Could a quantum computer simulate any system based on different types of logic?

[murtazashab]

Quantum computing is based on quantum mechanics (obviously) which has different logical rules than classical /Boolean logic.

However, does this mean that a quantum computer could simulate or process systems based on quantum logic and classical logic? Or could it also be used for every other kind of logic (https://en.wikipedia.org/wiki/Non-classical_logic/) (apart from classical and quantum logics)?

 

[.Scott]

A quantum computer is designed to manipulate a quantum superposition of states. Conventional digital circuitry is used to perform Boolean operations on representations (for example, voltage levels) of true and false value. Depending on the how the quantum circuitry was implemented, it might be possible for it to perform regular Boolean operations - but that would normally be considered a malfunction.

 

[f95toli]

There is no reason for why you can't use a quantum computer for "normal" boolean logic; you can simply just use gates that only transfers the qubits between |0> and |1> (the "north" and "south" pole of the Bloch sphere) without ever putting them into a superposition state (near the equator).
Note that a QC needs to only use reversible gates to stay "quantum" (that is, no "normal" AND or OR). In this context that means that you will be restricted to using it as a reversible Turing machine. However, I believe(?) these are still universal.

In practice, this would be much- much slower than just using a classical computer but if the question is if it possible in principle, then the answer is yes.