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So to start of the challenge we take a look at the instructions page and
see the definitions for this random secret gate of theirs.
Since I have worked we these kinds of gates before I see that the definitions
closely resemble that of the gate used for a Deutsch algorithm.
This is a algorithm that is used to minimize function calls to tell
whether a function is balanced or constant. The algorithm uses a auxiliary
qubit which is our second qubit in the 
state. Both qubits are then brought
into superposition using two hadamards and the unitary gate 
is applied across the two
qubits. The first qubit is then brought back to a single state using another hadamard.
In the case of Deutsch reading the first qubit then gives us the function calls
which is completely equal to 
.
Thus xor'ing these two possible function calls is given by
Where the first term will always be zero thus
So depending on the outcome of the first qubit we can find 
. If the outcome is
0 then is also 0 and the same for the outcome of 1.
Now the trouble was that we are only given a specific and we would really like all of 
.
This part is probably obvious to most but it took me a while to figure out. I discovered after
using Chrome's dev tools and looking around for a bit, that we get one cookie named "randomness"
which is set to a specific numeric value. I figured that this is probably used to set the value
for . So I wrote up a script in python (Babyquantum.py in rep) using selenium passed the circuit from Deutsch as
- H U1 H D
X H U2 H D
and went through the values 0-200 for the cookie, reading the output of the first qubit.
this gave me a binary.
10000010 00110010 00110010 10100010 11001010 11011110
11001110 11000110 00010110 01001110 11110110 10100110
00100110 10010110 01110110 11100110 10100110 01001110
11001110 11111010 01000110 10000110 01000110 10011110
10111110
Which again I looked at for quite a while not able to make sense of it.
I finally figured that since nothing else was given the flag probably had
ALLES in the start, which almost fit with what I had, Mathing up the letters
I realized that the binary string was flipped. Thus after flipping and converting
to ascii I got a flipped string which I again flipped giving the flag
ALLES{schroedingers_baby}
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