The issue is not the complexity, but the information content. As mentioned, n qbits can’t store more than n bits of classical information, so the best way to think of them is “n bits of information with some quantum properties”. Therefore, it’s implausible that they correspond to exponential utility.
What do you mean by store information? The state space of a quantum state is(/can be thought of as) a vector of 2^n complex numbers, it’s this that prohibits efficient classical simulation.
Perhaps you’re talking about storing and retrieving information, which does indeed have constraints (e.g. Holevo bound). Constraints that limit quantum computers as a kind of exponentially large memory stick where you store and retrieve information. But algorithms (like Shor’s) use this large space then carefully encode their output (using the structure in the problem) in a way that can be transferred off the computer without breaking the Holevo bound.
I guess I believe the state space that you can’t necessarily access is the important element, not the information being brought in and out of the system.
The issue is not the complexity, but the information content. As mentioned, n qbits can’t store more than n bits of classical information, so the best way to think of them is “n bits of information with some quantum properties”. Therefore, it’s implausible that they correspond to exponential utility.
What do you mean by store information? The state space of a quantum state is(/can be thought of as) a vector of 2^n complex numbers, it’s this that prohibits efficient classical simulation.
Perhaps you’re talking about storing and retrieving information, which does indeed have constraints (e.g. Holevo bound). Constraints that limit quantum computers as a kind of exponentially large memory stick where you store and retrieve information. But algorithms (like Shor’s) use this large space then carefully encode their output (using the structure in the problem) in a way that can be transferred off the computer without breaking the Holevo bound.
I guess I believe the state space that you can’t necessarily access is the important element, not the information being brought in and out of the system.
Yes, Holevo as you say. By information I mean the standard definitions.