Why do quantum gates have to be reversible? 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?
 A: There is conclusion in the Phd dissertation below:
"At  the  beginning  of  my  research  on  designing  reversible  logic  circuit,  one  of  the  first questions  I asked myself was  why we need reversible logic circuits? After completing initial research on the subject matter, I was convinced that the logical irreversibility of classical  logic  gates  inadvertently  causes  the  heat  dissipation  when  new  values  are
computed and old information is lost.
[...]
Concluding, there should be methods to synthesize Boolean circuits
using only reversible gates."
Shah, Dipal, "Design of Regular Reversible Quantum Circuits" (2010).
Dissertations and Theses.
https://doi.org/10.15760/etd.129
Landauer [Landauer61] proved that binary logic circuits built using traditional irreversible gates inevitably lead to energy dissipation, regardless of the technology used to realize the gates.
Zhirnov et al. [Zhirnov03] showed that power dissipation in any future CMOS will lead to an impossible heat removal problem and thus the speeding-up of CMOS devices will be impossible at some point which will be reached before 2020.
Bennett [Bennett73] proved that for power not to be dissipated in a binary logic circuit, it is necessary that the circuit be built from the reversible gates. A gate (or circuit) is reversible if it is a one-to-one mapping between sets of input and output values. Thus all output vectors are just permutations of input vectors. (Such a circuit can be described by a binary permutation matrix [Nielsen00]).
Bennett's theorem suggests that every future (binary) technology will have to use some kind of reversible gates in order to reduce power dissipation. This is also true for multiple-valued reversible logics, which is an
additional advantage because the multi-valuedness by itself demonstrates several potential advantages over binary logic.
These potentials of MV logic so far have not been taken advantage of since they bring no technological improvements when applied to existing technologies such as CMOS.
All these fundamental results of Landauer, Bennett and Zhirnov are technology-independent but practically applicable to future nano-technologies, especially to quantum technology as being the most advanced of all the
nano-technologies. They are also applicable in quantum dots and DNA circuit realization technologies."
References:
[Landauer61] R. Landauer, ―Irreversibility and Heat Generation in the Computational Process‖, IBM Journal of Research and Development, 5, 1961, pp. 183-191.
[Zhirnov03] V. V. Zhirnov, R. K. Kavin, J. A. Hutchby, and G. I. Bourianoff, ―Limits to Binary Logic Switch Scaling – A Gedanken Model‖, Proc. of the IEEE, 91, no. 11, 2003, pp. 1934-1939.
[Bennett73] C. H. Bennett, ―Logical Reversibility of Computation‖, IBM Journal of Research and Development, 17, 1973, pp. 525-532.
[Nielsen00] M. Nielsen and I. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2000.
A: 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.
