Quantum Supervision

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Ada is supervising Niels’ doctoral thesis. They’ve been
arguing about it for years. Today is crunch time: he has to
have it finished. Will he produce the goods? There are only
two possibilities: yes or no. Or maybe not.
Ada
So, Niels, what have you got to show me?
Niels
It’s finished. I worked on it forever; the
whole thing is done.
Ada
OK, show me. What title did you decide on
in the end?
Niels
“Urobus”. But I have to warn you: you
won’t like it. Not one little bit.
Ada
Let me be the judge of that. How many
words is it? I hope you’re inside the
100,000 limit.
Niels
Well, that’s the first problem. I don’t
know. At least, I know the upper and lower
bounds, but I don’t know the actual
number, because there isn’t one.
Ada
What do you mean, “there isn’t one”? All
you have to do is count from the beginning
to the end; even you should be able to do
that.
Niels
That’s the second problem. There isn’t
really a beginning or an end. It’s hard to
know where to start. That’s why I settled
on “Urobus” as the title; you know, the
mythical snake that swallows itself?
Ada
If there’s a bound copy, there is a first
page and a last page; start on page one
and count until you reach whatever page is
last. Are you trying to wind me up again?
Niels
There isn’t a bound copy in quite the
usual sense.
Ada
Either there is a bound copy or there
isn’t; which is it?
Niels
It didn’t work out like that. You need to
come down to the basement.
Ada
Excuse me?
Niels
It’s in the basement.
Ada
Then go and get it. I have more important
things to do than wander around the
building looking for a thesis I doubt
you’ve finished.
Niels
Oh, I’ve finished. It’s done. It’s
completely comprehensive, exhaustive and
definitive. But it’s in the basement.
Ada
Why?
Niels
Because it’s encoded into the qubits of
the quantum computer.
Ada
Encoded … Hold on, how is anyone supposed
to assess a thesis encoded in a quantum
computer? The regulations are quite
specific: submit a typescript bound in
three copies. University statute 31.4(d),
2020.
Niels
But I can’t write my thesis in a classical
book, so instead I’ve created a quantum
book along lines suggested by John
Preskill that contains a quantum thesis.
All the letters of all the words on all
the pages are stored in entangled states
in the qubits.
Ada
But nobody can read that.
Niels
No, that’s the third problem. I admit it.
Ada
Let me try to get this right. You are
proposing to submit as your doctoral
thesis something encoded in the university
quantum computer that nobody can read?
Niels
Correct. We are on the same page.
Ada
How do we know it isn’t gibberish?
Garbage? Trash? A joke?
Niels
You need to read it.
Ada
Remind me how many operational qubits our
quantum computer has these days. I’ve lost
track.
Niels
Fifty.
Ada
Fifty?
Niels
Fifty. That’s somewhere between 0 and 2^50
words. That’s roughly 10^15 words, so I
could be a bit over length; it’s hard to
tell without reading it, and it’s only
possible to read it once.
Ada
10^15 words? Only read it once? Are you
pulling my leg? That’s many times more
words than have been written in the
history of the world.
Niels
Yes, I told you it would take a while.
That’s partly why it’s a bit late. But
impressive; I thought you’d be pleased.
Ada
And it’s all stored in the basement QC?
Niels
Yes. Waiting for you to come down and read
it.
Ada
And how long exactly do you suppose that
is going to take?
Niels
Quite a while, I imagine.
Ada
You haven’t written anything at all, have
you?
Niels
Yes, in fact I’ve done better than that:
I’ve written everything that could ever
reasonably be written; several multiples
of everything that could ever be written,
actually, so there must be a decent
coherent world-class thesis in there
somewhere.
Ada
OK, I’ll read five pages and then we’ll
see whether I still take you seriously.
Niels
No, sorry, you can’t do that. The pages
make no sense by themselves; you have to
read the whole thing. Then it will all
make sense. Miss out one page, one section
of a page, and nothing will make sense.
They’re all entangled, as I said.
Ada
But doesn’t the process of reading it
cause each qubit to degrade into a
classical bit because we can’t read it
without performing a measurement?
Niels
Yes, of course. That’s obvious.
Ada
And what happens to the original thesis if
reading it causes the whole thing to
collapse into a string of classical bits?
Niels
It’s lost. That’s why I haven’t read it;
it would be a shame after all that work
creating the ultimate coherent thesis to
make it decohere straight away.
Ada
But you are ready to allow the examiners
to read it, even at the expense of
destroying it?
Niels
Of course. What would be the point of
writing a doctoral thesis nobody ever
read?
Ada
But what we would be reading wouldn’t be
your original thesis; it would just be the
version that a particular reading caused
to materialise.
Niels
If you don’t read it right, yes it could.
But I’m trusting you to read it carefully.
Ada
So if I read it with the external
examiners and we think it is worthless
nonsense, what will be your response if we
fail you outright without even a viva?
Niels
That you haven’t read it carefully enough,
because I can assure you that it’s world-
class and brilliant.
Ada
Even though you haven’t read it?
Niels
I’ve already explained why I couldn’t read
it. But I did write it. The rest is up to
you.

About the Author: 
Educational consultant, philosopher, part-time author, former headmaster and mathematics teacher.