Why haven't quantum computers factored 21 yet?

> I think a more plausible amount of optimization would produce a circuit with 500x the cost of the factoring-15 circuit

I don't get this part

If author already produced "115x", how can optimizations make it worse?

The 115x was obtained by doing a (less plausable) large amount of optimization...

I think the idea is the minimal implementation will be unstable and unreliable. I don’t know the details, but there’s much work and thought on quantum error correcting qubits - where you hook up N qubits in a clever way to function as one very stable qubit. Terms such as “decoherence time” make appearances. You can imagine this quickly expands into an awful lot of qubits.

The point was that the amount of optimization work that went into making the circuit for factoring 21 only ~100x larger than the one for factoring 15 is not feasible for larger numbers. So, the general rule should be that you need ~500x more gates for a similar increase in the number to be factored, not just ~100x.

The more plausible amount of optimization is less optimization. Or, more accurately, the benefits of optimization at large sizes is expected to be less beneficial than it was for the N=21 circuit.