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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)?

glS
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Quantum computers can simulate different logical systems that are used in Classical Computers, but the effectiveness of the simulation depends on the problem at hand. With the help of X, CNOT, CCNOT quantum gate and some ancilla qubit, classical NOT, AND, OR and XOR gate can be implemented.

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