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The Limits of Quantum Computing
Posted by
kdawson
on Tue Feb 19, 2008 06:52 AM
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."
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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)
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: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.
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.
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?
NP-Complete Problems (Score:4, Informative)
Response to an ironic accusation (Score:5, Interesting)
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.
Re:Well...... (Score:5, Funny)
Re:As usual (Score:5, Funny)
Re:As usual (Score:4, Insightful)
Best metaphor ever (Score:5, Funny)
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.)
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.
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)
Re:faster than light first post! (Score:4, Funny)
Re:Stupid much? (Score:5, Informative)
Re:Having actually read the article, a question (Score:4, Informative)
and lay off the trolling.
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: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.