Some new machine is built but the largest number its register's can hold is 1,000,000. So we can't add two numbers, or multiply two numbers if the result is greater than 1,000,000. Along comes some code that can use linked lists to create bigger numbers. One link in the list can hold a number's large lower portion "900,000", the next link can hold the number's upper value of "1,000", put the two links together to get: "1,000,900,000". ... and the algorithms do the rest of adding, multiplying, manipulating those larger numbers even though the hardware can only handle numbers no greater than 1,000,000. ... And so, we've made code that has surpassed the hardware's capabilities.
Thanks again for your input you definitely have a little bit more knowledge than myself when it comes to algorithms and how they are coming along. I only know the very basic parts of that whole sequence of implementing and testing. I know and understand how quantum resistant algorithms work and that they already exist. However never knew how suitable they were to the Bitcoin project and its "guidelines" that its followed over the years. I've always assumed that there's no rush for implementing an algorithm which could potentially affect the stabilization of Bitcoin so early on when there's no threat at the moment. Especially since when the time comes we might need to change again because as you say this field is a ever evolving system which does bring more discoveries every day. I would actually go forward and say computers in general are the leading industry in new discoveries ever since the basic computer was invented.
The example I quoted I think is the best explanation I've seen when coming to discuss quantum computers and the current limitations within the field. I've always considered that you need a computer to write the code a computer that is capable of writing the code and then the code side of things will evolve beyond the capabilities of the computer. However the linking together is a excellent way of demonstrating how this is actually achieved.
The reasons you have listed here are the exact reasons why I'm very interested in the current price it takes to operate a quantum computer specifically (because its now been mentioned) the D-wave quantum computer which to run requires being housed in a room at an incredible -273° C. The interesting part of this is its not a computer limitation or anything like that but a environment one. No matter how efficient we make things it doesn't look like we'll be able to cheaply make a room at -273° C. Yes with better technology we will probably see quantum computers not having to work so hard but as physics goes the amount of energy that goes into things you can expect less out of it. Which in my eyes I can't see us ever being able to cheaply operate a rooms temperature at such low levels for the duration of the time the quantum computer needs to operate. We could in the future have an unlimited qubit quantum computer able to crack things in seconds and therefore the running time wouldn't be long which in effect would reduce the cost of this however what I'm trying to get at is this will be an extremely long way off and quantum computers on mass will likely not be a problem for many many years.
The reason why I'm concentrating on the operating costs and the logistics of running something capable of breaking algorithms is that even if a quantum computer was theoretically released tomorrow with the required amount of qubits to breach algorithms it would still only limited to a few individuals which might not have any malicious intent meaning it might not even be a threat anyway. Regardless whether this is true or not obviously we would need to be prepared for the worst case scenario which I do believe judging on others comments on this thread we'll be ready with the technology already available at our disposal.