How do quantum computers represent data?

[nec209]

Well from what I understand quantum computers operate on 0s and 1s and both and being both at the same time. So this opens up big problem how could data be both there and not there?

 From what I understand computers today use 1s and 0s , but quantum computers use 1s, 0s and can be both 1 and 0 at the same time? So how can data be both 1 and 0 at the same time so data is there and not there? 

[studiot]

11 hours ago, nec209 said:

Well from what I understand quantum computers operate on 0s and 1s and both and being both at the same time. So this opens up big problem how could data be both there and not there?

 From what I understand computers today use 1s and 0s , but quantum computers use 1s, 0s and can be both 1 and 0 at the same time? So how can data be both 1 and 0 at the same time so data is there and not there? 

Hello,

Some preliminaries will help to understand.

In non quantum computing the computer can be designed to work in serial mode or parallel mode.
Both have their advantages and disadvantages.
This applies both to the hardware design and to the software design.
These are not independent but the detail only concerns implementation, not the end result.

Put simply

Serial mode involves doing things step by step, one thing at a time.

Parallel mode means doing several things at once.

For example consider the simple calculation add these two numbers together.

[math]\begin{array}{*{20}{c}}
   {62310721}  \\
   {\underline {25644387} }  \\
   {87955108}  \\
\end{array}[/math]

In parallel mode we would add each digit to its corresponding one simultaneously.
Because the addition is simultaneous we would not know what the carries are at that time so we would have to ignore them.
We would then perform a second step to add in the carries.

So this addition is a two step process if carried out in parallel as shown.

[math]\begin{array}{*{20}{c}}
   {62310721}  \\
   {\underline {25644387} }  \\
   \begin{array}{l}
 87954008 \\
 \begin{array}{*{20}{c}}
   {\underline {00001100} }  \\
   {87955108}  \\
\end{array} \\
 \end{array}  \\
\end{array}[/math]

 

To carry out this same operation in serial manner takes 8 steps, but includes the carries along the way.

[math]\begin{array}{l}
 62310721 \\
 \underline {00000007}  \\
 62310728 \\
 \underline {00000080}  \\
 62310808 \\
 \underline {00000300}  \\
 62311108 \\
 \underline {00004000}  \\
 62315108 \\
 \underline {00040000}  \\
 62355108 \\
 \underline {00600000}  \\
 62955108 \\
 \underline {05000000}  \\
 67955108 \\
 \underline {20000000}  \\
 87955108 \\
 \end{array}[/math]

 

 

Essentially quantum computing works in all parallel mode since quantum mechanics is all parallel

 

[Prometheus]

So we have all these ones and zeros in a superposition of states, but for the final output we want it to collapse to a single state: the right answer. How is this collapse controlled to that end? Or is this not how it works.

[studiot]

10 minutes ago, Prometheus said:

How is this collapse controlled to that end?

That is the 64 billion dollar question all right.