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."
Aaronson contends that any method for solving NP-complete problems in polynomial time may violate the laws of physics
Is this supposed to be informative in any way? Yes, that's one of the angles on the P=NP problem. No, you still haven't made any progress on it so it doesn't matter what you "contend".
Besides, I thought that "NP-complete" was a pure math term. Since when has pure math had anything to do with physics? I can understand that solving an NP-complete problem in polynomial time could be 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?
By the time we reach 100 letters, there are already more possibilities than there are atoms in a vat of 26^100 atoms.
Wow. Some less creative writers might say "there are more possibilities than there are atoms in the observable universe" or "more possibilities than there are protons in the known universe" or some other colorful metaphor. He goes straight for the "more possibilities than there are possibilities in a vat of 26^100 possibilities". Pure genius.
Shortest path isn't NP-complete; Dijkstra's algorithm can solve shortest path in O(V^2) where V is the number of vertices in the graph.
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.)
Your idea of "instantly" is confusing. Albeit, physics makes for an amazing computer; the problem lies in constructing the algorithm. Take, for example. a bunch of beads sitting on a counter. Each of these beads is connect by many strings of various lengths. Treat each bead as a waypoint and each string as the length between each waypoint. If I were to take two random beads and pull on them until one of the series of strings became taught, the first set to become taught is automatically the shortest path. Of course, it's best to assume that each string lacks the ability to produce resistance and is infinitesimally small. This system can scale to an infinite number of dimensions and can also allow for the idea of wormholes. It completely lacks a coordinate system as it doesn't need one. Essentially, it's a perfect waypoint-based pathfinding algorithm. The problem is, though, one has to reconstruct it each time. To reclarify my point, physics makes a stupendously efficient computer; but, lacks the programmability of logic-based circuitry.
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.
Chuckle... why in the world did you lose the context of GP's comment? It appears you thought GP was starting a discussion of non-electronic means of computing. It seems rather straightforward that he was discussing electric current (lightning) zapping through air in a maze in order to solve a shortest-path problem. 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
If Quantum Computers are a scientific impossibility, where does that leave us? There is only so much that current architectures can do. Does that mean we will hit the performance barrier and never be able to break through?
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.
What does it matter if it is perfect or not? Seems to me that it is much better than what we're working with now.
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'.
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'.
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.
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.
Or Lamport signatures [wikipedia.org]. Well, for signing, at least. 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]).
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.
This really have touched me deeply, specially the ending. Somewhat related to the article and perhaps one day it actually happens.
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
Not the first time I've read this, and I'm sure most people here are already familiar with it along with Asimov's other works.
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.
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?
The term "God-like" is a relative term. Either that or it's nonsensical. 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.
"Technology as magic" is a well explored theme - from quotes such as "any sufficiently advanced technology is indistinguishable from magic" to Babylon 5.
I think the "transcend the himan condition" comment may have been inspired by Roger Penrose's book "The Emperors New Mind", or a reaction to it. Penrose wants to believe that computers arn't capable of human thought, and supports this by claiming (against all evidence to the contrary) that the human brain and conciousness work at a quantum level rather than in the realm of classical physics and neuro transmitters. Quantum computers would at least remove this source of "incapable of human level thought &
You are confused as to what NP-complete means. It isn't that a protein folding is "NP-complete", but the algorithm for generally calculating protein folding is.
I know this is a no-no for Slashdot, but I have one thought and one question.
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
The difference is that, in a classical system such as your DRAM array, the state of the cells before we read them is either 0 or 1: we just don't happen to know which. The switching between states happens at the time when the UV light hits the cell. 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"
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.
Author here. I thought those who accuse me of drawing a false dichotomy -- between quantum computers as "godlike" on the one hand or a hoax on the other -- might be interested in the following quotes from the actual published article.
"although we should not accept the usual hype, in my view it is equally misguided to dismiss quantum computing as science fiction. Instead we should find out what the limits of quantum computers are and what we could really do if we had them." (p. 63)
"According to our current understanding, [quantum computers] would provide dramatic speedups for a few problems -- such as breaking the cryptographic codes that are widely used for monetary transactions on the Internet. For other problems, however -- such as playing chess, scheduling airline flights and proving theorems -- evidence now strongly suggests that quantum computers would suffer from many of the same algorithmic limitations as today's classical computers." (p. 63)
"If a large, ideal quantum computer would face most of the same limitations as our present-day classical computers do, should the physicists working on the extraordinarily hard task of building even rudimentary quantum computers pack up and go home? I believe the answer is no, for four reasons..." (p. 65)
"To some, the apparent limitations of quantum computers might come as a letdown. One can, however, give those same limitations a more optimistic spin. They mean that although certain cryptographic codes could be broken in a world with quantum computers, other codes would probably remain secure..." (p. 69)
In short, the precise misconception that I wrote my article to try to combat, is the one I then get accused of! Reading an article can, indeed, provide useful clues about its contents.
It looks to me as if Grover's Algorithm [wikipedia.org] should allow solving every NP problem in time proportional to the square root of the minimum number of operations a classical computer would require.
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
Yes, Grover's algorithm is important. As my article discusses, if all you're doing is brute-force search, then Grover's algorithm effectively doubles the size of the instances that you can solve with a given number of steps.
But there's a further wrinkle: in practice, people trying to solve difficult optimization problems on a classical computer usually use some sort of local search heuristic, which is much, much faster than brute-force. And while we do have a quantum analogue of local search (called the "quantum adiabatic algorithm"), it's not at all clear how much of a speedup it will give over classical local search on practical instances. Even the square-root speedup of Grover's algorithm might not be achievable in general (on the other hand, it's also conceivable that the speedup could be more than quadratic). If you're interested in this issue, see the original papers on the adiabatic algorithm by Farhi, Goldstone, Gutmann et al., as well as papers by van Dan, Mosca, and Vazirani and by Reichardt about the limitations of the adiabatic algorithm.
It seems as if most of the readers of Slashdot think quantum computers are the same as nondeterministic computers. Well, they are not. Nondeterministic Turing Machines (NTMs) are those that follow every computational path simultaneously and accepts if any path accepts. Quantum computers are more like Probabilistic TMs, which take a random branch at every step. The problems solvable in polynomial time by NTMs define NP, and RTMs define RP. The classes x-complete are the "hardest" of the problems in the class x. It is believed to be highly unlikely that any NP-complete problems are polytime on QCs.
Unless the post was from a computer, which may or may not exist, or may both exist and not exist at the same time, of which he would be an AI construct inside that brings up a whole new level of abstractness that... Oh dear, I've gone cross-eyed.
Completely off topic, not to mention wrong. Nearly all of the malware on Windows is stuff that stupid users install willingly.. a stupid user could just as well download a deb/rpm/tarball for a linux smiley toolbar or something and run it (typing in their password at the sudo prompt like hitting OK at UAC).. it's mostly the user's fault, not the OS's.
by Anonymous Coward
on Tuesday February 19 2008, @07:11AM (#22473448)
No no no. Factoring is not NP-complete. Sure, its in NP since you can verify a factoring in polynomial time. But the complete part is kind of important, here! Go read a book on complexity theory:)
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.
Efficiently seems to be the key word there. I'm not sure exactly what that means in this context, but does that mean there is an inefficient way to go about it?
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 infinite tape). 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
What the fuck?! I would outraged when this was at +4, but +5?!
NP-completeness relates to the scalability of the algorithm with the size of the input.
This is misleading. NP-completeness relates to how other problems 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 at least polynomial time and at most exponential time (on a classical computer), but beyond that, we know nothing.
Quantum computers "solve" NP-complete questions in "Polynomial time"
This is factually incorrect. So far we have not found a quantum algorithm to solve any NP-complete problem in less than exponential time.
(actually constant time?)
Ha!
they also limit the size of the input significantly.
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 not bound 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 not bound the size of their input.
Since Quantum Computers seem to run on inputs of a specific size, O() notation does not seem to apply at all.
This is factually incorrect. Almost all of 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 was mentioned 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).
So "solving" NP-complete problems cannot really violate laws of physics in this sense.
Non sequitur. It's not clear at this point. If you could answer that question, you'd probably be drowning in money right now.
As usual (Score:2)
Re:As usual (Score:5, Funny)
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Re:As usual (Score:4, Insightful)
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Re:As usual (Score:4, Interesting)
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Best metaphor ever (Score:5, Funny)
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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.)
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Re:NP complete is solved by nature (Score:4, Interesting)
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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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Re: (Score:3, Interesting)
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
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.
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Re:Okay Then. (Score:4, Funny)
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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.
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Re:Seems to me... (Score:5, Funny)
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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.
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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]).
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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.
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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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Don't Panic! (Score:3, Insightful)
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Is there a limit? How many times can you go around a circle?
It's cycles all the way back.
Nothing in between???? (Score:5, Insightful)
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?
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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.
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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.
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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: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.
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Guess I am one of the few who has RTFA (Score:2)
NP-Complete Problems (Score:4, Informative)
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)
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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.
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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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Re:Stupid much? (Score:5, Informative)
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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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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 infinite tape). 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 other problems 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 at least polynomial time and at most exponential 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 any NP-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 not bound 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 not bound the size of their input.
This is factually incorrect. Almost all of 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 was mentioned 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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