
Sex, Lies, And Quantum Computers - mike_esspe
http://rjlipton.wordpress.com/2013/04/27/sex-lies-and-quantum-computers/
======
ivan_ah
I can't comment on the theory side of quantum computation (BQP vs the
classical equivalent BPP), but I would like to make an _engineering_ comment
about why I think quantum computation will be _very_ difficult to scale, maybe
even impossible.

To have good quantum registers (long memory time), you want each qubit to
interact as little as possible with its environment. This means isolation
(qubits far apart) or encoding the information in systems that interact weakly
with each other.

However, to have good quantum computation (quick), you want strongly
interacting qubits.

The two goals are diametrically opposite, so it's not clear how we can achieve
both of them in a single system.

IMHO, the first interesting things that will come from quantum information
science will be about quantum simulations of physical systems and quantum
communication. Computation might come later... but I'm sure, by then, we'll
have moved away from RSA and ElGamal.

~~~
tedsanders
It's a fair argument that the problem is unlikely to be solved because the
solution wants to go in opposite directions (both weakly and strongly
interacting). However, let me point out that there are many technologies that
face strong tradeoffs and yet have been successful. Consider hard drive
memory, for example. You want it to be easily switchable so that you can
access bits quickly with little power. But you also want it to be hard to
switch, so that it remembers your data for a long time. The engineering
challenge is achieving both seemingly opposite goals at once. The success of
memory technologies (among others) makes me optimistic that this is a solvable
problem.

------
colanderman
> _The obvious solution is to write down the initial vector of size N=2^50 and
> start applying the quantum gates to the vector. […] The size is “just” a
> petabyte—or actually 1 /8 of a petabyte._

Um, NO. A quantum system is described by the _complex probability_ of being in
any of those states. You need more like 2^57 bits to represent that. 16
petabytes.

Source: I've written a 24-qubit quantum simulator.

~~~
j2kun
IIRC the models of computation with pure states and mixed states are
equivalent in power and efficiency (perhaps up to a polynomial blowup). In
fact, you don't even need complex numbers. This is probably Lipton's mindset,
seeing as he's a theorist.

~~~
colanderman
No, I'm referring to pure states (vector of complex probabilities), not mixed
states (matrix of complex probabilities). The latter would need 2^107 bits.

Every useful quantum algorithm manipulates the complex probabilities of the
system. You cannot observe these in a true quantum system but you must still
track them in a classical simulation.

~~~
j2kun
So you're saying it's because each probability is a 7-bit number? I guess
that's a valid issue, but it's still very "well, actually." So to counter with
my own "well actually," you don't need _complex_ probabilities, and the
computation only matters with probability bounded away from 1/2\. Surely you
could do enough engineering tricks to make that happen and keep it at about a
petabyte.

~~~
colanderman
No, it's because each probability is a _128-bit_ number (2^7 = 128; really two
64-bit numbers).

Yes, you very much DO need complex probabilities. The ability to phase-shift
qubits is key to most basic quantum algorithms.

I'm not sure what you mean by "the computation only matters with probability
bounded away from 1/2".

Almost by definition, the most "interesting" quantum algorithms are those
which are most difficult to simulate classically. e.g. you can use "tricks" to
greatly speed up simulation if your states are separable, but then you're not
really harnessing the full power of the quantum model. The most powerful
quantum algorithms entail maximum entanglement and worst-case simulation
performance.

~~~
j2kun
Now I think you don't understand quantum computing as well as you claim. The
standard model of quantum computing uses complex numbers, but it is well known
that you can do everything with just real numbers instead. See exercise
10.4-10.5 of Arora-Barak [1]. The key insight in quantum computing is not that
complex numbers are required, but that the invariant across computation is the
2-norm of a vector (as opposed to the 1-norm, as in the classic stochastic
model of randomized computation).

Further, the standard quantum model of computation is probabilistic in the
sense that you "compute" something if your program outputs the right answer
with probability at least 2/3\. But 2/3 is not special, you just need it to be
some probability bounded away from 1/2, in the sense that it can't get closer
and closer to 1/2 as the input size grows.

So it's certainly plausible that you could take advantage of this to reduce
the precision enough to get to the size bound Lipton mentioned, especially if,
as implied, you had the might of a hundred Google engineers working on it. And
the guy is so freaking smart and experienced in theoretical computer science
that chances are he thought of all this and considered it not interesting
enough to spell out for the people who will say "well actually."

[1]:
[http://www.cs.princeton.edu/theory/complexity/](http://www.cs.princeton.edu/theory/complexity/)

------
Tyr42
>Quantum Computers have been proved to be more powerful than classical.
_wrong_.

I take issue with that claim.

Take for example, the Deutsch-Jozsa problem. Given some function f, on n bits
to one bit, such that f is either {zero on all the possible inputs, or one on
all inputs}, or f is zero on half the inputs and one on the other half. To
tell which of those cases it is, it requires 2^(n-1) + 1 tests of f. You have
to test it on half the inputs, plus one.

With the added power of a quantum computer, we can solve it with only one call
to f.

Boom, there is exponential speedup with quantum computing. This is similar to
what lies behind Shor's algorithm for factoring.

Check it out, wikipedia has diagrams that I can't put in here.

[http://en.wikipedia.org/wiki/Deutsch%E2%80%93Jozsa_algorithm](http://en.wikipedia.org/wiki/Deutsch%E2%80%93Jozsa_algorithm)

EDIT: It seems he addresses this exact problem here
[http://rjlipton.wordpress.com/2011/10/26/quantum-
chocolate-b...](http://rjlipton.wordpress.com/2011/10/26/quantum-chocolate-
boxes/)

I apologize, I was a bit hasty to call him out, he does know what he is
talking about.

~~~
lauraura
Isn't "quantum computers are proven to be more powerful than classical" proof
that BQP != P, which would imply P != PSPACE, which hasn't yet been proven?

~~~
gizmo686
Not quite. Suppose there is some problem, whose best classical algorithm C,
and whose best quantum algorithm is Q, with Q in o(c) [0]. Given that this
relationship cannot exist in reverse (that is, quantum computers are at least
as powerful as classical ones), this would mean that quantum computers are
more powerful.

The statement BQP!=P means that there exists a problem that a quantum computer
can solve in polynomial time, but a classical computer cannot. This is a
stronger requirement.

For example, consider Shoore's algorithm, which can search an unsorted list in
O(sqrt(n)) time, strictly better than the O(n) time it takes a classical
algorithm.

[0] Note that the little-o means strictly less, whereas big-O means less than
or equal to.

~~~
j2kun
> Note that the little-o means strictly less, whereas big-O means less than or
> equal to.

Aaahhh! Please don't say that when you're clarifying a technical point about
theory!

Besides, it's explicitly stated in that article that "more powerful" is to be
interpreted as P != BQP.

------
judk
Interesting title. It is wordplay on the old movie title "Sex, Lies, and
Videotape", where 'videotape' gets changed to the topic under discussion.

Of those three, " videotape " is the only one that is obsolete, while the
others are timeless. While the original phrase goes increasingly obscure, the
wordplay remains fresh because the obsolete part is invisible.

------
mantraxC
> "With all due apologies to Soderbergh his title seems perfect for our
> discussion. There may be no sex, but there is plenty of sizzle surrounding
> quantum computation."

Right, the title "sex, lies and videotape" is perfect for the discussion.
There's no sex, and there are no videotapes, but there are quantum computers,
and the author's desperate attempt to cram some whimsy into his post.

I'll sum up the problem as I see it. The problem is that we're comparing real
(and thus limited by the reality of manufacturing etc.) classical computers,
with theoretically perfect quantum computers.

Well the idea of something is always better, faster and sexier (see, I worked
back sex into this) than reality, because as we get closer and closer to
building computers with a larger qubit number we'll start hitting all sorts of
engineering issues that would distance us from that perfect theoretical ideal
of a 100% efficient quantum computer.

And it may turn out that idealism is all the advantage quantum computers had
in the first place. It was all for naught. Not that we'll stop trying of
course.

