
Proof emerges that a quantum computer can outperform a classical one - jkuria
https://www.economist.com/science-and-technology/2019/09/26/proof-emerges-that-a-quantum-computer-can-outperform-a-classical-one
======
noname120
I'd like to take the opportunity to clear a misunderstanding that I've seen in
several threads related to quantum computing.

—————————————————————————————————————————————————————————

The classes of complexity of interest here are P, NP, BPP, and BQP.

— __P __corresponds to the problems that can be solved by a classical computer
(deterministic Turing machine) in polynomial time. For example finding a
shortest path between nodes in a graph is in this complexity class.

— __NP __corresponds to the problems where “verifying a solution” is in P. In
other words, it 's “easy” to check if a solution is actually valid. We know
that P ⊆ NP which means that when it's easy to find a solution, it's also easy
to check that a solution is valid (but we don't know if the opposite is true).
This class contains interesting problems such as prime factorization on which
all the current Web's security depends. It's easy to check if a factorization
is valid, but it's hypothesized that it's hard to actually find it. Now the
interesting part is that we're not _sure_ it's actually true, so the security
house of cards might actually tumble at some point (if it hasn't already
secretly).

— __BPP __contains all the problems that you can solve in polynomial time (so
like P) but with a chance of less than 1 /3 of being incorrect! In practice,
we run the algorithm several times to reduce the probability of being wrong to
less than 2^(−ck) (c is a positive constant, k is the number of times it's
run).

— __BQP __is probably the most interesting class here. It 's just like _BPP_
but on a quantum computer. Now the interesting part is that we don't know
(yet) an efficient way of finding the prime factorization on a classical
computer. But on a quantum computer, we have the infamous Shor's algorithm
which can solve this problem in polynomial time with a bounded error!

—————————————————————————————————————————————————————————

The current knowledge about complexity classes is that P ⊆ BPP ⊆ BQP. We don't
know how NP and BQP relate to each other.

What does this mean? We don't know if quantum computers can solve harder
problems _theoretically_. But they seem to do _sometimes_ in practice to the
best of our knowledge. Coming back to the Shor's algorithm example, we don't
know any classical algorithm that can solve the prime factorization problem as
efficiently. But this doesn't mean that such an algorithm doesn't exist!

Now you might think that all of this is only theoretical considerations that
only mathematicians care about. After all, we don't care if theoretically
there might exist efficient classical algorithms for supposedly hard problems
if we don't find them anyway right? This is a valid observation. If big enough
quantum computers become a reality one day, we'll be able to solve some hard
problems _right away_. However in the meantime, we might totally find
efficient classical algorithms making quantum computers less useful. Actually,
it has already happened last year[1]! A recommendation problem that we thought
was intractable by classical means (but easy to solve with quantum computers)
turned out to be solvable more easily than expected by a classical computer.
This classical algorithm draws inspiration from quantum algorithms however. So
if anything, quantum computing will force us to look at problems from another
perspective and solve them in novel ways.

[1] [https://arxiv.org/abs/1807.04271](https://arxiv.org/abs/1807.04271)

------
gus_massa
Note that they have a quantum computer that can solve a very specific type of
problem. (But it solves them exponentially faster than a classical computer).
They don't have a general purpose quantum computer, in particular, they can't
run Shor's algorithm to factorize numbers and break a big part of encryption
methods.

For a more detailed and better explanation than mine, you can read post of
Scott Aaronson
[https://www.scottaaronson.com/blog/?p=4317](https://www.scottaaronson.com/blog/?p=4317)
(HN discussion:
[https://news.ycombinator.com/item?id=21053405](https://news.ycombinator.com/item?id=21053405)
(595 points, 5 days ago, 207 comments))

~~~
statusquoantefa
> (But it solves them exponentially faster than a classical computer)

do you mean literally exponentially? or do you mean "a lot" faster?

~~~
cgearhart
Literally exponentially.

But keep in mind that QC does not mean you can solve _any_ problem
exponentially faster than a binary computer. If something is NP-Complete (or
any of the less familiar “hard problem” classes) then it’s still gonna be hard
for the quantum computer.

So you’ll get an exponential speed up for some specific problems like quantum
circuit sampling, but it can’t help you solve the Traveling Salesman Problem
any faster unless we find a new algorithm—and even then that would imply P=NP.

There’s still lots that QC could bring to the table even if it only works for
some problems, but it’s not expected to completely replace classical
computers—more like augment them with some new super powers.

~~~
primaryobjects
The Traveling Salesman Problem is indeed a potential application of quantum
computing. Grover’s Search could theoretically find a solution in quadratic
time (sqrt(n!) versus n!). On a physical quantum computer, this would have
profound impact to many different real-world applications.

~~~
teraflop
Grover's algorithm provides a quadratic _speedup_ , but sqrt(n!) is not
quadratic time; it's super-exponential.

------
neonate
[http://archive.is/QJ0ae](http://archive.is/QJ0ae)

------
conchy
No surprise coming from The Economist, this article has done the best job
(that I've seen) of explaining these complex topics in a language accessible
to most. I now understand the significance of this new discovery and its
limitations. And I like how they've stayed humble with their tie-in to
Watson's famous prediction in the last sentence.

------
bdamm
These little steps towards usable QC keep coming. Is there a paper or doc that
outlines what breakthroughs are still needed before we can consider ECC or RSA
broken? Is QC interesting for signal processing? How would having a million
Qbits in my iPhone change us?

~~~
krastanov
Predicting how home users will benefit from QC is like predicting the iPhone
on the day when Edison made an electronic tube. I am a researcher in the field
and have no idea how it would be useful in a smartphone.

However, here are the breakthroughs necessary for scalable QC: make the
quantum operations about 10 times more precise and the qubits about 10 times
more long lived (currently the information stored in the qubits decays a bit
too fast). Then make it possible to manufacture not just 50, but a couple of
thousand of the qubits. At that point you will be able to simulate important
chemistry (for drug discovery and material design) and important field
theories (for high energy physics and cosmology).

Breaking RSA will be possible later on when we get to millions of qubits, but
it is not that big of a deal as we can switch to other crypto schemes (but
recordings of important messages will be decrypted).

To your other question about signal processing: quantum computing is providing
technologies that would be very useful in metrology and the creation of crazy
sensitive sensors (sensing various fields or displacements or taking pictures
at crazy resolutions and signal to noise ratios).

~~~
todd8
Good points. It’s hard to predict where these QC developments will lead.

One little aside, John Ambrose Fleming[1] is credited for inventing the first
electronic tube (a vacuum tube based diode) around 1904 that initiated the
development of modern (tube based) electronics.

However, the work at Thomas Edison’s laboratories in previous decades on the
electric light bulb were almost certainly important prerequisites to Fleming’s
work. He even worked for Edison for a period of time.

[1]
[https://en.m.wikipedia.org/wiki/Fleming_valve](https://en.m.wikipedia.org/wiki/Fleming_valve)

------
lonelappde
How "big" is a qubit?

How many can fit in a server rack, now and in the near future?

~~~
krastanov
These are between micrometer and millimeter sized, depending on technology and
exactly what you count. But miniaturizing them is by far not the most pressing
problem. And it will not be a server rack for now, rather a helium dilution
refrigerator that works at less than 1 Kelvin.

------
talaketu
I love the teleological formulation "Proof emerges".

