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One possible reason I have come up with is that we are modeling quantum gates by unitary matrices. And since unitary operations are reversible we have to be able reverse the operation in the physical world as well. This is simply done by "remembering" which state has gone in and provide it as output if the reverse operation should be applied.

But what happens if we don't "remember" the input state? Are there certain operations that can be performed without the need of reversibility?

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    $\begingroup$ All quantum operations are unitary - it follows directly from the Schroedinger equation. The exception is measurement, which is not a gate. $\endgroup$ Jul 27 '16 at 23:19
  • $\begingroup$ All closed quantum systems are reversible, the open ones are irreversible. It's exactly like in classical mechanics (with a few caveats). $\endgroup$
    – CuriousOne
    Jul 27 '16 at 23:41
  • $\begingroup$ If the only exception is a measurement, does that mean that an operation which doesn't copy the input automatically causes the collapse of the superposition? $\endgroup$
    – Heye
    Jul 28 '16 at 6:28
  • $\begingroup$ @CuriousOne for classical mechanics I read here that "Given the initial conditions of a system, and a set of mathematical laws that model reality, we want to be able to tell what state the system will be in after a given time." which for me sounds like the other way around. The model we use has to be reversible to describe the physics. Also classical gates eg. AND are not reversible and that seems to be fine, the information that is lost is simply turned into heat. $\endgroup$
    – Heye
    Jul 28 '16 at 6:34
  • $\begingroup$ I didn't say that a classical gate is reversible and I have no idea what your statement is supposed to mean in this context. Physics is more than computing, much more and quantum mechanics is so much more than quantum computing, it's just that some fields narrow the view when stared at for too long and some experiences in my life suggest that computation is one of them. $\endgroup$
    – CuriousOne
    Jul 28 '16 at 6:45
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Quantum gates have to be reversible because quantum mechanics is reversible (and even more specifically it is unitary). It's just an observed fact about the universe. (Even measurement can be modeled as a reversible unitary operation, inconvenient though that may be.)

Actually, classical computers also have to be reversible. We just happen to be able to sidestep the problem by throwing out accumulated garbage information as we go. Throwing out garbage information during quantum computations would also be possible, but because discarded garbage information counts as a measurement and measurement tends to break quantum algorithms... not so viable.

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  • $\begingroup$ How does this relate to reversible computing? $\endgroup$
    – user56903
    Jul 28 '16 at 8:47
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    $\begingroup$ @DirkBruere Concepts from classical reversible computing are often applied to avoid creating garbage during quantum computations. That's how I see them relating. $\endgroup$ Jul 28 '16 at 14:56
  • $\begingroup$ If a computation procedure is regarded as a curve in the state space, then the full power of quantum computation can only be achieved by a curve that stays far enough from the classical state space. Keeping the QC reversible ensures to explore the full Hilbert space and therefore to achieve an efficient QC. Otherwise your curve will easily fall in/near the classical state space so that your QC may fail. $\endgroup$
    – XXDD
    Jul 28 '16 at 16:04
  • $\begingroup$ @CraigGidney, what do you mean by the statement "Quantum Mechanics is reversible", does it mean the if the time is reversed in principal everything can go back in time? If that is the case, classical mechanics is also reversible I guess, which may imply that classical computations should also be reversible. what are your thoughts on this? $\endgroup$ Mar 17 at 5:39
  • $\begingroup$ @dhirajsuvarna Yes, that's what I mean. Classical mechanics is also reversible; in fact both classical and quantum mechanics satisfy Liouville's theorem which is even stronger than just reversibility. That being said, there are some corner cases where it can get ambiguous due to singularities in the math. It's not really my expertise. $\endgroup$ Mar 17 at 6:24

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