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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)?

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  • $\begingroup$ Any logical system which can be simulated classically is, of course, simulable quantumly also. My (uninformed) intuition is that all the non-classical logic systems can be simulated classically. That is, by adding enough ancillary variables, you could "program" a computer with the rules for any of these systems - would you agree? $\endgroup$
    – jecado
    Commented Aug 22, 2023 at 18:04
  • $\begingroup$ Quantum computing has it mathematical model (Deutsch model), hence it can be simulated classicaly. Conversely, Toffoli gate behaves as NAND gate which is universal for classical computing, hence a quantum computer can simulate classical computer. In their essence, both are Turing machines, hence equivalent. Of couse, their HW base and implementation of logical functions are very different. $\endgroup$ Commented Aug 22, 2023 at 21:21
  • $\begingroup$ @vengaq Your question (on both sites) may benefit from being more specific, eg. which logical system in particular are you interested in processing? On this site, it would also be especially helpful to describe why a classical computer may not satisfactorily process that logical system. $\endgroup$
    – jecado
    Commented Aug 23, 2023 at 22:43

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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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    $\begingroup$ what does "the effectiveness of the simulation depends on the problem at hand" mean in this context? $\endgroup$
    – glS
    Commented Aug 26, 2023 at 14:18

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