
Quantum Computing for the Curious - roi
https://quantum.country/qcvc/
======
abdullahkhalids
I have a PhD in quantum information/computing and I knew everything in the
essay before reading it, but the additional understanding I got from doing the
given spaced repetition flashcards significantly improved my understanding of
the material. Everyone who is reading this essay, should sign up and give
spaced repetition a try.

------
extr
As someone with more of a math than a physics background I really enjoyed
this, but I guess I'm surprised by how, for lack of a better word, basic, it
seemed? Maybe that serves as a compliment to the author, in the past I have
been snowed by all these vocab words when it turns out it's mostly just linear
algebra. A lot of what I enjoyed here were the sidebars explaining that
concept X was really just rebranded Y, detail Z is not really important for
intuition, etc...

A random question along those lines: why represent states as 2d complex
vectors instead of quarterions? Aren't they the same thing? As soon as I read
that I spent the rest of the article wondering if everything it would make
even more sense cast that way.

~~~
ahelwer
This is the great secret of quantum computing! People assume it must be
difficult because their exposure to quantum mechanics has been a hundred
incomprehensible pop science articles written by people who have no idea what
they're talking about. In fact quantum computing requires only extremely basic
knowledge of linear algebra.

~~~
chilukrn
ok, extremely basic is a bit oversimplifying it. When you start reading
quantum algorithms, you will inevitably come across Shor's factorization
algorithm, which requires (quantum) phase estimation:
[https://en.wikipedia.org/wiki/Quantum_phase_estimation_algor...](https://en.wikipedia.org/wiki/Quantum_phase_estimation_algorithm)
which requires quantum Fourier transform and some good deal of math. This is
when you don't go into the physical implementations. If you want to look at
that aspect, things may become a bit more complex.

This is not to discourage anyone, but underselling it as requiring elementary
linear algebra is not very helpful (the pop-sci articles have already been
overselling it as "magical"/"mind-blowing" etc.).

~~~
ahelwer
There are algorithms which involve advanced mathematics on classical
computers, too. You don't have to understand them to understand how classical
computers work. I've never bothered to learn the general number field sieve,
and similarly I've never bothered to learn Shor's.

I say if you understand gates as unitary matrix multiplication, representing
multiple qbits with the tensor product, entanglement, and projective
measurement, you basically understand quantum computing. Throw in an algorithm
or two to convince yourself of the benefits.

~~~
chilukrn
True, but: 1\. Any serious quantum computing course/book will have Shor's
algorithm in the first few chapters (in fact there are not a lot of quantum
algorithms which have clear advantage over classical ones). One can teach
quite a bit of useful classical algos (sort, binary search, tree/graph-based)
without going into mathematics like FFT or jpeg coding.

2\. Again valid, but IMHO measurements (and PoVMs) can lead to deep rabbit
holes, and I found myself digging in much deeper.

Probably I should read easier expositions to see how effectively they teach.
(I come from a EE+physics background, so I do gravitate to math-heavy rigorous
explanations)

------
jen729w
Hobby physics nerd here. This thing is mental. I clicked it, saw how long it
was, and abandoned. Comments here took me back in and it’s going to turn out
to be a real gift.

------
kgwgk
Note that this is written by one of the authors of
[https://en.m.wikipedia.org/wiki/Quantum_Computation_and_Quan...](https://en.m.wikipedia.org/wiki/Quantum_Computation_and_Quantum_Information)

------
mikro
This is absolutely fantastic. Now I'm wondering if there are resources for
doing spaced-repetition for other computer science topics. Has anyone seen
anything like this?

------
nonsapreiche
Good time for a
[https://en.wikipedia.org/wiki/Spaced_repetition](https://en.wikipedia.org/wiki/Spaced_repetition)
that remember me of
[https://metacpan.org/pod/Quantum::Entanglement](https://metacpan.org/pod/Quantum::Entanglement)
(good old perl ~20 years old :)

------
Yajirobe
So why does the Hadamard+CNOT acting on two qubits give an entangled state,
but a Hadamard acting on a single qubit does not give an entangled state?

~~~
nonsapreiche
I think you need 2 qbit to have them entangled

~~~
onorton
Exactly. The point of quantum entanglement is that the state of two (or more)
qubits cannot be separated. To entangle a single qubit is meaningless.

For two qubits, the simplest entangled states are the Bell States[0]
(generated from a CNOT and Hadamard gate). The article gives an example of one
of them.

[0]
[https://en.wikipedia.org/wiki/Bell_state](https://en.wikipedia.org/wiki/Bell_state)

~~~
Yajirobe
What's the difference between an entangled state and a mixed state?

~~~
onorton
Knowledge is a bit rusty (took a module in Uni) but I'll try to answer.

A mixed state is that which is a linear combination of pure states e.g. a|0>
\+ b|1>

What determines an entangled state is that qubit values will correlate exactly
with each other. |00> \+ |11> would be an example of an entangled state as
measuring one qubit determines the value of the other with certainty. If you
measure |0> for the first qubit, the second will definitely be |0> and vice
versa.

They are also not mutually exclusive as mixed entangled states exist.

~~~
Yajirobe
> A mixed state is that which is a linear combination of pure states e.g. a|0>
> \+ b|1>

Here
[https://en.wikipedia.org/wiki/Qubit#Mixed_state](https://en.wikipedia.org/wiki/Qubit#Mixed_state)
it says that 'Mixed states can be represented by points inside the Bloch
sphere'. However, points ON the sphere correspond to linear combinations of
the pure states. How to reconcile this?

~~~
onorton
Like I said, my knowledge is rusty.

I've gotten pure states mixed up with |0>, |1>

I believe what it's saying is that with a mixed state |a|^2 + |b|^2 does not
need to equal 1.

So pure states are a|0> \+ b|1> where |a|^2 + |b|^2 = 1

------
gazarullz
Very interesting article, I would love to have it in a portable/printable
format (e.g. .pdf) can anyone help me out ?

------
cloogshicer
This is absolutely wonderful!

------
tehsauce
Very nice article!

------
simonsays2
Everyone should read this. It is an amazing effort in education. Almost too
good. I wonder what techniques they used to compose it. Seem like it might
have been machine assisted?

~~~
andymatuschak
One of the authors here. While the study schedule is regulated by algorithm,
the questions themselves were hand written. We have found it’s quite difficult
to write good questions, needs lots of revision and thought. Glad you enjoyed!

