Simulate roughly means designing a quantum computer that mimicks the dynamics of a real quantum system and then run a simulation of that to learn how it would behave under certain conditions e.g. to optimize its parameters. Similar to how we simulate planes or complex circuits today. Quantum systems are everywhere e.g. lasers, cold atoms, transistors or other complex semiconductors, superconductors, enzymes, … I’d say if we don’t develop the ability to understand these systems through simulation we will never progress beyond a certain technological boundary, and quantum computers are a necessary technology for that, just like classical computers were instrumental for the past scientific revolution.
A simulation of a plane is a model, implemented by humans, of how physics works.
A simulation of a quantum system is still a human implementation of mechanics. A quantum computer per my understanding should not be able to add anything to that. You’re not able to just say well this thingy has quantum mechanics and this is a quantum computer so it’s better able to do that. Quantum computers are about speeding up calculations by structuring specific problems such that wrong answers are not calculated. Not emulating quantum mechanics and then pulling the answer from the ether.
So… what am I missing here? How could quantum computer aided search spaces specifically aid simulating quantum systems that are not quantum computer aided search spaces?
“Wrong answers are not calculated” is a popular simplification of this, but it's misleading you here.
Quantum computers are a means of systematically creating and modifying complicated sums of exponentially large FFT's, and then efficiently sampling from the resulting distribution.
Note that you typically still need to sample many times to get a meaningful answer, which is where the “wrong answers are not calculated” ultimately comes from: if you can arrange for most or all of the factors corresponding to “wrong” answers in the sampled distribution to cancel out (such as the term for the number 4 when trying to factor 15), then when you sample several times from that distribution, very few or perhaps none of those samples will have been drawn from the “wrong” part of the distribution, and so you waste less time testing bad samples.
A quantum computer is potentially useful for simulating quantum systems because the _models_ for those systems are ridiculously complex in _exactly_ this way. It won't help if the model is wrong, but our problem is currently that we can't really run the calculations our current models imply beyond slightly-larger-than-toy examples.
How is this not “wrong answers are not calculated”? You gave a lot more detail on the mechanics of how these probability amplitudes are canceling each other out but the answer seems the same?
I don’t follow how this maps to helping simulate the quantum systems. Quantum computers are good at finding solutions to problems efficiently. But the quantum systems we are describing are not solution seeking systems. They’re going to be just interacting components with entanglement whatever’s going on. How would the avoidance of bad samples aid the simulation of a system like that?
But simulating a process is not the same thing as efficiently routing space exploration. Quantum computing grants you the latter. Why does it impact the former?
No that’s not how it works, quantum mechanics cannot be simulated efficiently on a classical computer, the state space grows exponentially with the number of degrees of freedom, every degree has relative phases to every other degree even when only looking at pure states, that’s why even the largest super computers cannot simulate more than 50 quantum degrees of freedom currently (see quantum supremacy).
I’m not claiming quantum mechanics can be efficiently simulated on a normal computer. I’m questioning whether arbitrary quantum mechanics systems can be effectively simulated by a quantum computer.
I have not seen any description of a general-purpose programmable quantum computer, which could simulate an arbitrary quantum system, like a digital computer.
All the examples given that I have seen were for making a hardwired simulator for a concrete quantum system, e.g. some chemical macromolecule of interest, to be used much in the same way as analog computers were used in the past for simulating systems governed by differential equations too complex to be simulated by the early digital computers in an acceptable time.
Are hard coded quantum simulators even the same thing though? Like, if we’re saying that the goal of a quantum simulator is merely to run a high dimensional problem and exploit the nature of qubits to make it simpler to handle those imaginary vectors and what not…
Does that actually follow the same framework as “traditional” “quantum computing”, e.g. struggles with error correction / problem formulation specifically designed to avoid unnecessary calculations?
It feels like although a quantum simulator could viably work to simulate a specific system, it shouldn’t make it any easier to actually understand the system it is simulating and could maybe just indicate how complex by the amount of variation in simulation outcomes (which isn’t useless). Is that accurate?
