Landauer: information is physical
Landauer's principle states that erasing one bit of information requires releasing a minimum amount of heat equal to temperature times Boltzmann's constant times the natural log of two. This heat cost arises because erasing a bit destroys information about the system's previous state, reducing two possible microstates to one. A classical AND gate illustrates the point: it maps four possible input pairs to only two outputs, so information is permanently lost and heat must be dissipated. Classical computers tolerate this constantly, but quantum computation cannot, which sets up why quantum logic gates must work differently.
- The factor of log two in Landauer's formula reflects the entropy of a two-state system, since a bit has exactly two microstates: zero and one.
- An AND gate with inputs A and B produces output zero for three of the four possible input combinations, meaning a zero output gives no way to reconstruct which of those three inputs produced it.
- Krishna frames the heat released as the cost of losing the ability to reverse the computation, connecting information erasure to an arrow-of-time argument.
Transcript
This chapter, from the episode video's captions · 521 words
25:58there's a fundamental minimum amount of thermal energy that needs to be dissipated into an environment um and the amount of energy for erasing a bit and I'll tell you what that means like what does erasing a bit mean but in any case the fundamental amount of energy that you need to erase a bit and to to let go of that heat is the the temperature multiplied by Boltzman constant multiplied by log of two the KBT is like the amount of jiggle that you have for every thing that can jiggle every degree degree of freedom and the log two is like it reminds you of like uh entropy is the log of the number of microates. In this case the number of microates is two because it's a zero or a one. Okay. So that's the amount of heat that you have to put out. Now for
26:39normal computers that's fine because we actually use reversible gates in our logic all the time. Our computers the algorithms and our phones everything uses like and gates or gates things like that. If we just look at an ANDgate for example let me show you how this thing erases information. Okay, an ANDgate takes your inputs. There's two inputs that are either 0 or one. And if they're only if they're both one does the output become one, right? Now, what that means is there's four different possibilities, right? 0 0 1 1 0 1 1. But they get mapped to only two. Right? The first three get mapped to zero because at least one of them is zero. And only the last one, the 1 one gets mapped to a one. Now this is irreversible
27:22because if I were to give you the output the table in C you could not tell me the input the A and B right because there's redundancy yes >> like if if I gave you the output is one then of course you could tell me it's 1 one >> but if the output is zero then you couldn't tell me which of the three it came from >> so that's an eraser of information because you lost a bit of information before you had two bits now you've only got one bit okay so whenever you implement an ANDgate land's principle comes comes in and you're going to have to release some amount of heat. >> Okay. >> And like the the ability to go back is what's being released in the heat. The degradation of like understanding what your previous state was. >> Exactly. Exactly. It's kind of like an
28:02arrow of time argument that you're making >> TVA from Loki season 1. >> Yeah. And this is totally okay for classical computing. Okay. We use so many gates and not gate and or gates in our exor in our classical laptops. Right. fine in quantum mechanics this is not okay. Okay, there's two reasons. The first one is kind of simple, right? If we want to use quantum mechanics to do computation, um we want to work with the
From How Quantum Computing Actually Works (Part 1)
Part I of our quantum computing deep dive traces the field from Bell and Feynman to Deutsch and Shor—and explains what quantum computers actually do differently from classical machines.