In section 3.2.5 of Nielsen and Chuang (starting page 153) they talk about Landauer’s principle, where they discuss the lower bound on the thermodynamic cost of erasing information.
In irreversible computing (i.e. classical computers), we can build any algorithm from a series of NAND gates. Since NAND gates take 2 inputs and give 1 output, a bit of information is erased (i.e. lost) and therefore Landauer’s principle is in effect.
Nielson and Chuang discuss reversible computing and how it would not incur the cost of Landauer’s principle.
QUESTION
Irreversible computing incurs the thermodynamic cost from Landauer’s principle and reversible computing does not. Heat and noise can ruin quantum states within quantum computers, is this related to Landauer’s principle?
I don’t see any direct statements connecting Landauer’s principle to why quantum computers must be reversible. Can someone clarify the exact role Landauer’s principle plays in the reversibility of quantum computers and its relation to the unitary nature of quantum gates?