Christmas with Quantum Mechanics

Christmas is wonderful time, although not without challenges. Particular challenge for me is to keep mind fresh and not sleep all the time. I like the atmospehere of going to saint masses and eating good food (with couple of drinks) and stuff but as always I felt a little bit lazy.

So to exercise my brain a little I found out this course in quantum computation. It was great fun in short. I was constantly on the edge of my cognitive possiblities, but the material was made crystal clear. I developed a particular method to finish one module at the time in the afternoon and rehearse reading part during mornings. I had a little bit of crysis on first day of Christmas but managed to carry on half consciously.

And finally on the return home I passed the test with 75% score.

Foundations are key

I was surprised that the boring linear algebra stuff I studied on freshman year on univesity actually makes a big difference. In fact 3/5 of the material is just plain algebra. I was also shocked how much I remebered. I think that because quantum setting is relatively new people try to comprehend it by analogy to classical settings. There is a huge overlap between mathematical model of classical and quantum mechanics.

The quantum operations are basically multiplication of state vectors by operation matrices (with particular properties). There is also place for for Bayes Theorem when measuring the quantum state.

I liked the matrial for one particular reason: the intuition goes first. The math apparatus are just a means to succintly and without confusion describe simple concepts. The course showed a huge effort to develop mathematical feeling when describing classical and quantum state.

Each module builds on the previous so if you suck at one particular part, you won't be able to fully understand the next parts. The most difficult part for me was to imagine operations on matrices and state vectors. Also around the module 2-3 the atmosphere gets dense and you have to be in shape to ingest the material.

Humble beginnings

Recently Google unveiled their quantum chip Willow with 105 qbits. Well I don't even imagine somebody crossing the barrier of 1000 qubits. I mean the math is so advanced that for circuits with 2 qbits is hard to understand enough.

But I guess with time the same will happen as with classical chips. Somebody will develop apt abstractions on top of this advanced math so that programming will be possible on higher level. I wonder what that language will look like. Keyword entangle(a,b)? Possibly. Or maybe p_measure(pi, X, Y)? Anyways today state of art is just like classical chips 60 years ago.

But still improvement

Over the time of course I had a possiblity to learn what makes quantum computation special. It is this entanglement property that has several astonishing uses.

First the quantum teleportation. It's not like teleporting the matter as in television, but rather it is a protocol. So if you have 2 qbits in entangled state you can instantly (faster than light) switch on qbit and the second one sets different. But after that - poof the first qbit is gone as well as share e-bit. And here is the disappointing part - even if the information does really teleport, then you still have to send the classical bit by classical means (slower than speed of light) or you won't be able to read it.

Second there is superdense coding that allows to exchange one qbit with 2 classical bits of information, but on the condidtion that you have e-bit (entangled two qbits). And this operation uses e-bit without coming back.

And finally when you have entangled qbits you can beat upper limits for classical strategies for cooperative games like CHSH game. To have an entangled qbit is like having agreed on particular strategy between players without communication. Interesting...

So much to discover...

There are more courses from IBM on quantum so maybe when I have time I will proceed with next modules. But for now a brief pause.

This is fascinating branch of science and who knows what will come next. From this time on I will follow the news more closely.

Thanks.