Ciro Santilli @cirosantilli 35

As en.wikipedia.org/w/index.php?title=ZX-calculus&oldid=1071329204#Diagram_rewriting tries to explain but fails to deliver as usual consider the GHZ state represented as a quantum circuit.

How can we easily prove that that quantum circuit equals the state:?

The naive way would be to just do the matrix multiplication as explained at Section "Quantum computing is just matrix multiplication".

However, ZX-calculus provides a simpler way.

And even more importantly, sometimes it is the only way, because in a real circuit, we would not be able to do the matrix multiplication

What we do in ZX-calculus is we first transform the original quantum circuit into a ZX graph.

This is always possible, because we can describe how to do the conversion simply for any of the Clifford plus T gates, which is a set of universal quantum gates.

Then, after we do this transformation, we can start applying further transformations that simplify the circuit.

It has already been proven that there is no efficient algorithm for this (TODO source, someone said P-sharp complete best case)

But it has been proven in 2017 that any possible equivalence between quantum circuits can be reached by modifying ZX-calculus circuits.

There are only 7 transformation rules that we need, and all others can be derived from those, universality.

So, we can apply those rules to do the transformation shown in Wikipedia:

and one of those rules finally tells us that that last graph means our desired state:because it is a Z spider with $m=3$ and $n=1$.

Bibliography:

This is an interesting initiative which has some similarities to Ciro Santilli's OurBigBook project.

The fatal flaw of the initiative in Ciro Santilli's opinion is the lack of user-generated content. We will never get there without UGC and algorithms, never.

Also as of 2021, it mostly useless business courses: learn.saylor.org unfortunately.

But it has several redeeming factors which Ciro Santilli aproves of:

Licensing appears to be a mixed mess between the dreaded CC BY-NC-SA and the good CC BY, e.g.:?

The founder Michael J. Saylor looks a bit crooked, Rich people who create charitable prizes are often crooked comes to mind. But maybe he's just weird.

This experiment seems to be really hard to do, and so there aren't many super clear demonstration videos with full experimental setup description out there unfortunately.

Wikipedia has a good summary at: en.wikipedia.org/wiki/Double-slit_experiment#Overview

For single-photon non-double-slit experiments see: single photon production and detection experiments. Those are basically a pre-requisite to this.

photon experiments:

electron experiments: single electron double slit experiment.

Non-elementary particle:

Experiments that involve sequencing bulk DNA found in a sample to determine what species are present, as opposed to sequencing just a single specific specimen. Examples of samples that are often used:

One related application which most people would not consider metagenomics, is that of finding circulating tumor DNA in blood to detect tumors.

Caused by slipped strand mispairing.

Bibliography:

The Dirac equation can be derived basically "directly" from the Representation theory of the Lorentz group for the spin half representation, this is shown for example at Physics from Symmetry by Jakob Schwichtenberg (2015) 6.3 "Dirac Equation".

The Diract equation is the spacetime symmetry part of the quantum electrodynamics Lagrangian, i.e. is describes how spin half particles behave without interactions. The full quantum electrodynamics Lagrangian can then be reached by adding the $U(1)$ internal symmetry.

As mentioned at spin comes naturally when adding relativity to quantum mechanics, this same method allows us to analogously derive the equations for other spin numbers.

Bibliography:

Spin is one of the defining properties of elementary particles, i.e. number that describes how an elementary particle behaves, much like electric charge and mass.

Possible values are half integer numbers: 0, 1/2, 1, 3/2, and so on.

The approach shown in this section: Section "Spin comes naturally when adding relativity to quantum mechanics" shows what the spin number actually means in general. As shown there, the spin number it is a direct consequence of having the laws of nature be Lorentz invariant. Different spin numbers are just different ways in which this can be achieved as per different Representation of the Lorentz group.

Video 1. "Quantum Mechanics 9a - Photon Spin and Schrodinger's Cat I by ViaScience (2013)" explains nicely how:

Has the property of visiting all descendants before the parent.

The dot product is a positive definite matrix, and so we see that those will have an important link to familiar geometry.

This is a family of notations related to the big O notation. A good mnemonic summary of all notations would be:

The perfect Middle Way between command-line interfaces and GUIs. A thing of great beauty.

ISO is the main culprit of this bullshit, some notable examples related to open source software:

The only low level thing that escaped this was OpenGL via Khronos, what heroes those people are.

How the hell are you supposed to develop an open source implementation of something that has a closed standard?

Not to mention open source test suites, that would be way too much to ask for, those always end up being made by some shady small companies that go bankrupt from time to time, see e.g. .

Some anecdotes.

Ciro Santilli never splits up functions unless there is more than one calling point. If you split early, the chances that the interface will be wrong are huge, and a much larger refactoring follows.

If you just want to separate variables, just use a scope e.g.:

int cross_block_var;

// First step.
{
    int myvar;
}

// Second step.
{
    int myvar;
}

Ciro has seen and had to deal with in his lifetime with two projects that had like 3 to 10 git separate Git repositories, all created and maintained by the same small group of developers of the same organization, even though one could not build without the other. Keeping everything in sync was Hell! Why not just have three directories inside a single repository with a single source of truth?

Another important case: Linux should have at least a C standard library, init system, and shell in-tree, like BSD Operating Systems, as mentioned at: Section "Linux".