628-EN, The Hashrate-Grover problem
Quantum Grover isn't difficult.
What it's doing is just probability calculation.
Very simple.
It's just a little frightening.
What can be said, at the very least, is this:
each trial is independent,
theoretically repeatable without limit,
failures are not recorded, and no correlation remains.
And success, only needs to happen once.
From a security perspective, I'm sorry to say it, but
these are extremely harsh conditions.
Now, suppose we prepare 100 quantum Grover systems.
In each quantum system, let us assume that the probability amplitude assigned to the target region
(hash < target)
is about 0.001% higher than that of the other candidates.
Then, across the entire quantum system,
the probability that a single quantum operation yields the correct answer - and remember,
one success is enough-becomes:
1 - (1 - 0.00001)^100 = 0.00099 ...
That is, almost 0.001…, close to 0.1%.
Furthermore, suppose that within a single block generation interval,
this quantum system can perform 100 quantum operations.
Again, since one success is enough:
1 - (1 - 0.001)^100 = 0.095 ...
This means that a single block is obtained with a probability just under 10%.
If this succeeds three times consecutively - in other words, three blocks in a row-then:
(0.1)^3 = 0.001
Therefore, if 144 blocks are generated per day:
1 - (1 - 0.001)^(144 / 3) = 0.0468 ...
In other words, there is approximately a 4.7% probability per day that,
in the vicinity of the Hashrate-Grover boundary,
quantum Grover breaks through the hash-rate defense.
This probability... is far too high.
Let us take the difficulty adjustment interval to be 14 days. Then:
1 - (1 - 0.047)^14 = 0.49 ...
About 49% in 14 days.
A level that can practically be called success.
Yes.
This is the basic structure of quantum Grover.
There are, of course, other techniques as well-methods for manipulating probability amplitudes.
And this...
this Hashrate-Grover problem is nothing less than
a test of whether crypto -cryptocurrency- can continue to exist at all.
I am an observer.
I won't speak of hard forks.
I simply record, carefully, which worldline is chosen.
