# How many elements could a 64 qubit quantum computer hold hypothetically compared to a 32 qubit computer?

I understand that for standard bits the difference between a 64 bit memory and a 32 bit memory is 2^64 divided by 2^32. This means that with 64 bits we can access approximately 4294967296 or about four billion times the physical memory than with 32 bits.

Now I am wondering what the difference is for quantum computers, if theres is any.

Can you explain this to me please? Thank you!

• You are looking for Holevo's theorem (en.wikipedia.org/wiki/Holevo%27s_theorem), which says that the amount of retrievable information in $n$ qubits is simply $n$ bits. Dec 6, 2022 at 5:59

## 1 Answer

To amplify what @Rococo said, qubits are way more powerful than bits, but in the end you can only extract a small amount of information from it.

Theoretically, you could store all of Shakespeare's works on a single qubit. But then you ask the qubit a single yes/no question about Shakespeare's works ("are there more 'e's than 's's in the corpus?") , and it forgets everything it knew about Shakespeare except the answer to that single question.

• How do you store all Shakespeare's work on a single qubit, theoretically? May 6, 2023 at 2:10
• Theoretically, a qubits specifies an infinite precision probability of being read as "1" in the Z axis with a probability of between 0 and 1. Obviously, no such qubit exists in practice, but that is the theory. All of Shakespeares works can likewise be encoded as a very precise fraction between 0 and 1. May 6, 2023 at 5:54