives:

{
  rss: 138969088,
  heapTotal: 105246720,
  heapUsed: 70103896,
  external: 285296,
  arrayBuffers: 10422
}

Disaster! Memory usage is up to 70 MB! Why?? We were expecting only about 24, 4 baseline + 2 * 10 for each million int?!

And now an equivalent version using class:

node --expose-gc bench_mem.js class

gives the same result.

Let's try Array:

node --expose-gc bench_mem.js arr

is even worse at 78 MB!! OMG why.

{
  rss: 164597760,
  heapTotal: 129363968,
  heapUsed: 78117008,
  external: 285296,
  arrayBuffers: 10422
}

Let's change the number of fields on the object? First as a sanity check:

node --expose-gc bench_mem.js obj 2

produces as expected the smae result as:

node --expose-gc bench_mem.js obj

so adding properties one by one doesn't change anything from creating the literal all at once. Good.

Now:

node --expose-gc bench_mem.js obj N

gives heapUsed:

1: 70M
2: 70M
3: 70M
4: 70M
5: 110M
6: 110M
7: 110M
8: 134M
9: 134M
10: 134M
11: 158M

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Geocentric model by

Ciro Santilli 35  Updated 2025-03-28  +Created 1970-01-01

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Universal wavefunction by

Ciro Santilli 35  Updated 2025-03-28  +Created 1970-01-01

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ARTIQ by

Ciro Santilli 35  Updated 2025-03-28  +Created 1970-01-01

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Biconvex spherical lens by

Ciro Santilli 35  Updated 2025-03-28  +Created 1970-01-01

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Focal length

Each side is a sphere section. They don't have to have the same radius, they are still simple to understand with different radiuses.

The two things you have to have in mind that this does are:

converges parallel light to a point at center at distance $f$ known as the focal length.
This is for example why you can use lenses to burn things with Sun rays, which are basically parallel.
Conversely, if the input is a point light source at the focal length, it gets converted into parallel light.
image formation: it converges all rays coming from a given source point to a single point image. This amplifies the signal, and forms an image at a plane.
The source image can be far away, and the virtual image can be close to the lens. This is exactly what we need for a camera.
For each distance on one side, it only works for another distance on the other side. So when we set the distance between the lens and the detector, this sets the distance of the source object, i.e. the focus. The equation is:
$\frac{1}{f} = \frac{1}{S _{1}} + \frac{1}{S _{2}}$
(1)
where $S_{1}$ and $S_{2}$ are the two distances.

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