The Smallest Bitcoin Miner Possible

If Bitcoin somehow survives the ego of world governments, massive FUD, and the next asteroid impact, our great-grandchildren might see the smallest Bitcoin miner theoretically possible.

Note: This idea is from the very far future of Web 2.5

The Universe is Quantum

If you have watched any of the Ant-Man films, then you have taken a glimpse at how small the quantum world is.

Thing is, the quantum world is really small.

If an electron is made the size of a dust particle, then a tree becomes almost as big as the Milky Way galaxy.

As a budding quantum information scientist, I have worked with these tiny particles called electrons on both classical computers and on cloud quantum computers.

On quantum computers, electrons traveling inside circuits called Josephson Junctions can exhibit extra impressive behaviors like superposition and entanglement. These extra behaviors can then be used to build quantum computational circuits.

It turns out that having extra behaviors makes classical computational circuits a subset of quantum computational circuits by way of computational complexity.

In simpler words, the theory says you can exactly simulate any classical computer on a quantum computer. The reverse is not fully possible. This is because things like “entanglement” can only be approximated on classical computers.

As Professor Michio Kaku colorfully puts it, “.”

The Hamiltonian

If we can simulate any classical computer on a quantum computer, we can simulate any classical computational system (just a big computer made up of networked smaller computers) like Bitcoin on a quantum computer.

But Bitcoin is a very big, complex, open-ended classical computational system. It is, by all means, quite hard to even think of how any Physicist could try to capture it all in a few equations.

However, in Physics, a quantity called the Hamiltonian can help us capture the energy budget of a Bitcoin miner’s repetitive process.

Definition – The Hamiltonian of a system is a mathematical expression of the total kinetic and potential energy contained in that system.

Without going into the weeds of how the core software on a Bitcoin miner consumes energy, its Hamiltonian can be simply described as follows;

Hamiltonian of Bitcoin Miner = Energy spent mining blocks (1) + Energy spent synchronizing with the blockchain (2).

How small can the energies in (1) and (2) be?

Assuming SHA256 remains latched to Bitcoin for all those centuries as well, threats from Shor’s factoring algorithm be damned, then all we have to do is count the minimum number of ASCII characters that need to be shuffled in totality during the mining process. This number will then give us our Hamiltonian.

This great video by Ken Shirriff on mining bitcoins using pencil and paper will give us a good idea of what we are dealing with. Watch the video and count with me each bit he writes down, erase, or counts.

You will notice that he:

1. Writes down 96 bits +

2. majority counts (XOR addition of three bits) to get 32 bits +

3. (ignore converting back to hexadecimal)

4. shifted (a form of counting) 96 bits +

5. XOR addition of three shifted bits to get 24 bits +

6. Write down 96 bits +

7. Choosing (compare two bits + write the one chosen) = 64 bits +

8. shifted 96 bits +

9. XOR addition to get 32 bits +

10. add five 8-character hexadecimal numbers which is a XOR addition (with carry) of five 32-bit numbers to get 32 bits + 32 carry bits (theoretical upper limit) = 64 bits +

11. a repeat of step 10 above for three 8-character hexadecimal numbers = 64 bits +

12. new E value = 64 bits

Total bits altered (require Kinetic energy) = 728

Bits stored along the way(require Potential energy) = 1112, which includes bits for XOR addition. Refer to the image below to check my maths (remember to convert all hex values to binary).

Minimum energy for mining a Bitcoin block

1840 bits were written and stored by Ken Shirriff, and it is true his hand is not the most efficient Bitcoin miner.

His 1840 bits are only 0.67 hashes. Mining a Bitcoin block will take a lot more than that, and as Ken’s blog enlightens us, we could mine a block with only 128 rounds of the full SHA256 hashing process. That is; (128*1840/0.67) to give us 351,522 bits.

This is for the mining process - part (1) of the Hamiltonian. But let’s roll with it. After all, it is nicely clocked at a constant of 10 minutes and is thus the part that will be least changing at the lower limit.

Landauer’s limit

This pertains to the minimum energy required to change one bit of information, whether that be erasing a bit or writing a new one.

“At room temperature, the Landauer limit represents an energy of approximately 0.018 eV (2.9×10−21 J)” – Source

So 351,552 bits = 1.019×10^−15 J

We can now finally ask what particle has a Hamiltonian close to 1.019×10^−15 J.

That will take some asking around, but it is about the energy of 1 million glucose molecules only.

In better comparison, one AAA battery from a Game Boy could power 1 billion such miners.

Conclusion

Bitcoin miners can go atomic before they hit their shrinking limit.

But before that, we have proven there is a big chance that we shall be mining Bitcoin on our smartphones one day.

It is true what Feynman said: there is plenty of space at the bottom.