No. of bits in 160 qubits computer

Question

I read in a book that (https://hub.packtpub.com/quantum-expert-robert-sutor-explains-the-basics-of-quantum-computing/)

160 qubits (quantum bits) could hold $2^{160} \approx1.46\times 10^{48}$ bits while the qubits were involved in computation."

How does this calculation come about?

The context of the statement is that a caffine molecule would require $10^{48}$ bits to be represented by a classical computer. However a quantum computer would require 160 qubits and is thus well suited for such representation.

If I look at this question on Quora, a 512 bit computer (which I suppose are real) would give a largest 155 digit number (https://www.quora.com/How-many-digits-are-in-a-512-bit-number). Isn't that big enough to represent atoms, molecules etc.?

Answer 1

If you have $n$ bits you can combine them in $2^n$ different bit string (this come from combinatorics). Now take $n$ qubits. As any qubit can in superposition of two state, i.e. 0 and 1, $n$ qubits can be in superposition representing all $2^n$ possible bit strings.

The notion that $n$ qubits can hold $2^n$ classical bits is unfortunately misleading because when you measure the qubits, they will collapse to one particular state. This means that information content of $n$ qubits is $n$ classical bits.