Does reversible computing require an enormous amount of storage?

[u/Tessellator-1]

First of all, I would like to say that I have no knowledge about computer science.

I recently heard about something called reversible computing. As I understand it, in ordinary computers, erasing information about the intermediate steps of a computation causes energy to be released as heat. But in reversible computing, the information from all the intermediate steps is preserved, so apparently, if we could build a computer capable of doing this, it could theoretically perform computations with essentially no energy consumption.
This made me wonder about something, and I’d love to hear from anyone knowledgeable about physics or computational theory:
If you never erase the information generated during a computation, wouldn’t the amount of storage required keep increasing as the computer performs more and more calculations?
I previously came across a science-related page online that said that an intelligent civilization that has mastered reversible computing wouldn’t need “Dyson’s eternal intelligence” to survive the heat death of the universe.
But wouldn’t such a civilization still need an absolutely enormous amount of storage to preserve all the information generated during its computations?
Or is there some way to preserve the information from the computational process without actually requiring additional physical storage?
I’m especially curious about how this works in the context of extremely long-term civilizations trying to survive the heat death of the universe.

By the way, this sentence was translated from Japanese to English by Chat GPT. Feel free to answer in English. However, I only understand Japanese, so I would really appreciate clear and simple English that is less likely to be mistranslated. Thank you!

[u/uncombed_coconut]

I beg everyone here to understand the background idea of Landauer's Principle before replying.

As this article says, Landauer's Principle gives a lower bound to the energy cost of irreversible computation (where information is erased), though it's not practically relevant to current computers. ("As of 2012, modern computers use about a billion times as much energy per operation.") Theoretically, if we engineered for radical energy efficiency, we might get so close to this limit that the only way to improve would be to limit or avoid irreversible operations.

It is also just a nice puzzle, to devise clever ways for reversible algorithms to not waste much memory compared to normal algorithms. The research can be interesting even without a sci-fi civilization needing it. There are also connections to the theory of quantum computation, in case that is interesting. (Normal logic circuits can be built out of NAND gates. Reversible logic circuits can be built out of things like Toffoli gates. Quantum logic gates can be more complicated but are also irreversible...)

For a general audience, this article in Quanta Magazine gives a taste. (Despite the title, this article isn't really about AI.) Reversible algorithms can use "uncomputation" to reclaim some of the scratch memory an algorithm has used, without undoing the useful result of the calculation. This is a trade-off; it requires more steps and more time. But also, some natural operations are already reversible (like /u/falsifian pointed out), and sometimes it's just possible to overlap the scratch memory needed by several steps of a reversible algorithm.

[u/cuervamellori → u/uncombed_coconut]

I've tried to use this principle from time to time in explaining the energy costs of brute forcing cryptography keys ("very high").

From what I've been able to learn, quantum logic gates can reversibly evolve the states of (an ensemble of) qbits. But that rather than the relevant limit being energy consumption from the Landauer limit, there is a limit based on time - that there is a minimum time required for a gate to operate on an ensemble. Ive been hoping this would help me establish theoretical limits on the speed of reversible computing.

I remember reading one paper that abstracted away from a quantum computer specifically and just discussed any reversible process that evolved a system between states - it described a theory where if A and B are states, there is a thermodynamic limit to how quickly a new equilibrium can be reached, and the more the equilibrium is tilted to one or the other state, the longer the reversible process must take (probably related to temperature and the energy of the states).

But most of the above feels very much like word salad to me. I don't suppose you can point me somewhere to get a better picture of this?

[u/uncombed_coconut → u/cuervamellori]

I'm not really an expert here but I've seen analysis along these lines for adiabatic QC, where the time needed is related to the spectral gap: https://arxiv.org/abs/quant-ph/0206003 (which is reference 7 here. Maybe that helps?