We wrote a book intended to give an intuition for how quantum algorithms work for an audience who do not necessarily want to dive into the detailed linear algebra:
I really like a cloud chamber that I can put together in the pub whilst potentially drunk. A pint glass and some dry ice does the job (dry ice being obtainable from a fire extinguisher - not that I'd recommend you grab one off the pub wall without replacing it refilled).
Since a lot of general intros to QM are being suggested (rather than technical/historical texts), then here's another recommendation which is not technical nor historical, but comes as close as you can get to a proper understanding of QM without mathematical detail:
Not to be too contrary, but I disagree with this sentiment. First let me say I'm assuming that the OP wants to involve a historical narrative to gain a deeper conceptual understanding of quantum mechanics.
Under that assumption, the interesting thing about QM is that there is very little inherent conceptual justification for the technical descriptions we have of quantum systems other than that 'they work'. Or more precisely, understanding why QM systems are mathematically described in the way they are is still an active area of research.
Therefore, often the closest you can come to a deeper understanding is by tracing how someone stumbled into, or was forced into, using a particular mathematical approach. At least then you are left at the same precipice of knowledge over which experts have been dangling for nearly 100 years now.
I hope that one day we can give deeper explanations for why we have Hilbert spaces and what-not, but until then, learning the history is the closest you can get to understanding why things ended up the way they are on a technical level. And assuming a decent mathematical background, there's no reason you can't also learn the technical detail itself for the first time right along with that historical narrative.
> there is very little inherent conceptual justification for the technical descriptions we have of quantum systems other than that 'they work'.
That's true of all scientific theories when you reach their roots. That does not change the fact that QM pedagogy is generally a disaster because it follows the historical development and emphasizes the single-particle case and de-emphasizes entanglement and decoherence, which makes the measurement process appear deeply mysterious and incomprehensible when in fact it is quite simple and straightforward. It's still very weird and unintuitive, but it is far from incomprehensible, as Feynman famously claimed. It is simply not true that "no one understands quantum mechanics" and it hasn't been true for a very long time.
There are some translation/copy-writing issues but don't let that put you off. It has a solid coverage of quantization of Hamiltonian mechanics in both matrix mechanics and wave mechanics, and then the unification of the two - all following the historical narrative.
The autopricers are a pox on the market. It's even worse when you contact the seller, making them a reasonable offer, and they reply that their pricing algorithm knows better.
I know. There was an amusing article a while back showing autopricers from two merchants fighting with each other. I think one of the lessons was that you can pretend to have your own copy for sale, then keep lowering the price. The bot will follow you all the way down to almost zero—then you buy the book.
I don't understand. The proposal is to use no classic channel?
The idea is to entangle all the photons of a star? All the photons in a narrow band?
From another star you can not magically distinguish the entangled photons. You can only make some measurements, and compare it with the measurements of the photons are entangled with, and get some correlations.
For example, you can create a pair of entangled photons in A, send one of them to B. In B the other person/alien can "transfer" the entanglement to a thermal photon from B and send it to A. Now in A you can measure the polarization of the photon you saved and the photon you received from B. Depending of how the other person/alien "transferred" the entanglement, you will get the same or opposite results when you measure the polarizations. So B can use "same" or "opposite" to transmit a bit of information to you.
The difficult part is to pick the correct photon in with a star making a gazillion of photons in the background.
You can create a gazillion of pairs of photons in A and send one half of each pair to B and get later the photon form B. But you must match exactly each received photon with the correct photon of the other half of the pair that you stored. Matching the wrong photon will produce only random noise.
IIUC the idea is that B will not entangle one photon but a gazillion of photons. It is possible to create in B an entangled state where the photon stored in A has the same or the opposite polarization of a gazillion of photons in B and send them. So now it would be easier to pick one of them.
The problem is that someone E in the middle can also look at the photons. Without the photon stored in A, the other person E can only measure random noise, it's impossible to know if B was transmitting "same" or "opposite". The problem is that the intermediate person E will see that in the polarizer all the photons pass or not pass together, never 10% of them pass and the other 90% don't pass.
The intermediate person E will see that half of the time all the photons pass and half of the time all the photons don't pass. This is a clear sign that the photons are entangled. So the secrecy of the quantum communication will be broken, in spite the content will never be discovered.
* Matching the wrong photon will produce only random noise.
Not really related to what you have commented, but I wanted to mention it:
Back in Earth, our communication protocols usually have lots of redundancy. Whatever redundancy you can get into the channel, it usually gets inserted at whatever cost it takes - slowing down things a bit here and there - but ensuring a proper message gets to arrive to the other side (at the receiver).
I'm far (FAR) away from trying to sketch here an interstellar quantum comms protocol, but I find certain that if there aliens out there deploying quantum networks, they almost certainly will have redundancy at the level required (to overcome entropy), to get proper messaging in the used channel.
I agree, but for comparison, let's look at the laser than the NASA uses to measure the distance to the Moon. It has a pulse of 75mJ in 10ps, i.e. 7,000,000 Watts for a very short time, and they get back only a few photons. Alpha Centauri is 100,000,000 times more far away, so the signal is 1e16 times dimmer. You need a bigger laser or a lot of time just to be lucky to get a photon there.
Also, in comparison, the Sun has 3e26 Watts. That's distributed in the full spectrum, and the laser has a very narrow bandwidth. I can't find the exact number now, but from https://en.wikipedia.org/wiki/Laser_linewidth my guess is that it's 1/100000 of the energy is in the same band of the laser, that is 3e20Watts. Let's remove a few zeros to be sure, like 6 zeros, so my guess is something like 3e14Watts.
Comparing the guess of 3e14Watts of the Sun to the 7e6Watts of the laser. So it's not only difficult to see even a photon, there is a lot of noise in the background. I've measured signals like 1/100 of the noise level using a lock-in amplifier, and I think 1/1000 is possible, but 1/100.000.000 looks very difficult.
And now we must consider the quantum part, that is the interesting part of the post. If you generate a lot of pairs of entangled photons, after the trip you must match the photon that traveled with the photon you keep at home.
If you pick the right photon to compare, you theoretically get 100% of agreement, but my guess is that in a lab you will get 90% or less. After an interstellar trip, I'd be happy to get a 1% of correlation, and use a lot of redundancy and error correcting codes to fix it.
The problem is if you pick the wrong photon. You get perfect random noise. Absolutely no information. You can't fix it with redundancy. And with interstellar distances, you must generate a really huge number of photons just to be able to detect a photon in the other side of the communication.
Building a good-enough optical table relatively cheaply isn't too hard. Use cinder blocks for legs and then alternately layer plywood and carpet, with a layer of spaced out wheelbarrow inner-tubes midway through. You can even add a final layer of sheet steel if you're using magnetically mounted optical components. You can test the stability by reflecting a laser-pen off a dish of water and watching the reflection on a piece of paper/wall. Most important is to be away from traffic etc...
We wrote our O'Reilly book, "Programming Quantum Computers", precisely to fit your use case. It assumes no advanced mathematics, doesn't shy away from really delving into how algorithms work, and also has an online simulator to let you experiment with actual code. I am of course biased, but I would say that it's the resource out there requiring the least mathematics needed to get some practical knowledge and a chance to experiment in code:
Shameless plug dealt with, the text I'd next point you to for being grounded more in the Real world rather than Hilbert space is Mermin's. Modulo his insistence on using the term QBit rather than qubit, it's a great pedagogical work by someone with a very deep understanding of quantum mechanics. It's also in hardcover, which also helps lend it more weight:
As others have recommended, anything by Scott Aaronson is gold. Computational complexity is his passion, and although I think his work is very thorough and accessible, I would suggest it's a little less hands-on. However for very, very deep insights there's nowhere better to go. Alongside his book, Aaronson's blog at https://www.scottaaronson.com/blog/ is also revered by both QC enthusiasts and professionals alike and a great place to follow debate on the latest developments in the field.
The most mathematically demanding text (or most thorough, depending on how you look at it) I'd consider is Nielsen and Chuang (a.k.a "Mike 'n' Ike", a.k.a "The bible"). It's slightly out of date in some more recent concepts regarding the implementation of quantum computing (not wrong, just a tad incomplete), but is still solid and indispensable for the core concepts and insights behind quantum computing.
If you're interested in the physical implementation of a quantum computer (i.e. what does it _look_ like inside), then Mike 'n' Ike is the only one that will come close to satisfying you. The real world is so damn messy, and quantum hardware is no exception. QC tech moves fast and the money is still on the table as to just what that tech might look like inside the million qubit quantum computer of the future. Mike 'n' Ike does discuss some specific types of qubits, but I'm not aware of a book providing a truly comprehensive and up to date description of today's most promising approaches.
To second rjurney’s comment, I’ve also recently had the pleasure of working with Mike Loukides, and his feedback has always been hugely insightful and valuable.
https://www.oreilly.com/library/view/programming-quantum-com...