The Mathematics of Quantum Computers | Infinite Series

The videos by Microsoft Research[1] and PBS[2] are perhaps the most accessible and yet accurate explanations of quantum computing I have found so far. [1] link [2] ▶ this video

It's not that they can execute a computation faster in the traditional sense. It is that you can exploit the quantum behaviour in some types of computation (e.g. factoring primes) to make the answer more probable, and thus more likely to be "observed", when you read the state of the quantum computer and thus make it easy to locate the correct answer compared to traditional algorithms. PBS Infinite Series has several videos on quantum computing and Shor's algorithm: 1. ▶ this video "The Mathematics of Quantum Computers" 2. link "How to Break Cryptography" 3. link "Hacking at Quantum Speed with Shor's Algorthm"

You should check out these videos, one of them might give you an understanding! - link | Quantum Computers Explained - ▶ this video | The Mathematics of Quantum Computers - link | Hacking at Quantum Speed with Shor's Algorithm - link | A series by the author of the standard textbook These are videos I particularly like!

Issac Arthur has his stuff together. His videos are for the most part well researched and contain a lot of interesting hard sci-fi ideas. The only time I've seen him fall down is his video about quantum computing, but to be fair, a lot of people get caught by the same mistake. It's not the case that a quantum computer is trying out all of the bit-strings that are possible answers in a kind of quantum-superposed parallel computing. That's not exactly what is happening. One of the key insights: Qubits store complex numbers! ▶ this video

A note for the savvy: A quantum computer is not a magic bit-string that mysteriously flips to the correct answer. A n-qubit quantum computer is not like 2^n phantom computers running at the same time in some quantum superposition phantom-zone. That's the popular misconception, but it's effectively ignorant techno-woo. Here's what really happens. If you have a string of n-qubits, when you measure them, they might end up randomly in of of the 2^n possible configurations. However, if you apply some operations to your string of n-qubits using quantum gates, you can usefully bias their wave equations, such that the probabilities of certain configurations are much more likely to appear. (You can't have too many of these operations, however, as that runs the risk of decoherence .) Hopefully, you can do this in such a way, that the biased configurations are the answer to a problem you want to solve. So then, if you have a quantum computer in such a setup, you can run it a bunch of times, and if everything goes well after enough iterations, you will be able to notice a bias towards certain configurations of the string of bits. If you can do this often enough to get statistical significance, then you can be pretty confident you've found your answers. ▶ this video link EDIT: I rather like Issac Arthur, but unfortunately, his Quantum Computing episode is an example of exactly this kind of popular misconception. I've called him out on it in comments. link EDIT: I can't find my comment anym