Quantum Computer Demoed, Plays Sudoku

prostoalex writes "Canadian company D-Wave Systems is getting some technology press buzz after successfully demonstrating their quantum computer (discussed here earlier) that the company plans to rent out. Scientific American has a more technical description of how the quantum computer works, as well as possible areas of application: 'The quantum computer was given three problems to solve: searching for molecular structures that match a target molecule, creating a complicated seating plan, and filling in Sudoku puzzles.' Another attendee provides some videos from the demo." Anyone want to guess how long before "qubit" gets compressed to "quit" (as "bigit" became "bit" in the last century)?

BIGIT??

[CmputrAce]

Never heard of one (bigit). I have, however, heard of the "binary digit" that was shortened to "bit". Given that history, "qubit" is short for "quantum binary digit" - which is an oxymoron since quantum digits can be any (or all) of several states, not just on or off (binary). A more accurate acronymish shortening would be "quigit" - which sounds awkward enough to be shortened to "qit", (pronounced KIT rather than QUIT to avoid confusion).

I think "qubit" is here to stay, though.

Re:For real?

[jason8]

Apparently not a true quantum computer. From a wired news article:

D-Wave held its first public demonstration Tuesday of a machine it claims uses quantum mechanics to solve a certain type of problems, such as searching a database for matching molecular structures.

But the company did not make the machine available for inspection and instead showed video from a remote location, saying it was too sensitive to be easily transported.

And notwithstanding lofty claims in the company's press release about creating the world's first commercial quantum computer, D-Wave Chief Executive Herb Martin emphasized that the machine is not a true quantum computer and is instead a kind of special-purpose machine that uses some quantum mechanics to solve problems.

Re:Traveling Salesman

[gazbo]

Even if you could solve TSP in polynomial time on a quantum computer, it still wouldn't show that P=NP as the machine would be nondeterministic. The goal of quantum computers is to sidestep the NP issue, not reduce it to P.

Common misconceptions

[rbarreira]

To save some work to people replying to misconceptions, here's a list of the common misconceptions about quantum computing that I've seen lately:

• Quantum computers can solve NP-complete problems quickly (in polynomial time) -> not true, the speedup given by Grover's algorithm [wikipedia.org] is quadratic, not exponential. This means that an NP-complete problem which would take O(2^n) in a classical computer would take O(2^(n/2)) in a quantum computer, which is clearly not polynomial time in n
• Quantum computers with N qubits are as efficient as 2^N classical computers -> not true, not all algorithms can get an exponential speedup with quantum computing
• Quantum computers will render cryptography useless -> not true, breaking asymmetric ciphers with QCs are subject to the quadratic speedup I explained above which means it will be enough to double the size of the key in order to account for QCs. Some symmetric ciphers (i.e. public key systems) are broken by quantum computing (for example RSA and discrete logarithm), but it is thought that there are some symmetric ciphers which are not vulnerable to attacks by QCs (excluding by the grover search algorithm, which as I explained above is not very hard to account for). Quite ironically, I remember reading that the same attack which renders discrete logarithm public key cryptography useless also allows for the existence of a public key encryption which requires fast calculation of discrete logarithms.

Re:Traveling Salesman

[Anonymous Coward]

You are pretty much correct--traveling salesman is NP-hard and most theorists believe that BQP, the class of problems efficiently solvable by a quantum computer in polynomial time, is strictly smaller than NP (and therefore contains no NP-complete problems). This is, of course, not shown--for all we know, it could even be strictly bigger than NP. The evidence is that the only two problems quantum computers can solve in polytime right now that a turing machine can't are integer factorization and discrete log, neither of which is believed to be NP-hard.

BTW, of course a problem instance must fit in memory--but the idea is that we should be able to build a 1000 qubit computer, while going through 2^1000 possibilities to brute-force a problem of size 1000 is intractable. But with our knowledge now, even if you fit a traveling salesman instance, the quantum computer wouldn't know what to do with it.

As GP pointed out, we do have excellent approximations for TSP and most practical problems--the issue is mathematical--that we don't have algorithms that can guarantee the absolute best solution. The one place quantum computers are potentially useful is crypto--nearly all of which revolves around the hardness of factoring and discrete logs (which I think is a very strange coincidence, if it is one).

"Bigit" never existed.

[caveat]

Claude E. Shannon first used the word bit in a 1948 paper. He attributed its origin to John W. Tukey, who had written a Bell Labs memo in 9 January 1947 in which he contracted "binary digit" to simply "bit".

No mention of "bigit", seems to have just been invented today.

http://en.wikipedia.org/wiki/Binary_digit [wikipedia.org]

More info...

[Panaflex]

Some more videos...
High level explanation [youtube.com]
Protein matching [youtube.com]
Sudoku [youtube.com]

Also, here's some slightly older talk at Stanford with a higher-level audience [stanford.edu]

Additionally, it's not exactly a "true quantum computer"(tm) - but it utilizes quantum mechanics as a quantum computer would. So it quacks like a duck, etc.

Ask the companies founder - here's his blog:

[RMH101]

Geordie Rose's blog: http://dwave.wordpress.com/ [wordpress.com]

Re:Traveling Salesman

[hotdiggitydawg]

all a Sudoku puzzle is, at it's core, is a depth first search.

Which is not an algorithm that runs in polynomial time. It is a DFS of all (legal, remaining) permutations, which is an exponential number.

even on a moderately fast PC a DFS is fast enough to get a solution to a Sudoku puzzle in the blink of an eye.

Regardless of how easy a 9x9 grid seems, Sudoku is still at its core an NP Complete [u-tokyo.ac.jp] (PDF warning) problem. Why is it therefore any less valid than any other NP complete problem? Travelling Salesman is also pretty easy with less than 10 nodes... likewise you can feasibly crack any encryption scheme by brute-force if you constrain it to have a tiny key size. It's all about scale.

The beauty is, if you solve any NPC problem you solve them all, by definition. So, Mr. Smarty Pants, if your Sudoku solver is good enough to solve any grid in polynomial time, please show the rest of us, as you've just cracked every encryption scheme invented to date.

Yeah, I didn't think so.

Re:Traveling Salesman

[Anonymous Coward]

We already have a solution to the Travelling Salesman Problem. Do you really think NP-complete problems are so hard and mystical that we can't currently run computers to solve them? Yes, the best (100% accurate) solutions we have currently increase the execution time exponentially with the problem size. So what?

NP-complete != impossible. NP-complete != slow. NP-complete = slow for big problems. A few years ago I was playing around with NP-completeness in my spare time. Using GNU Guile [gnu.org] (hint: this was not a blazingly fast implementation), I was able to solve a typical n=1000 subset sum [wikipedia.org] instance in under a minute on commodity hardware.

With a clever heuristic or two, and a clever programmer, and a clever optimizing compiler, I wouldn't be surprised if USPS could solve Travelling Salesman Problems where the number of nodes is on the order of magnitude of 10000, without overly exorbitant hardware costs. Maybe I'm naive, but I don't think USPS has more than 10000 stops on most of its shipping routes.

If USPS wanted to use the Travelling Salesman Problem, they would be using it already. Using a quantum computer would do nothing for them but add headaches and cost. NP-complete problems are only hard when you're looking at big data sets, and I just don't think USPS making shipping routes would fall into that category.

Re:Traveling Salesman

[GBladeCL]

What are you talking about? DFS is only linear in the best case where the solution is on the first branch. If the depth of the tree is d then at the worst case you will have to search every node which would be 2^(d+1) - 1 nodes. That's exponential time.

There is already a good solution

[Peaker]

There is already a P partial solution to the travelling salesman. It does not find the best path, but it is proven that it finds at worst a path that's twice as long.
With a few heuristics, the worst case becomes very rare, and it usually finds something closer to the best solution.

So if we solve the NP travelling salesman in a perfect way, at most we'll get paths that are half the length.
That could be an improvement, but not a revolution.