## Solid State Quantum Computer Finds 15=3x5 — 48% of the Time 262

mikejuk writes

*"The Shor quantum factoring algorithm has been run for the first time on a solid state device and it successfully factored a composite number. A team from UCSB has managed to build and operate a quantum circuit composed of four superconducting phase qubits. The design creates entangled bits faster than before and the team verified that entanglement was happening using quantum tomography. The final part of the experiment implemented the Shor factoring algorithm using 15 as the value to be factored. In 150,000 runs of the calculation, the chip gave the correct result 48% of the time. As Shor's algorithm is only supposed to give the correct answer 50% of the time, this is a good result but not of practical use."*
## Maths (Score:3, Funny)

Sometimes 2+2=5, give the thing a break!

## Re:Maths (Score:4, Funny)

Of course 2 + 2 = 5. Take two strings. Tie 2 knots in each. Then tie them together and count the knots.

## Re: (Score:2)

If you define the operator + as +: x +_ y +_ 1 for all x,y in some magma, where +_ denotes the common addition +, then yes.

magma? volcanoes can do math now?

## Re: (Score:2)

If you define the operator + as +: x +_ y +_ 1 for all x,y in some magma, where +_ denotes the common addition +, then yes.

magma? volcanoes can do math now?

Yes. And they're really bad at it.

## Re: (Score:3)

Oh come on! They're right almost 48% of the time!

## Re: (Score:2, Funny)

## Re: (Score:3)

## Can someone explain... (Score:5, Insightful)

From TFA:

As Shor's algorithm is only supposed to give the correct answer 50% of the time, this is a good result.

How is it useful to have the correct answer 50% of the time? When designing computing algorithms, wouldn't you want it to return the correct answer 100% of the time?

## Re:Can someone explain... (Score:5, Informative)

Consider problems which take a lot longer to compute than to verify. It may be much faster to compute the answer with a quantum computer, then check it with a regular computer, than to simply compute it with a regular computer.

## Re: (Score:3)

The main problem is the "there is no solution" answer. What if we use the algorithm for a number N for several iterations and found that there are no valid decompositions. Can we ensure that the number is prime?

## Re:Can someone explain... (Score:5, Informative)

## Checking (Score:3)

Consider the "use quantum computing to get an answer, use regular computing to verify answer" post higher in this thread.

While it's computationally intensive to factor number, it's absolutely trival to check factors' prdocut against target number.

Yes, it's possible that the quantum computer will give a false positive half of the time like "13 = 3 x 5"

On the other hand, it's quite trivial to see that 3 x 5 make 15 and not 13 and thus this was a false positive.

It can be a viable pre-filtering technique. Curre

## Re:Can someone explain... (Score:5, Interesting)

That may be so, but computing the prime factorization of 15 is

not in that class.I don't think you should even get to call something a middle-school dropout can figure in his head faster than he can say

"Fries with that?"computation. So-called quantum computers still barely qualify as expensive but useless toys.Post again when a quantum computer can solve a real mathematical puzzle at a speed comparable to what a traditional computer can do.

That would be news.Scientists have been touting the supposedly vast potential of quantum computing for decades now. D-E-C-A-D-E-S. But thanks to fundamental limitations of the nature of what they are, it's

really hardto get them to barely work at all. It appears we could forever be stuck at the point where the qubits can be minimally processed but quantum decoherence can't be held off long enough to get a useful result. Meanwhile traditional methods of computing continue to forge ahead, although the rate of increase is slowing. Just keep in mind: quantum computing is 2500 years behind traditional computing methods in general, 175 years behind automated mechanical methods and more than 70 years behind electronic computers.Electronic computing methods overtook all other methods extremely quickly, but they faced only

technical challengesnot challenges posed by the fundamental nature of what they were trying to do. You can regard them in some ways as fancy abacuses: they literally count chunks of charge the way an abacus uses the position of beads to represent numbers (or in principle anything else). With qubits, you are attempting to getdefinite resultsby exploiting theindefinite characterof things like the spin states of electrons. That's not just hard. It may be intractably hard. But if somebody can get it to work it might be very valuable to the NSA and anybody else interested in cracking the security of computing systems.## Re:Can someone explain... (Score:5, Insightful)

Yeah, scientists were theorising about the Higgs-boson for deacdes as well. Sometimes it takes that long to get somewhere.

It's very early days for quantum computing. The fact that they've taken something from pure theory and made it actually do something is a fantastic indicator that they're onto something. So what if it takes another 5 decades to get there, the implications would still be incredible by that point.

## I'm sorry, that's a crappy example. (Score:3)

because-- we haven't 'gotten there' with the higgs yet-- still may NEVER..

## Re: (Score:3)

Er yes we have? Where have you been for the last month?

## Re: (Score:2)

Yes, I'm reporting back from next year: we have time machines. (No replicators or transporters yet.)

## Re: (Score:2)

(No replicators or transporters yet.)

Do you mean ST or SG replicators?

## Re: (Score:2)

And there were people who could outrun the first adding machines by doing it in their head. Nobody said that the this was in itself useful. It IS one more step along the way. It may be that at some point the next step will prove impossible or it may be that step by step we'll get there, but either way, we'll likely learn a few things that do prove useful.

All the same, I'm not going to hold my breath.

## Re: (Score:3, Insightful)

yeah. the wright brothers built some stupid linen and balsa wood thing that fluttered above the ground for a few seconds. useless. they've been talking about flight for centuries

morse can send little tappity taps on a wire? big deal. i can't figure out what it means, and does anyone actually believe we're going to string wires all over the country? impossible!

and i heard of this television device. what a crazy unweildy delicate gizmo. shows a fluttering image you have to squint to maybe make out what they a

## Re: (Score:2)

As has been pointed out in postings above, if you have a device that returns the correct factorization half the time, then by running it multiple times, you can easily determine the factors of a composite number--because it's easy and fast to _check_ the answers with a classical computer.

Or if you don't know whether the number is composite or prime, then by running it N times and checking the answer each time, you can reduce the uncertainty that a number which happens to be prime is prime to 1/2**N.

In both cases, you can arrive at negligible error rates in reasonable time.

(BTW, I believe factoring has been shown *not* to be NP hard, but it has some similarities: hard to come up with answers, easy to verify them.)

With only four-bit computations, it's useless. It needs to be scaled up by several bits just to show that their hardware approach has the

potentialto solve problems that aren't trivial.## Re:Can someone explain... (Score:5, Insightful)

There should be a "-1 Bitching That This Doesn't Meet My Personal Criteria For News" mod. Every. Damn. Article. Somebody has to come write an essay on how completely not interesting or impressive this is to them.

Yes, factoring 15 isn't particularly impressive. Thank you, Captain Fucking Obvious.

Now if you'd bothered to RTFA, you'd have noted it already directly discusses this:

So they can instantly factor numbers (well, with ~50% success), with an approach that *seems scalable*. That's news to me.

Maybe in a few months, there will be another story about how they failed to scale this approach up. That will be an additional piece of news. Failure can be news.

Some of us are interested in the journey, not just the destination.

## Re: (Score:3, Informative)

With qubits, you are attempting to get definite results by exploiting the indefinite character of things like the spin states of electrons. That's not just hard. It may be intractably hard.

Actually, the math and abstract procedure of how to do this is pretty well understood. The question of how to get definite answers from such quantum states is solved, in the sense the algorithm's results are very quickly and easily shown to have worked or not (and not just by multiplying the two factors, the result of the quantum portion of calculation has to be converted into actual factors via classical computation, and is obvious when this fails). The jump from probabilistic states to definite answers

## Re: (Score:3)

## Re: (Score:2)

I guess somewhat close to halfway there. If they had also computed the factorization of 14 with about 48% correct results, I'd be 100% more confident that they were onto something. What they've

shownis that they made a quantum device that can produce results of 3 and 5 about half the time. Wouldn't you be happier if you knew that it didn't produce 3 and 5 half the timeregardless how they program it?The original abstract (http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys2385.html) mentions t

## Re: (Score:3)

That may be so, but computing the prime factorization of 15 is

not in that class.Actually, it is. There is a reason that kids are taught multiplication long before factoring. It just happens that for numbers this small you can do both in your home.

If I handed you a pencil and paper and asked you to factor 1474 to primes it would take you a LOT longer than if I gave you the factors and asked you to multiply them.

Verifying the factorization of even a 2048 bit number by hand on paper is probably doable, though likely pretty tedious. Calculating those factors if they are just two primes

## Re:Can someone explain... (Score:5, Informative)

That depends. Sometimes you have a hard time finding a possible result, but verifying it is simple. Factorization is just such a problem. So you repeat the algorithm and test the result until the test succeeds. If this is on average faster than a completely deterministic approach, you have won.

## Re:Can someone explain... (Score:5, Insightful)

For a concrete example, the RSA public key includes a number n, which is the sum of two secret primes p and q. The encryption is broken if an attacker can derive p and q from n by factorization. ( http://en.wikipedia.org/wiki/RSA_(algorithm)#Operation [wikipedia.org] )

if you could factorize an RSA public key 48% of the time then it would be a pretty big deal, since it would render RSA completely obsolete.

## Re:Can someone explain... (Score:5, Informative)

RSA public key includes a number n, which is the sum of two secret primes p and q

Just FYI, it's the

productof two secret primes. Product is for multiplication, while sum is for addition.## Re: (Score:2, Funny)

Well, at least the poster was half right...

## Re: (Score:2, Insightful)

But we are a very long way from that. Right now it takes enormously more effort to do the job with a quantum computer and it can only be done

at allwith very small numbers like 15. And the results show that hardware is not scalable. It's supposed to get the answer right 50% of the time and it only gets 48% in 150,000 runs. The 2% difference is significant and whatever the cause of that is, it's almost certain to not scale well:If a 4 bit number gives you a 48% correct rate, that means that it gets the

## Re: (Score:3)

That's a lot of extrapolation from a single data point.

## One word: (Score:5, Funny)

Close enough for government work.

## Re: (Score:2)

I'm satisfied with that answer.

Not really, but I did get a good chuckle...

## Re:One word: (Score:4, Insightful)

In this case, I suspect that the NSA would readily agree... This quantum computer is far too

smallfor any practical purposes that couldn't be brute-forced with a TI-83 much more easily; but tepid accuracy isn't a big deal if checking your work is computationally inexpensive...## Re:One word: (Score:5, Funny)

Close enough for government work.

Did you count that with a quantum computer, because by traditional methods I get 5 words 100% of the time.

## Re:Can someone explain... (Score:5, Funny)

How is it useful to have the correct answer 50% of the time?

Cat life-support devices.

## Re: (Score:2)

I assume that you are supposed to run the algorithm a few times and see which answer comes up most often (about 50% of the time) and assume it is true. The point being that running this algorithm a few times is significantly faster than running the equivalent algorithm on a non-quantum(?) computer (particularly when dealing with huge near-prime numbers), so what you lose in accuracy you make up for in time.

This is the basis for most "quantum" things (such as qubits); you can theoretically encode an infinite

## Re: (Score:3)

Nah, as others have pointed out, what you do is run the Shor's algorithm, then verify it. If it's wrong, run Shor's again. If it's right, you know you have the factorization. In this way, you can be 100% sure that you've correctly solved the problem, even if Shor's only provides the correct answer some percentage of the time.

What I don't fully understand is why 48% makes this impractical. Having not read TFA, the only way I can imagine that would be the case is if somehow not having exactly a 50% chance

## Re:Can someone explain... (Score:4, Informative)

I believe it's just confusing wording. They're saying 48% is good because at best it could only have been 50%. It's impractical because it is only 4 qbits and so conventional computing can easily do the job faster and cheaper for numbers that small (for that matter, it' small enough that a lookup table is an attractive solution).

## Re:Can someone explain... (Score:4, Insightful)

By that law I predict Shor's algorithm works in practice as follows:

6=2x3 96%

15=3x5 48%

35=5x7 24%

77=7x11 12%

143=11x13 6%

Good luck breaking RSA.

## Re: (Score:2, Insightful)

It's useful because checking that the answer is correct or not is trivial, and having to run the algorithm twice (long term average) is still exponentially faster than relying on classical methods.

## Re:Can someone explain... (Score:5, Informative)

How is it useful to have the correct answer 50% of the time?

In many cases, it is

veryuseful. If you need to crack a code by factoring a 200 digit number, getting the right answer 50% of the time would be fantastic. You just try repeatedly until you get the right answer.When designing computing algorithms, wouldn't you want it to return the correct answer 100% of the time?

Of course. That is why the "quantum" computer would be just part of the solution. Overall, your algorithm would look like this:

correct_answer() {

for (;;)

answer = quantum_result();

if (verify_answer(answer)) {

return answer;

}

}

}

This solution would be

good enoughfor any problem where verifying an answer is much faster than finding an answer. Most NPC problems [wikipedia.org] fall into this category.## Re: (Score:2)

Most NPC problems fall into this category.

Actually, by definition, *all* NP-complete problems fall into this category (unless P = NP)

## Re: (Score:3)

Well, when I'm brute-forcing the bits of a 128-bit encryption key, I get the right answer 50% of the time too. The problem is that I need 128 answers ;)

No, your problem is that you have no way of verifying individual bits.

I remember the scene from Terminator 2, where the teenage John Conner is stealing money from an ATM. He is cracking the encryption, and each digit takes the

same amount of time. But that is nonsense. Once you find the first digit, you are 90% done, and all the others combined would take only 10% more time. The other problem is in the final scene, where they are fighting the T-1000 in the smelting plant, and Arnold destroys him by shoo## Re: (Score:2)

Sometimes it's good enough, sometimes it's not.

## Re:Can someone explain... (Score:5, Insightful)

An algorithm that could factor a 4096 bit number even 10%

of the time would be enough to consider 4096 key as completely unsafe

for cryptography.

It is easy enough to verify the result.

## Re: (Score:2)

Well, since time isn't linear in this case, and so each step/change (time is advancement through possibilities) is not fixed, you can bump into 48%, when measured in linear time.

## Re: (Score:2)

Just like converting between units:

(1/3)+(2/3)=1;

0,333333333~+0,666666666~=0,99999999~;

1=0,99999999~.

So in this case, the conversion hit 48% linear time here (and 52% elsewhere, hehe), so (48+52)/2=0.

But math isn't pure logic, and so there can never be proof/disprove of what I have typed in this post...

## Re: (Score:2)

OK, I'm sorry; (48+52)/2 equals 50 (%). I even forgot what I was calculating... Damnit. I realy need to stop taking these cianide pills.

How stupid of me to see the Universe as a corral, with all possible branches (time is change, right?), counting in relativity (in time), multiverse Quantum Physic behavior (48% versus 52%, damn how retarded) and the fact that we are observing multiverse behavior in just 'side' of the universe, while testing a mathmetical theory without checking all infinite numbers. Holy sh

## Re: (Score:2)

If I want to be on the convincing bandwagon, I'd get into politics.

Instead I'd like to see you prove me wrong.

Proof in front of every reader here why I'm wrong, and even I will be convinced that I am stupid.

Some would call this "put up or shut up". There; I made a punchline. Like me now?

## Re: (Score:2)

Just run the program multiple times and take the mode.

## Re: (Score:3)

I have a device that gives you the winning lottery numbers ahead of time, but it has only a 10% chance of being correct. Is it useful?

## Re: (Score:3)

10% accuracy is useful if their are less than 10 results? Like, in case you want to make this 8-number lottery more exciting by reducing your chances? Actually, that's brilliant. The 8-number lottery wouldn't pay out well, but it'd be so cheap everyone would enter just for the fleeting feeling of winning something... They might even go so far as to reduce their own chances to make it more of a rush when they win. We'll be rich.

## Re:Can someone explain... (Score:5, Funny)

If you can factor really large prime numbers,

I can factor really large prime numbers in my head.

## Re: (Score:2)

Actually, grade-school children can factor really large prime numbers in their heads. The trick is factoring the product of two really large prime numbers in your head without knowing either of the primes. You can get two of the factors (one and the product) but neither of those is particularly useful to the problem at hand.

## Re: (Score:2)

## If I calculate 135257x15643 in my head (Score:2)

If I calculate 135257x15643 in my head, the correct answer is found pretty close to zero in five attempts. Is that good?

## Size, not reliability (Score:5, Interesting)

## Why isn't 48% good enough? (Score:2)

## Re: (Score:3)

Why isn't getting the correct answer 48% of the time impractical?

It's not the 48% that is not good enough, it's factoring a number such as 15, which is easy enough to do already without going through all the trouble of using a quantum computer. Basically, this is a very significant stepping stone, but we're not living in a world of quantum computing yet.

## Re: (Score:3)

Then the summary was worded terribly.

## Re: (Score:2)

## Re: (Score:3)

And besides, the quantum computer got a higher score on that math problem than the average American student. That's got to count for something.

## Re: (Score:2)

Don't know much about higher mathematics, but based on the post and the explanation of Shor's Algorithm from wikipedia, its not an issue of how easy it is to factor a small number or how practical. Its more of a benchmark for quantum computing. If the ideal success rate is 50%, then 48% is an indicator of how well the system is operating.

And besides, the quantum computer got a higher score on that math problem than the average American student. That's got to count for something.

Not really. 48% is plenty good enough, if you have a solid state quantum computing device that can use Shor's algorithm on larger numbers.

As mentioned above by other people, the way you'd use Shor's algorithm is use it to get the factors, then multiply them together using a conventional computer and see if you get the original number back. Multiplication is a pretty fast operation, compared to factorization, so the verification isn't really very costly. With a 50% success rate for Shor's algorithm, on ave

## Re: (Score:2)

## Well heck, Intel might buy it. (Score:5, Funny)

Historically, they're a bit more tolerant about that math thing.

## Re: (Score:2)

Historically, they're a bit more tolerant about that math thing.

Yes, they do show at least a qubit of interest in this.

## NSA likely already built one (Score:5, Interesting)

It seems that quantum computing has consistently been viewed as harder than it really is, judging by the ever-decreasing timescales between breakthroughs. Judging from the history of cryptography, and the military value of being able to break RSA, it's not unreasonable to expect that the NSA may have been trying to build such a chip for some time and could potentially have succeeded.

Some months ago James Bamford, who is the premier chronicler of the NSA and has a history of being given accurate leaks, claimed the NSA had made a "huge breakthrough" in its ability to break codes [wired.com] - and that the datacenter they're currently building is a part of the solution. The NSA denied everything of course. But if academics are now able to build a working implementation of Shors algorithm for small numbers, that strongly implies that a focussed team with practically infinite budgets could have already succeeded in building one that can handle crypto-sized numbers.

## Re:NSA likely already built one (Score:5, Insightful)

And before anyone freaks out and thinks that the NSA is reading their e-mail, keep in mind that they have to be

veryselective about how and when they use results from their quantum computer. This is similar to breaking ENIGMA--you want the enemy to think that their codes are secure, so you don't suddenly counter all of their plans perfectly. You certainly don't turn this on e.g. classical organized crime, as that could give away your capabilities on a considerably less valuable target.## Re: (Score:3)

Nah, they just have to act "correctly" on the intel without it being statistically obvious.

## Re: (Score:2)

## Re: (Score:2)

## Re: (Score:3)

And before anyone freaks out and thinks that the NSA is reading their e-mail, keep in mind that they have to be very selective about how and when they use results from their quantum computer. This is similar to breaking ENIGMA--you want the enemy to think that their codes are secure, so you don't suddenly counter all of their plans perfectly. You certainly don't turn this on e.g. classical organized crime, as that could give away your capabilities on a considerably less valuable target.

That's not much comfort, because there's a subtle distinction you blur. After cracking ENIGMA, they were aware of much more than they acted upon, in order to keep the breakable communication flowing. It doesn't mean they decided not to crack as much enemy communication as possible. Similarly, it doesn't mean they won't actually monitor "classical organized crime," but rather that they might not act upon the information they glean from monitoring it.

The only thing that will limit their reach is capacity. T

## Re: (Score:2)

It seems that quantum computing has consistently been viewed as harder than it really is, judging by the ever-decreasing timescales between breakthroughs. Judging from the history of cryptography, and the military value of being able to break RSA, it's not unreasonable to expect that the NSA may have been trying to build such a chip for some time and could potentially have succeeded.

Well, of course, they got it from the aliens at area 51 decades ago. They've just been spoonfeeding us the tech, bit by bit.

## Re: (Score:2)

or perhaps someone managed to sell them the idea that by using billion bucks they would then have that?

## Re: (Score:2)

Absolutely. It is naive and foolish to believe that there is any publicly available encryption that actually works. Some things are

born secretand will stay that way until it's no longer usefulDon't be silly. There are symmetric ciphers that have been proven to be "unbreakable" in a sense that to open them would take time comparable to brute forcing.

Factoring large prime composites and RSA is another matter, but to entangle 4000 qubits right now? I seriously doubt it.

And I think you're also wrong on the availability aspect. It's naive to think that anything but public encryption methods actually work.

## 50% of the truth (Score:2, Interesting)

Could it be that the reason the algorithm is only supposed to get the rich answer 50% of the time is that there is a parallel universe out there where 5 x 3 is not 15???!?!?

## Huh? (Score:2)

I get the correct answer 99% of the time. Too bad I hit that remaining 1% during my entire period of elementary school :/

## Re: (Score:2)

A little offtopic, but your post reminds me of something I read not so long ago

"If religions say that life is eternal, why are they so worried about what you do in your first century?"

## The most important part is knowing the question. (Score:2)

## What comes after? (Score:2)

If quantum computing is the end of encryption as we know it, then soon the internet as we know it will end too.

How will electronic communication be secured after quantum computing?

Someone call Al Gore: We need a new internet.

## Re: (Score:2)

In any case fundamentals of cryptography should be the least of your concerns as vulnerabilities are usually found in the implementation and usage.

## solid state quantum computer, since when? (Score:2)

Solid-state sounds a lot cheaper.

## Oh no! That's my public and private keys! (Score:2)

Crap! I knew it was only a matter of time before these new fanged quantum computers cracked my 4 bit RSA encryption key!

## Bourbon (Score:3)

## New Math (Score:2)

Its sufficient to understand what you are doing. Never mind getting the right answer [youtube.com].

## Great! Congrats! (Score:5, Interesting)

Disclaimer: I am a former researcher in the field, left to some other job.

What you can see at UCSB is what happens when a team of scientists which ae skilled in engineering, working as a team, and collaborating with everybody happens to have the right guy as the leader (with the right policy about co-authors on publications).

Everybody whom i met from this team was open, honest, and friendly; they have worked hard and long on it and they accumulated some of the best people.

They deserve the success they have now! I think there may be a small break now in their publications, since i have the ffeling they now may work on overcoming the next big roadblocks (but now they they have all the backing they could need for it).

I also have to state it will be a long long way to the first QC. While i believe that every step like this will be more than just replicated at the NSA, i believ that they wont be more than 10 years ahead, and i estimate 20y-30y until qc works better than classical qc (although I also hope and believe that breaktroughs are possible).

## Re:That's no moon... (Score:5, Funny)

To be fair, it could have been either until we looked.

(And you could have posted either here or at the correct story.)

## Re: (Score:2, Insightful)

It was both a moon and a space station at the same time.

To the jerk who modded the parent down:

Read up on schroedinger's cat you doofus.

Then you can have your geek card back.

## Re: (Score:3, Informative)

Schrödinger wrote about the cat idea in order to demonstrate how ridiculous that particular model of quantum physics is; he'd be rolling in his grave if he knew that people were taking it as truth...

## Re: (Score:2)

## Re:That's no moon... (Score:4, Informative)

That case happens rarely. The case you're actually looking for is values of a where the function has even period.

The reasoning behind it is this:

Suppose that N has at least two distinct prime factors. (If it isn't, then N is either prime or a perfect power of a prime. There are efficient algorithms for detecting the latter case.) Further suppose that the function f(x) = a^x mod N has minimum period 2r for some r. (That is, f(x+2r) = f(x), but f(x+q) f(x) for any q < 2r.)

In this case, a^(2r) is congruent to 1 modulo N, but a^r is NOT congruent to 1 modulo N. That is, a^r is a square root of unity modulo N, but it isn't congruent to 1. If it also isn't congruent to -1 (which is the case that you mentioned), then it's a nontrivial square root of unity.

Now consider the number d = gcd(a^r-1, N). If d=N, then N is a factor of a^r-1, that is, a^r is congruent to 1 modulo N. This is a contradiction (since we eliminated this case above), so it can't happen. Similarly, if d=1, then a^r is congruent to -1 modulo N, which is the other case that we eliminated above. (Exercise: prove this!)

So d is a divisor of N (because it's the gcd of N with some other number), but it isn't 1 or N. Therefore, it's a nontrivial factor of N.

Of course, it's not obvious that there should be an a for which f has even period, but that's where the hardcore analysis comes in.

## Re: (Score:2)

## Re: (Score:2)

As others have said the real issue isn't the success rate they have. The real question is can they make it scale to bit counts where it is actually useful while maintaining a tolerable success rate? That means increasing the number of bits dramatically.

## Re: (Score:3)

I don't understand how this isn't of practical use.

Size. In order to attack larger problems, you need more entangled qubits. For some mixture of engineering and physics reasons that I am deeply unqualified to discuss, building systems capable of keeping qubits in their proper state seems to get increasingly hairy as the number of qubits you need grows.

That's why '15' is a popular number to factorize in quantum computing experiments. It's really small. Since classical computers are far more mature, and a great deal cheaper, the problems that very small quant

## Re: (Score:2)

No acceptable compiler refactors math equations in a way that breaks numerical accuracy, unless the user explicitly requests it (gcc's

-funsafe-math-optimizationscomes to mind). Optimizing compilers are useless if they give the wrong answers for the most compute-intensive problems.## Re: (Score:2)

## Re: (Score:3)

I agree. The AC's comment which is blatantly wrong is more specific:

High-performance numerical algorithms are written with the expectation of a well-behaved compiler which will

notattempt to refactor mathematical expressions on the basis that it may change the numerical error. The mathematicians wh## Re:First post - from a quantum computer (Score:4, Funny)

They've done studies, you know. 48% of the time, it works every time.