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:

One of the four following states:

When unqualified as in "the Bell state", it generally just means $|{\Phi }^{+}⟩$.

The Bell states are entangled and non-separable. Intuitively, we can see that when we measure that state, the values of the first and second bit are strictly correlated. This is the hallmark of quantum computation: making up states where qubits are highly correlated to match a specific algorithmic answer, and opposed to uniformly random noise. For example, the Bell state circuit is a common hello world, e.g. it is used in the official Qiskit hello world.

One of the causes Ciro Santilli care the most about: motivation.

Ciro Santilli's view of the ideal teaching method: how to teach.

A list of complaints against education: Section "Education is broken".

How to improve education? Simple:

Whenever Ciro Santilli walks in front of a school and sees the tall gates it makes him sad. Maybe 8 year olds need gates. But do we need to protect 15 year olds like that? Students should be going out to see the world, both good and evil not hiding from it! We should instead be guiding them to the world. But instead, we are locking them up in brainwashing centers.

Video "The Purpose of Education by Noam Chomsky (2012)" puts it well, education can be either be:He has spoken about that infinitely, e.g. from when he was thin: www.youtube.com/watch?v=JVqMAlgAnlo

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Similar to quantum supremacy, but add the goal that the computation must be useful, i.e. make money or solve some open mathematical problem, Ciro Santilli's wife was quite excited about the possibility of finding some counter examples in number theory with quantum computers.

Metric created by IonQ.

See also: e-learning website.

This is something worth investigating!

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If school weren't bullshit, 99% of students would be in gifted education for what they truly love and are good at.

What is sad about many programs is that they are exclusivist and non scalable, selecting people some how and non scalably educating them. We need a more "here's some projects let's do them whoever can" approach to things, maybe like Google Summer of Code.

Related programs: