You really have to work at it, but this CPU would make a supernova look like a dim bulb.

Oh wow, unexpected answer. I thought maybe like destroy HTTPS or something, not THE ENTIRE WORLD.

Also, for the counter, do you mean 3/4 of the energy in the galaxy for just this one computer in one second? What about a modern network of computers implementing this counter over a year?

@moby If you had a computer that consisted of just a single 256 bit register, which started at 0, and all the computer did was increment it over and over until the value reached 2^256-1, that computer would consume 3/4 of the energy in the galaxy as an ultimate lower bound. Every second, this alien computer would burn 3/4 of the energy in the galaxy or more. 2^256 is just that big. As for modern computers, they're actually far less efficient than that lower bound. I don't remember the exact efficiencies, but I think they're a trillion times less efficient than that ideal computer.

Trying to do this kind of brute force calculation with modern computing technologies instead of ideal computing technolgies may consume all the energy in the known universe, just to crack one key!

For the record, is there a theoretical limit to the number of instructions a computer could perform in a second, such that this alien computer wouldn't even be possible in the first place?

There are some interesting limits. I'd read the article on Sentience Quotient. The limit given there is in terms of bit/s per kilogram, because you can always make the computer bigger to do more unless you're energy bound. A SQ of +50 is the highest you can go using the known laws of quantum physics, which is 10^50 bits/s/kg. This is about 2^166 bits/s/kg, so you'd need about 2^90kg (10^27 kg) of matter to keep up with that processing rate. That's about half the mass of Jupiter, all of it processing at a QM theoretical limited rate.

The solution to this, of course, is to use reversible computing instead of irreversible computing. This sidesteps all of these pesky limitations.... or might sidestep them. I'm not entirely qualified to talk to what a reversible computer can or cannot do. I do know that we still don't fully know the extent of BQP, which is the set of problems that a quantum computer can solve in polynomial time, and a quantum computer is just one of many reversible computers people have explored.

You beat me to it. This. I can't vouch for the specific numbers you quote, but the gist is most definitely correct.

"…clearly shows that there is no such minimum energy limit and that a logically irreversible gate can be operated with an arbitrarily small energy expenditure…" phys.org/news/2016-07-refutes-famous-physical.html

Great answer! I'm wondering, is Cort Ammon a pseudonym of Randall Munroe? :-)

@CortAmmon The number you give for the energy to perform an (irreversible) operation is at room temperature - the energy is proportional to temperature. Very cold, close to 0K (which we might imagine that these aliens can achieve), it would be much lower, perhaps even on the scale of achievable.

@Eoin Even if so, you would need the energy to achieve that low temperature in the first place. It might possibly be a net gain (someone would have to do the math for us to know for sure), but a computer like the one posited in the question will still require enormous amounts of energy to work, no matter how you slice, dice or quantize it. Thus, the bottom line still holds, even if the energy isn't used directly for computations, but rather to enable the possibility of the computations.

What if the computer is attached to a 0K Handwavium heat reservoir? And also a finite-but-arbitrarily-high-temperature Handwavium reservoir, since we've got some extra, and of course, the whole thing is sealed in a Handwavium case.

@FrerichRaabe Cort Ammon is unchallenged at the top of the Worldbuilding SE reputation league. And, I think I dare say, for good reason.

@Alpha3031 At that point, you are invoking magic and can essentially declare that the device does whatever you need for it to do for the plot to go the way you prefer, possibly but not necessarily limited to that and nothing more. Otherwise known as deus ex machina.

Are you claiming that quantum computing is not possible because information is loss to avoid super heating? cool, better remove my shares from quantum computers...

And this answer is why I love Stack Exchange :D bows to Cort Ammon

@CortAmmon But if you have a limit for max. computations per kg and you have some density limit it means more computations = bigger computer. And if we are already talking the size of jupiter the speed of light will become a real limitation to how fast one part of the computer can communicate with another, synchronization between parts will become a major time-factor.

@Falco: Depends on the algorithm. Some things can be parallelized quite nicely, and brute-forcing cryptography should fall in that category. You can simply ditribute which part of the Jupiter-sized computer tries which keys, and then you have no communication until one part find the answer and the whole machine gets powered down or whatever.

@MvG of course you can, but you cannot call that a general purpose 2^256 calculations per second computer. - because you can only calculate a certain subset of calculations with 2^256 and others much slower...

The device might need to operate at millikelvin temperatures, but a 'fridge and battry for powering that is “not included” in the package. So it’s not such a bomb; it requires a power source to be supplied to run it.

This is an alien computer. Alien meaning strange and unknown to us, so to say "It couldn't do this because..." is not answering the question.

How does this answer affect the result?

Many mathematical conjectures would be disproven probably, and we will get much much stronger evidence for the ones that are true.

But a counter is reversible.

@JukkaSuomela Thank you for that link! That's actually quite the interesting paper. It does show that you can do calculations using conserved quantities other than energy using a really neat trick to sidestep Landauer's principle. However, the paper does point out that there is no known way to generate the spin resevoirs they rely on without far more energy than you save in the computation. Such a reservoir would effectively be a battery, charged up with spin rather than energy. It does open the door for some interesting possibilities though, if some yet unknown effect generated the reservoir

@Eoin If you had a large reservoir at temperatures lower than 3K, you could do the computations using less energy. However, you have to generate that lower temperature, which takes work. By the laws of thermodynamics, it would have to take at least as much energy to generate that heat sink as it would take to do the computation, and likely far more because refrigeration often comes with losses. Doing it at 3K at least lets us use the universe as our heat sink.

@Alpha3031 If you're including handwavium solutions, then all bets are on. But if we're including compounds that are not believed to exist in this universe, the options for handwavium computing grows dramatically. You might even be able to simply use a reversible computer with enough handwavium!

@DarioOO Quantum computers use a different approach to computing entirely. With quantum computing, you can theoretically do some reversible computing algorithms, sidestepping Landauer's limit. For example, Shor's algorithm is already known to solve the discrete logarithm problem in polynomial time. You still pay an energy price to get the answer from the system, but you pay for the cost of the bits you measure, not all of the reversible calculations you did along the way, so it can be astronomically cheaper. You may look at BPQ for more.

@JDługosz See my comment to Jukka about your link. It's a fascinating answer, relying on a spin reservoir to be a sort of battery to draw from rather than a heat reservoir.

@Falco True, we do need to consider the architecture of the computer into account when we talk about numbers of operations. If we are defining number of operations in terms of a Von Neumann architecture, you would indeed have to admit that such a computer cannot be a general purpose computer. However, note that it is the mass of Jupiter that was used in that comment, not its size. Other limits like the Berkstein bound start to become important if we scrunch all that information into a small region. Too small and it becomes a black hole!

@user23013 Good point about the counter. A counter could indeed be reversible, if it were implemented as such. I used a counter implemented irreversibly (such as a register and an ALU) as my surrogate for doing any of the arbitrary 2^256 operations moby wanted the computer to do. In theory, this is only 256 times more expensive than the most trivial operation, so it was a good lower bound. I've added a edit to my answer to reflect this. Good catch!

Phew! It looks like others had as much fun with this answer as I did. I awoke to 17 new messages related to this answer =D !! I think I responded to every comment. Let me know if I missed yours!

@FrerichRaabe Thank you! That's probably the highest complement I've received in quite some time!