Quantum Computing: Explaining the Number System & Its Power

[Shano]

I have seen other posts here on PF and I have done some internet research. In what I have found so far it is hard to get a plain English answer around the number system that is used in quantum computing. A lot of references are made to binary with a superposition.

Is there a way to simple way to explain the number system in quantum computing?

Also is the number system of quantum computing what makes this type of computing so much more powerful than traditional computing?

 

[FactChecker]

I am not sure that you want to call it a different "number system". (Although there certainly is a lot of advanced math involved). The huge advantage of the quantum computer is that it can consider many possible solutions at the same time and it can narrow down to a solution state in one step. Suppose you have a problem where the correct solution answer is 5 and a traditional computer must test the numbers 1, 2, ...,10 to find the solution. The traditional computer could step through at least 5 states (checking 1, checking 2, ...) to discover that 5 is the solution (state="found solution 5"). Now suppose you have a quantum computer that can consider all possibilities 1, 2, 3, 4, 5, 6, ...,10 at the same time (state="considering 1,..,10) . Also suppose that you can "program" it to narrow down to the solution 5 in one step (state="found solution 5"). That would be powerful.
A quantum computer with 100 qbits might be able to simultaneously consider 2¹⁰⁰=10²⁹ possible solutions in one step. Now consider how powerful it would be if it were possible to build one with hundreds of thousands of qbits.

 

[Shano]

Ok, that makes a whole lot more sense than the information that I have found so far. So based on the example you have given where the solution is 5, would it be far to say that in a traditional computer you may iterate through a loop to find the answer of 5 whereas a quantum computer would not need to loop at all, it would have found 5 at the first iteration. Or I guess you could say it completed all iterations at the same time in parallel.

Also realize I am most likely really over simplifying this, however I am only looking for the general idea as I do not have the maths skills to understand the technicalities involved. (apologies for my ignorance)

 

[FactChecker]

Ok, that makes a whole lot more sense than the information that I have found so far. So based on the example you have given where the solution is 5, would it be far to say that in a traditional computer you may iterate through a loop to find the answer of 5 whereas a quantum computer would not need to loop at all, it would have found 5 at the first iteration. Or I guess you could say it completed all iterations at the same time in parallel.

Yes. That is the key advantage that quantum computers have. They also have some great disadvantages that people are working on now. One is that they are very sensitive to heat or energy disturbances and must run at extremely low temperatures. Another is that creating "programs" to make them solve the desired problem is very difficult. Some approaches only get "near" the solution with a certain probability. But the potential of quantum computers is so great that I am confident that the problems will be solved.

PS. Being able to consider several possible solutions simultaneously is where the "binary superposition" comes in.