Comment by wolverine876 | Hacker News Reader

Comment by wolverine876 | Hacker News Reader

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That is very well-written, as someone else pointed out, though this common explanation for laypeople needs work (I'm not blaming Signal's blogger, who wrote it more carefully than most):

"Instead of bits as in a classical computer, quantum computers operate on qubits. Rather than 0 or 1, qubits can exist in a superposition of states, in some sense allowing them to be both values at once."

'Instead of beads as in a classical abacus, our Quabacus operates on Quabeads! Rather than positions 0 or 1, quabeads can be in both positions at once!'

Beads that are simultaneously in both positions sounds like a f$@!#g annoying glitch and not a feature - how does that help anyone record or calculate numbers? ('Would someone take a look a this broken Quabacus-abacus and resolve these g#$%!m glitching quabeads?!!!') It mocks the non-technical reader, who assumes they must have been given enough information to understand why it's faster and possibly how it works, but can't figure it out.

They have not been given enough. Does anyone who perhaps understands it better than I do want to take a stab at a new commonplace explanation, one that connects the dots between quantum superposition and performance (for certain calculations)?

You are correct. That is a horrible explanation. And incomplete.

* The state of a qubit has two basis states. Arbitrary states are linear combinations (=superposition) of these basis states. Importantly, the coefficients in the linear combination can be positive or negative.

* The state of N qubits has 2^N basis states. poly(N) gate can put the state of the N qubits in which each of the 2^N basis states has a non-zero coefficient.

* In quantum algorithms, we play with the coefficients. Basically, certain problems (like factoring) have structure such that you can change the coefficients so that the ones corresponding to the correct answer have magnitude approximately 1, while other coefficients have magnitude 0. This is enabled by the fact that coefficients are positive and negative, and so by mixing them, you can cancel some out.

* When you measure the qubits, the random answer you get is proportional to the coefficients squared. Hence, with high probability you get the right answer.

Where does the speed up come from? When you put the state of N qubits in the linear combination of 2^N basis states, and run it through the problem, that is akin to computing all answers in parallel. Like for factoring, checking all possible divisors to see which ones work. But to extract the answer out in the way described above, you have to do additional processing. This only works for some problems, with the right structure.

Thanks.

> In quantum algorithms, we play with the coefficients.

Is it accurate to say, more simply (simplicity being a high priority here), that 'we play with the probabilities' of collapse to one basis state or to the other - thus skipping the need to explain linear combinations or coefficients?

Well, all the playing happens with the positive/negative coefficients. Without explaining that you can cancel them out with each other, it will not be clear how all-positive probabilities collapse to some basis states.

In fact, classical stochastic computational models have exactly this deficiency. You can't pump up probabilities of some unknown states. They can only tend towards a uniform mixture.

Everything is in the minus sign.

There isn't really a great way of explaining quantum behavior using everyday (classical) terms. Any analogy you come up with will be deeply flawed yet unsatisfactory opaque to the reader.

The only way is to gear up on math to the level where you can if not reason within the theory then to at least make sense of its presented conclusions.

You're frustrated because it's a bullshit answer based on a lack of understanding of what a superposition of states represents and what quantum computing is calculating. Qbit superpositions represent probability distributions between 1 and 0. And quantum computers calculate probable ranges of correct results of certain types of problems. They can produce these ranges of probable correct results using much less memory and time then it would take a classical computer to calculate similar results. We're talking exponential improvement of using 1 more qbit compared to 1 more classical bit. For example, in 2019, Google used a 53 qbit quantum computer to complete a task in 200 seconds that Google claimed would take 10,000 years to finish with the best known classical computer at the time. (Note that IBM claims that it would only take 2.5 days on their classical computer, but you can see the scale of improvement is huge either way)

Thank you.

The shortest possible answer is that qubit states are modeled as two-dimensional vectors on the complex unit sphere. We arbitrarily designate two orthonormal vectors on this sphere as corresponding to classical states 0 and 1. If the qubit vector isn't in the 0 or 1 state, it's in some linear combination of them. This is called superposition. Since most people don't know what linear combination means, superposition is explained as "sort of both at the same time". Upon measurement the qubits are collapsed to 0 or 1 with some probability proportional to how close they are to the 0 and 1 states. The precise probabilities are given by something called the Born rule. I gave a longer talk aimed at computer scientists if you're interested beyond this explanation: https://youtu.be/F_Riqjdh2oM

Thanks

I don't really understand your objection, that description seems like about as well as you can do when trying to summarize quantum mechanics in one sentence.

It summarizes quantum mechanics, but not how it helps to store numbers and perform certain kinds of calculations.

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