Why haven't quantum computers factored 21 yet?

Because they haven't actually factored any other smaller number yet.

If your program has a compilation process that requires you to already know the answer to the problem you're trying to solve, then what they did was not factorization, but "print 3" with extra steps.

The article, if examined by a non-specialist like me, seems to contain an answer to this concern at the end:

> There are papers that claim to have factored 21 with a quantum computer. For example, here’s one from 2021 [1]. But, as far as I know, all such experiments are guilty of using optimizations that imply the code generating the circuit had access to information equivalent to knowing the factors.

[1] https://arxiv.org/abs/2103.13855

The article claims that 15 was done without precompilation (in the 2015 experiment but not the 2001 experiment), but only because 15 is a very unique number (after decomposition, only the last multiplication has to be performed because all the previous multiplications involve multiplying by 1).

That said, we are REALLY far off from having a useful quantum computer. Jensen was probably being conservative when he said 20-30 years away, hence the immediate pressure he received form the investor community to reverse his statement followed by the flood of ridiculous press releases from the usual companies claiming to be 2-3 years away.

deriving arithmetic from lambda calculus is not "arithmetic with extra steps"... not sure what I mean by that, but seems like that implies there is arithmetic without extra steps, then you just print the answer