Since I retired, I’ve been learning and exploring the mathematics and details of quantum mechanics. There is a point with quantum theory where language and intuition fail, and only the math expresses our understanding. The irony of quantum theory is that no one understands what the math means (but it works really well).
Recently I’ve felt comfortable enough with the math to start exploring a more challenging aspect of the mechanics: quantum computing. As with quantum anything, part of the challenge involves “impossible” ideas.
Like the square root of NOT.
To be clear, that’s not some poetic phrasing, the NOT in question is the logical gate that turns its single input into what it is NOT. (Concretely, it turns a 0 to a 1 and vice versa.) And we do mean the square root (√) math operation, too.
So how does one take the square root of a logical operation?
Part of the intuition involves the same line of thought as taking the square root of minus one. Whatever weird magic the square root of minus one might be or involve, we can count on multiplying it by itself (squaring it) to give us good old -1. No weirdness there.
Therefore, whatever weird magic the square root of NOT is, we do know that:
√NOT × √NOT = NOT
So two √NOT operations in a row give us a normal NOT we can deal with.
In a quantum computer, a single √NOT operation (or gate) results in a superposition of the qubit.
Another quantum gate we can take the square root of is SWAP, which has two inputs and two outputs. Obviously the SWAP operation does what its name implies. As with the NOT, we have:
√SWAP × √SWAP = SWAP
So two in succession result in a concrete swap of inputs. A single gate results in an entanglement of the two inputs.
Thus, in quantum computing, superposition and entanglement come, at least in part, from these gate operations.
All of which is to introduce this 2018 presentation from The Royal Institute (which does some outstanding lectures; I highly recommend the channel to all science geeks):
There was some synchronicity for me here in that the two speakers are chaired by Philip Ball, whose book, Beyond Weird: Why Everything You Thought You Knew About Quantum Physics Is Different, I bought and have started reading.
I didn’t know Ball was in this video! It begins with a speech from the Netherlands Ambassador, which I skipped through and, thus, missed the introduction of the male speaker who came next.
The video’s description first has a long paragraph about Artur Ekert, who “works on information processing in quantum-mechanical systems.” He was the first actual lecturer. The two paragraphs after Ekert’s name Harry Buhrman, the second speaker, a C.S. PhD and executive director or QuSoft, the Dutch research center for quantum software.
I was paying attention to the video so didn’t read all the way down to the last paragraph. I just assumed the guy I was watching must be Ekert.
The the more he talked, the more I thought, “Gee, he sure looks like Philip Ball.” (I’d seen him in an RI video not that long ago.) The speaker seemed to be more framing the lecture than giving the lecture, so I went back to the video description and read more carefully.
The last paragraph, just one sentence, starts off, “The event is chaired by award-winning science writer Philip Ball, whose latest book…”
Ah, no wonder that guy looks like him.
If you want to skip the introductory stuff, Ball starts speaking at 4:54, which is brief and I’d say worth watching. Ekert starts at 11:45, and Buhrman starts at 59:50. The whole thing is about 90 minutes. There doesn’t appear to be a Q&A.
I recommend this to anyone with a interest in quantum computing. It’s a pretty good introduction and was exactly the sort of thing I was looking for.
Plus, it introduced me to √NOT. I love learning a new concept!
Quantum computing involves the double-whammy of the math and understanding of quantum theory plus that of computer science.
I’ve dabbled in the latter since I was in college, and I’ve always been interested in basic physics. However both domains are the kind of thing where people can dedicate entire careers to studying in deep detail just one aspect. No one can learn it all nor even most of it, not in deep detail; to get to those depths one must specialize.
Me, I’m just getting to the point where I can take off the water-wings, strap on a snorkel, and do some free diving in the more accessible shallows. I think I’m still a ways away from anything that doesn’t involve holding my breath (so to speak).
I will say that I’m really enjoying Ball’s book, Beyond Weird. I’ll talk more about it when I’m done.
In the meantime, here’s the lecture Ball gave at the RI about the book.
It really is a great YouTube channel; lots of good science!
Stay superposed, my friends! Go forth and spread beauty and light.