## The Limits of Quantum Computing 228

Posted
by
kdawson

from the floor-wax-and-dessert-topping dept.

from the floor-wax-and-dessert-topping dept.

The Narrative Fallacy writes

*"Scott Aaronson has posted a draft of his article from this month's Scientific American on the limitations of quantum computers (PDF) discussing the question: Will quantum computers let us transcend the human condition and become as powerful as gods, or are they a physical absurdity destined to be exposed as the twenty-first century's perpetual-motion machine? Aaronson says that while a quantum computer could quickly factor large numbers, and thereby break most of the cryptographic codes used on the Internet today, there's reason to think that not even a quantum computer could solve the crucial class of NP-complete problems efficiently. Aaronson contends that any method for solving NP-complete problems in polynomial time may violate the laws of physics and that this may be a fundamental limitation on technology no different than the second law of thermodynamics or the impossibility of faster-than-light communication."*
## As usual (Score:2)

## Re:As usual (Score:5, Funny)

## Re:As usual (Score:4, Insightful)

## Re:As usual (Score:4, Interesting)

couldbe mathematically/logically impossible, but calling it "violating the laws of physics" should be a misnomer. Would a number that's greater than 2 and less than 1 violate the laws of physics? How about a triangle with 4 sides?## Re: (Score:2)

How about a trilogy in five books? Don't Panic.

## Re: (Score:2, Informative)

From a mathematic point of view, solving an NP-complete problem in polynomial time is not a problem at all. The class NP is defined as the set of problems that a non-deterministic Turing machine can solve in

polynomial time.## Best metaphor ever (Score:5, Funny)

## NP complete is solved by nature (Score:2, Interesting)

NP completeness is only a problem for us because we don't understand the mechanics of the solution. It is not an unsolvable problem,

## Re:NP complete is solved by nature (Score:5, Informative)

Maybe you're thinking of the often repeated claim that one can find a Steiner tree (the determination of which is NP-complete) using soap and a physical setup. But that, too [scottaaronson.com], is false.

Kieu tried to find a way to make quantum trickery (in ordinary quantum computers) calculate NP-complete problems (and a lot more) in polynomial time, but his hypercomputation algorithm was later disproved. So just as P = NP in classical computing seems to be very hard to prove or disprove in the general case, so appears its quantum mechanical analog to be, as well. (But as the paper states, some computers using exotic physics could be able to solve NP-complete problems easily; for instance, a time-traveling computer could solve PSPACE-complete problems without much difficulty, and if loop quantum gravity is true, a computer making use of it might be able to solve NP-complete problems as well.)

## Shortest path (Score:2)

## Re:NP complete is solved by nature (Score:4, Interesting)

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What I believe the GP means is that using electricity as described earlier in the thread would be "poor" in a programmable sense because it would be rather difficult or tedious to recreate the p

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I was thinking similar stuff to you with regards to the beads thing that the problem was getting shifted to how the beads are connected and such, though I wasn't able to think about it so clearly as you put it because I was having trouble

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You may end up finding out that yes - the electricity makes it through the 'maze' in the same amount of time each time.

But you may find out that each time it passes through the maze, it takes a different route. IANAP (physicist), though.

Letting the concept ruminate, it would probably end up that said electricity would take the same route through the maze eac

## Re:NP complete is solved by nature (Score:5, Informative)

All you've done is parallelize the problem. Each string is its own highly limited computer. You'll note that to scale to larger graphs, you need to scale the number of strings. That is, you kept the running time the same but had to increase the power of the computer in proportion to the number of edges. Each bead, as a place where forces are summed, also represents a limited power computer. Diskstra's algorithm runs in roughly O(V^2) time when E is comparable to V^2, or O(E*log(V)) time when it's much lower. Not coincidentally, your physical computer's computational power grows at comparable rates.

Physics doesn't make a particularly more or less efficient computer than a Turing machine; there's no good comparison. What it does do is provide ways to massively parallelize some problems. The shortest path algorithm can be done in O(edges in path) time on a conventional computer with unlimited processors and no communications bottlenecks, which is very similar to what you have described.

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As mentioned, the shortest path algorithm is polynomial. Perhaps you were thinking of the NP complete Traveling Salesman Problem? Even if it coul

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## Okay Then. (Score:2)

Byebye Star Trek future... *sobs*

## Re:Okay Then. (Score:5, Funny)

We need a way to disregard or at least completely reinterpret the laws of physics, and do without money, and all get on, and find entire worlds whose populations all conform to some stereotype.

And are green.

## Re:Okay Then. (Score:4, Funny)

today!## Re: (Score:2)

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(But yeah, it's a TV show, they're stupid like that.)

## Superb doctors (Score:2)

Nobody is obese because nobody has to be. Medicine in the Star Trek universe is IMHO far more advanced than their grasp of physics is.

## Star Trek does not voilate physics. (Score:2)

## Trek Talk Never Off Topic! (Score:2)

We don't need Quantum computing for a Star Trek futre. We need a way to disregard or at least completely reinterpret the laws of physics, and do without money, and all get on, and find entire worlds whose populations all conform to some stereotype. And are green.It's interesting that the Star Trek universe doesn't seem to have "money", yet, they do have scarcity. They often had shortages of starships, and they had limits as to how fast they could develop technology. And, there really doesn't seem to be m

## Re: (Score:2)

Only if you define "better economy" as "access to spaceships" (and that point isn't actually even accurate in Star Wars...). I mean, Owen Lars was a moisture farmer. Vader started out as a slave. There's a huge criminal underground/slums, etc.Yeah, but you could build up so much money that you could be a Trade Federation, and build up your own giant robot army. Don't see that in Trek. I wonder who had the better life, though, before defeat - Harry Mudd or Jabba the Hut?

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## Seems to me... (Score:5, Insightful)

If we want to start talking in that tone, well our "micro" processors and new fangled technologies didn't solve the mysteries of the universe, so we should have stuck with computers the size of buildings that have trouble doing more than adding, subtracting, and multiplying. Hell - they were good enough to design the atomic bomb and our space program, and that's good enough for me!

Besides, does anyone seriously think that we'll gain God-Like-Powers from quantum computing? The only God Mode I expect from the computer starts with the phrase 'iddqd'.

## Re:Seems to me... (Score:5, Insightful)

If I were offered a single magic power over the physical world it would be either invisibility or the ability to see behind walls. If quantum computing means whoever has it can bust all the crypto's in a realistic time (eg: a second or two), then we have a problem, because that group of people will have God Mode when it comes to money, intelligence, all that. Worse is if we don't know they have quantum computing, then all our shit is belong to them.

If quantum computing means they can break a crypto in a month whereas before it took them forever, there is hope in that quantum computing will become prevalent before anyone is able to totally compromise all communications. Of course I'm guessing there is no such agency that can do this yet.

## Re:Seems to me... (Score:5, Funny)

NoSuchAgency that can do this yet## Re:Seems to me... (Score:5, Interesting)

Well considering it's rumoured (and probable) that electricity was used and available significantly before its public demonstration, also with radio communications and other groundbreaking technology, one can reasonably predict that a whole lot of people are up to stuff which the public will find out about only when too many other people know how its done. A bit like the situation with audio bugs. Once bugging of meetingrooms and so on became too easy, people just decided to make all the basic tech public so everyone can see how trivial it is and take appropriate precautions when necessary to counter the possibility. But before that, for decades, bugs were tinfoil hat fodder and most people didn't believe in them. People tend only to look behind doors if they have stood there themselves.

I suppose its time for someone to sit on the toilet for a week and come up with a cryptographic algorithm that resists a quantum computer, whatever that happens to be.

## Re: (Score:2, Interesting)

Something based on Quantum Cryptography [wikipedia.org] maybe?

## Re:Seems to me... (Score:4, Informative)

If all else fails, it's back to the days of number stations and couriers, since symmetric crypto will resist quantum computers fairly well (just double the key size to thwart Grover's algorithm [wikipedia.org]).

## Magic Power (Score:2)

If I were offered a single magic power over the physical world it would be either invisibility or the ability to see behind walls.I'd choose the ability to make other people do as I wish.

## Re:Not all encryptions are prime-based (Score:5, Informative)

I wondered the same thing. I've talked to several experts and have been told that, indeed, a quantum computer can break elliptic curve encryption efficiently. This [psu.edu] paper, for example, seems to cover adapting Shor's algorithm to breaking elliptic codes.

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## The last question... (Score:5, Interesting)

Following by Isaac Asimov

The last question was asked for the first time, half in jest, on May 21, 2061, at a time when humanity first stepped into the light. The question came about as a result of a five dollar bet over highballs, and it happened this way:

Alexander Adell and Bertram Lupov were two of the faithful attendants of Multivac. As well as any human beings could, they knew what lay behind the cold, clicking, flashing face -- miles and miles of face -- of that giant computer. They had at least a vague notion of the general plan of relays and circuits that had long since grown past the point where any single human could possibly have a firm grasp of the whole.

Multivac was self-adjusting and self-correcting. It had to be, for nothing human could adjust and correct it quickly enough or even adequately enough -- so Adell and Lupov attended the monstrous giant only lightly and superficially, yet as well as any men could. They fed it data, adjusted questions to its needs and translated the answers that were issued. Certainly they, and all others like them, were fully entitled to share In the glory that was Multivac's.

For decades, Multivac had helped design the ships and plot the trajectories that enabled man to reach the Moon, Mars, and Venus, but past that, Earth's poor resources could not support the ships. Too much energy was needed for the long trips. Earth exploited its coal and uranium with increasing efficiency, but there was only so much of both.

But slowly Multivac learned enough to answer deeper questions more fundamentally, and on May 14, 2061, what had been theory, became fact.

The energy of the sun was stored, converted, and utilized directly on a planet-wide scale. All Earth turned off its burning coal, its fissioning uranium, and flipped the switch that connected all of it to a small station, one mile in diameter, circling the Earth at half the distance of the Moon. All Earth ran by invisible beams of sunpower.

Seven days had not sufficed to dim the glory of it and Adell and Lupov finally managed to escape from the public function, and to meet in quiet where no one would think of looking for them, in the deserted underground chambers, where portions of the mighty buried body of Multivac showed. Unattended, idling, sorting data with contented lazy clickings, Multivac, too, had earned its vacation and the boys appreciated that. They had no intention, originally, of disturbing it.

They had brought a bottle with them, and their only concern at the moment was to relax in the company of each other and the bottle.

"It's amazing when you think of it," said Adell. His broad face had lines of weariness in it, and he stirred his drink slowly with a glass rod, watching the cubes of ice slur clumsily about. "All the energy we can possibly ever use for free. Enough energy, if we wanted to draw on it, to melt all Earth into a big drop of impure liquid iron, and still never miss the energy so used. All the energy we could ever use, forever and forever and forever."

Lupov cocked his head sideways. He had a trick of doing that when he wanted to be contrary, and he wanted to be contrary now, partly because he had had to carry the ice and glassware. "Not forever," he said.

"Oh, hell, just about forever. Till the sun runs down, Bert."

"That's not forever."

"All right, then. Billions and billions of years. Twenty billion, maybe. Are you satisfied?"

Lupov put his fingers through his thinning hair as though to reassure himself that some was still left and sipped gently at his own drink. "Twenty billion years isn't forever."

"Will, it will last our time, won't it?"

"So would the coal and uranium."

"All right, but now we can hook up each individual spaceship to the Solar Station, and it can go to Pluto and back a million times without ever worrying about fuel. You can't do

## Re:The last question... (Score:4, Insightful)

The obvious question would then be, that if all existence is cyclical, how many times has it been reset? And, what kicked it off to begin with? The biblical tie in is a convenient reconciliation of science and (mostly Christian creation myth) religion, but it's a cheat. It doesn't actually answer any questions at all. It is something interesting to think about though.

## Re:The last question... (Score:5, Funny)

I don't think there is sufficient data to give a meaningful answer to these questions.

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I don't think there is sufficient data to give a meaningful answer to these questions.Not unless we find some ``counter++'' variable, somewhere in physical laws, that only gets executed during boot.

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1 + 1 = 2

Beauty is in the eye of the beholder, as is existence.

Everything is math...

It's all just an equation...

## Don't Panic! (Score:3, Insightful)

## Re: (Score:3, Interesting)

Is there a limit? How many times can you go around a circle?

It's cycles all the way back.

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The obvious question would then be, that if all existence is cyclical, how many times has it been reset?

An infinite number of times.

What kicked it off to begin with?

Nothing. It has always been.

Religion doesn't help, at least not for me. (Where does God come from? Same thing.) You can't solve these questions thinking about the physical world. Think abstract. Car analogies are doomed. Maybe try math.

For how long have pi been pi? How many times has sinusoid function peaked and what started it? How may times has "2 + 2" equaled "4", and since when did it start doing so?

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It's funny how broad such writings are - that I can scoff at antiquated terms like "analog computer" and "microvac", and be moved by aggregation of all thought and matter, in the same piece.

## Nothing in between???? (Score:5, Insightful)

Will quantum computers let us transcend the human condition and become as powerful as gods, or are they a physical absurdity destined to be exposed as the twenty-first century's perpetual-motion machine?No, they won't let us defy physical laws and become omnipotent. No, quantum mechanics, being a whole class of physical laws, isn't going to have absolutely no practical use. How about something in between that doesn't come from the over-used plot of a bad sci-fi show?

## Re: (Score:3, Interesting)

If it means "someone who can break physical laws" then it's a non-concept, because the moment you learn of a way (any way!) to break a certain rule, that rule is no longer a "physical law". For example, we used to think that all conductors has resistance, but the first person to manage sending electricity trough a conductor with -zero- loss did not become a "God", instead we adjusted our understanding of physics.

In relative terms, "God-

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My favourite description of technology, though, is Strongbad's here: http://www.homestarrunner.com/sbemail143.html [homestarrunner.com]

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## Protein's fold in real time. (Score:3, Interesting)

They solve the problem in real time (way better than Polynomial), by actually folding.

Therefore either

It is possible to solve NP-complete problems in better than polynomial time. We just have to figure out how. Quantum may be a solution

OR

Protein folding is not NP-complete problem.

## Re: (Score:3, Insightful)

generallycalculating protein folding is.## Re: (Score:2)

This is where you make your mistake, the protein folding problem can be summarized as: What are the valid ways for a prot

## Having actually read the article, a question (Score:2)

The thought is that this is a sober and sensible article, free of hype, and does us all a favor. Thanks.

The question is this. In the article, Scott describes an imaginary quantum computer with 1000 electrons that can be spin up or spin down. I do not understand how this is different from the following conventional silicon scenario:

Imagine 1000 DRAM cells in a matrix. Each one consists, basically, of an insulated gate MOSFET. The

## Re:Having actually read the article, a question (Score:4, Informative)

and lay off the trolling.

## What an rude person you are (Score:2)

Is there nothing you yourself know little about but would like your curiosity sa

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In the case of the electron, when we read the spin we always get either "up" or "down", but if we read "up" this doesn't mean that the spin was "up" immediately before we read it. Instead, the electron was in a weird condition where its spin was a mixture of "up"

## Re: (Score:2)

Granted, I didn't really grasp the point about how you collapse the probablistic distribution to the correct state unless you have a lot of these 1,000 electron computers. maybe somebody else could explain that? It's more than 20 years since I did the und

## Re: (Score:2)

## Re:Having actually read the article, a question (Score:5, Informative)

The (fundamental) difference is that the bits in the DRAM cells are in a well-defined state of either 0 or 1, but you just haven't measured them yet. In the quantum computer, the qubits are in a superposition of 0 and 1 at the same time.

To be more precise, the 'state space' of a classical bit is, well, 1 bit. Either 0 or 1. In the scenario that you describe, you don't know what the bits are until you measure them, but that is nothing special (imagine another example: tossing a coin with your eyes closed. You don't know the outcome until you open your eyes, but that doesn't mean that anything quantum-mechanical is going on!).

The 'state space' of a qubit, on the other hand, is an angle. Put the '0' result along the x axis and the '1' result along the y axis. Angle 0 corresponds to '0', 90 degrees corresponds to '1', and so on. But the possible physical state is anywhere on the unit circle, not just '0' and '1'. If the physical state of the system is 45 degrees then it really is a mixture of '0' and '1', and you can do interesting things with this state. For example, you can add it to some other state (at a different angle) and get wave-like interference effects.

## Re: (Score:2)

For some weird reason, someone else (above) accused me of trolling. However, IANA quantum physicist (obviously) and I actually wanted clarification on this point. You have provided it, and I will now slink off suitably ashamed of my ignorance.

On the other hand, now I think about it, why is it trolling on /. to admit to ignorance? "Read Wikipedia" is NOT the answer to everything.

## Guess I am one of the few who has RTFA (Score:2)

## NP-Complete Problems (Score:4, Informative)

## Am I Missing Something Here? (Score:2)

"Aaronson contends that any method for solving NP-complete problems in polynomial time may violate the laws of physics and that this may be a fundamental limitation on technology no different than the second law of thermodynamics or the impossibility of faster-than-light communication."

I don't know much about Quantum Computing and it's been a while since I've studied algorithms and computability. However, NP-complete is an algorithm and complexity question, not necessarily one of speed and

## So uh, where do the wires go? (Score:2)

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## Theory need not reflect reality (Score:2)

The proposals and attempts at quantum computing are based on predictions made using quantum theory. But how well does quantum theory reflect reality? There is good reason to seriously question that, and by implication, question the fundamental feasibility of quantum computing.

The first problem with quantum theory is that the mathematical formalism leaves a lot of leeway in how to interpret it. There are many interpretations of it http://en.wikipedia.org/wiki/Interpretation_of_quantum_mechanics [wikipedia.org]. These most

## Re: (Score:2)

The proposals and attempts at quantum computing are based on predictions made using quantum theory. But how well does quantum theory reflect reality? There is good reason to seriously question that, and by implication, question the fundamental feasibility of quantum computing.

Quantum mechanics encompasses a variety of related theories, and some of those are very solid indeed. Wave-particle duality, the Heisenberg uncertainty principle, quantum state, interference, entanglement... These standbys of quantum computing are going nowhere. The underlying causes and specifics of energy states of hydrogen atoms that they predict may not yet be completely understood, but there's more than enough right now to build a few quantum number-crunchers off of.

## Re: (Score:2)

The mathematical formalism may be very solid, but that does not imply that reality is like that. Only experiment can show how well theory reflects reality. And there is no such thing as proof by experiment since there always remain domains in which no experiment has tested the theory yet.

Let's take the Heisenberg uncertainty principle (HUP) you mention as an example. It can be derived from the commutatio

## Does quantum computing create quantum errors (Score:2)

## Another example of SciAm going down the tubes (Score:2)

Again, assuming that the summary is correct (I won't read SciAm again) what rational researcher would pose their hypothesis in such ab

## Quick Observation (Score:2)

I've never been one to completely adhere to laws, but that last one sticks out to me.

If somthing was able to communicate faster than light, how would be observe it happening ?

## I'm gonna be flamed for this, but... (Score:2)

You might be interested in knowing what the author of TFA thinks about his article and the discussion here [scottaaronson.com]

## If P != NP Is a really a law of Physics (Score:2)

## Response to an ironic accusation (Score:5, Interesting)

## For other problems... many of the same limits? (Score:3, Interesting)

This moves a huge class of problems from not solvable in less than millions of years to solvable in about one year, which seems like a pretty big impact to me...

I understand that as a complexity scientist, reduction that only halves the exponent of the number of operations is of merely practical importance and therefore b

## Re:For other problems... many of the same limits? (Score:4, Interesting)

## snake oil in training (Score:2)

One upon a time thermodynamics was an open frontier.

## Background Info (Score:5, Informative)

These are very informal definitions. Look at

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

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

http://en.wikipedia.org/wiki/Quantum_computer#Quantum_computing_in_computational_complexity_theory [wikipedia.org]

for more details.

And yes, I am a mathematician.

## This is (largely) an area of useless discussion. (Score:2)

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## Re:faster than light first post! (Score:4, Funny)

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## Re:Well...... (Score:5, Funny)

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Pics or it didn't happen!

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## Re:Stupid much? (Score:5, Informative)

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efficiently.I'm not sure exactly what that means in this context, but does that mean there is an inefficient way to go about it?

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## Re: (Score:3, Insightful)

The input has a constant size, and the computation is bound by some constant time.

If you want to be technical like that, your current computer is a finite state machine (it doesn't even support true Turing algorithms as these in the general case require an

infinitetape). Any input/output to computations is bounded by the size of your cache, memory and disk space. You could try and say that net access grants more storage, but this is still technically a) finite and b) bound by low seek times.The first generation of computers had low storage / computation space. They grew as engineeri

## Re:NP-completeness (Score:5, Informative)

What the

fuck?! I would outraged when this was at +4, but +5?!This is misleading. NP-completeness relates to how

otherproblems can be reduced to it. Currently we can't say much about how NP-completeness and complexity relate. We know that if a problem is NP-complete, it must take atleastpolynomial time and atmostexponential time (on a classical computer), but beyond that, we know nothing.This is factually incorrect. So far we have not found a quantum algorithm to solve

anyNP-complete problem in less than exponential time.Ha!

This is factually incorrect. Perhaps you're getting confused by the fact that quantum algorithms are often described in circuit notation. Classical algorithms are also sometimes described in circuit notation, but this is much less common. In any case, quantum algorithms do

notbound the size of the input any more than classical computers do.For instance, quicksort on a classical computer might be "bounded" in that you cannot sort an array of 50 billion petabytes. This is not inherent in the algorithm; it's inherent in our inability to construct a computer with 50 billion petabytes of memory. Similarly, we have not been able to use quantum computers to date to factor integers larger than 15. This limit is not inherent in the algorithm; it's inherent in the fact that engineers have not been able to construct a viable quantum computer to date with more than 5 (if I remember correctly) qubits.

Again, quantum algorithms to

notbound the size of their input.This is factually incorrect. Almost

allof the research into quantum computation in the past 10 years has been in the area of quantum complexity. Perhaps you have heard of the BQP complexity class [wikipedia.org], which wasmentioned in the article you were supposed to have read. By the way, BQP can in some way be thought of as quantum computers' "P"; i.e., the class of problems which can viably be computed on a quantum computer in polynomial time.Quantum complexity very much uses big-O notation (as well as big- notation and any other complexity notation used in classical complexity theory).Non sequitur. It's not clear at this point. If you could answer that question, you'd probably be drowning in money right now.

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That said, a lot of American's do seem to be a bit religion obsessed. However, I'd save such observations for threads on politics.

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