Quantum is overrated, but see https://arxiv.org/pdf/1710.10377.pdf

In the event that quantum computing could be an imminent threat to Bitcoin, the protocol could be upgraded to use post-quantum algorithms.

Over here we already support big RSA keys

yes, I like some new innovations in this network.

I think the snowfield is one of the most interesting

https://youtu.be/edERx4x5eY0?t=126 YouTube Video: Hand soldering a WLCSP package

hand soldering mm/mn level chips, oof

@Clueless -- quantum computers attempt to find the 'ground state', or lowest energy state of electrons, which is analagous to finding the eigenvalues of the associated matrix of the Hamiltonian system (which is just an energy system) of the problem that is being encoded in a probabilistic manner by running hundreds of thousands of simultaneous calculations. The big idea here is that randomness is used quite a bit. In the adiabatic model, you start at a problem to which you already know the solution and slowly transform the Hamiltonian to the system that you are interested in. The issue is that during the transformation, you may approach a degeneracy, i.e. a Hamiltonian state where there is a collapsing of the eigenpairs onto each other. Now, from any undergrad linear algebra course, you should learn that a random matrix is simple, i.e. it has unique eigenpairs. We will also call a random matrix a generic matrix, because of the overlap with algebraic geometry and that the eigenpair problem can be cast as a system of polynomial equations and then the zero set or the solutions of these polynomial systems are known as algebraic varieties. Genericity is the terminology used in AG for randomness. Degeneracy is when you have a solution with a multiplicity higher than 1. In the case of a 'degenerate matrix', this means that there is a multiplicity solution corresponding to the eigenpair problem, i.e. there exists an eigenpair that has a higher multiplicity than 1. Now what's the deal with all this randomness? It turns out that if you transform from a starting Hamiltonian to the final Hamiltonian and do so using a random path, i.e. for every Hamiltonian that is not at the starting or end points, the associated matrix of the Hamiltonian matrix is random, then you are guaranteed to have a simple matrix, i.e. no degeneracy or collapsing of the eigenstates. This is is good because in the adiabatic model, it suffices to follow the ground state from the start Hamiltonian to the final Hamiltonian (meaning, we are following the lowest energy state, or the smallest eigenvalue for all the random matrices in between the initial and ending ones).

However, the real problem comes into play because we do not know how _close_ to a degeneracy we may get while on this random path. All we know is that no collapsing of the eigenstates occurs. If the ground state and the next excited state of the electrons are too close, when following the ground state, we may inadvertently jump to a higher state. This is why quantum computers have a probabilistic component, i.e. here is the answer with 85% assurance. That's just saying that the quantum computation computed the same state to be the ground state 85% of the time (and even, this may not be the correct answer ...). Interestingly, there are some basic facts that are learned in freshmen linear algebra courses that most of these quantum physicists either willingly ignore or have forgotten. One of them is that for a random matrix, the average distance between eigenvalues (after an appropriate normalization), is 1/n, where n is the same of the matrix. It turns out that if you have k qbits, the size of the associated matrix of the Hamiltonian system is 2^k x 2^k. This means that the average distance between any two eigenvalues is 1 / 2^k. In other words, as the number of qbits increases, the distance between the ground state and the next excited state decreases exponentially on average. This is actually quite bad since as the distance between two eigenstates decreases, it is more likely that a 'state jumping' will occur, while tracking the lowest energy state, which leads to a higher chance that the energy state that is found for the final Hamiltonian is not the ground state. tl; dr -- quantum physicists are not mathematicians. Whether or not they are willful in their ignorance (I know of no papers on quantum computation that address these issues) or are aware but don't want to kill the golden goose, i.e. millions in nation-state funding to continue to do research, is a question I don't want to ask.

`encoded in a probabilistic manner by running hundreds of thousands of simultaneous calculations`

in lock picking, sometimes you just jam/vibrate the pins up/down a lot and apply pressure until the tumbler turns and things just "align"

Ya -- basically quantum physicists treat the whole adiabatic process as a black box. No idea how it works.

Which is more or less to say that they don't know basic linear algebra.

:smile:

I don't even know basic linear algebra. :(

no BLAS for you!