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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.

  

![](/MjSandberg/CTF-
writeups/raw/solved/2019/ALLESCTF/tex/166ec9a8fa1d0703dd6161f0c1fabafb.svg?invert_in_darkmode&sanitize=true)

  

![](/MjSandberg/CTF-
writeups/raw/solved/2019/ALLESCTF/tex/9e8514ae528c0c828aea8603bce5e0a1.svg?invert_in_darkmode&sanitize=true)

  

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 ![](/MjSandberg/CTF-
writeups/raw/solved/2019/ALLESCTF/tex/ec2376fb49efb4243a3f5d76fe720bbb.svg?invert_in_darkmode&sanitize=true)
state. Both qubits are then brought  
into superposition using two hadamards and the unitary gate
![](/MjSandberg/CTF-
writeups/raw/solved/2019/ALLESCTF/tex/f30c6bdebe1ddebdec6bb56fee7a3364.svg?invert_in_darkmode&sanitize=true)
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  
![](/MjSandberg/CTF-
writeups/raw/solved/2019/ALLESCTF/tex/31a6bef948c533616d360da71a62ac2a.svg?invert_in_darkmode&sanitize=true)
which is completely equal to ![](/MjSandberg/CTF-
writeups/raw/solved/2019/ALLESCTF/tex/c73b6615f0c7bd519371e439b4efff6d.svg?invert_in_darkmode&sanitize=true).

  

Thus xor'ing these two possible function calls is given by

  

![](/MjSandberg/CTF-
writeups/raw/solved/2019/ALLESCTF/tex/70c04e97552b8950725615a8c02fc4b8.svg?invert_in_darkmode&sanitize=true)

  

![](/MjSandberg/CTF-
writeups/raw/solved/2019/ALLESCTF/tex/0fd22aefb18e071e1162d7d79754c301.svg?invert_in_darkmode&sanitize=true)

  

Where the first term will always be zero thus

  

![](/MjSandberg/CTF-
writeups/raw/solved/2019/ALLESCTF/tex/95397cbaab58b38a581647f951865244.svg?invert_in_darkmode&sanitize=true)

  

So depending on the outcome of the first qubit we can find
![](/MjSandberg/CTF-
writeups/raw/solved/2019/ALLESCTF/tex/4fa3ac8fe93c68be3fe7ab53bdeb2efa.svg?invert_in_darkmode&sanitize=true).
If the outcome is  
0 then ![](/MjSandberg/CTF-
writeups/raw/solved/2019/ALLESCTF/tex/4fa3ac8fe93c68be3fe7ab53bdeb2efa.svg?invert_in_darkmode&sanitize=true)
is also 0 and the same for the outcome of 1.

  

Now the trouble was that we are only given a specific ![](/MjSandberg/CTF-
writeups/raw/solved/2019/ALLESCTF/tex/4fa3ac8fe93c68be3fe7ab53bdeb2efa.svg?invert_in_darkmode&sanitize=true)
and we would really like all of ![](/MjSandberg/CTF-
writeups/raw/solved/2019/ALLESCTF/tex/6f9bad7347b91ceebebd3ad7e6f6f2d1.svg?invert_in_darkmode&sanitize=true).  
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 ![](/MjSandberg/CTF-
writeups/raw/solved/2019/ALLESCTF/tex/4fa3ac8fe93c68be3fe7ab53bdeb2efa.svg?invert_in_darkmode&sanitize=true).
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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