5 ms·

The claim about relative performance of continuous variable models versus circuit models is completely unsubstantiated. Especially given that most uses of the c

The claim about relative performance of continuous variable models versus circuit models is completely unsubstantiated. Especially given that most uses of the continuous variable systems is to encode discrete qubits on top of them with GKP/cat/binomial codes. Is there any Complexity Theory work published about continuous variable models? And photonic systems do not magically fix the noise issue. Noise grows in a fast non-linear fashion with the size of the system, so the "constant factor" noise suppression you gain from switching to photonic systems is quickly washed away.

adamnemecek 8y ago
> Especially given that most uses of the continuous variable systems is to encode discrete qubits Current uses, maybe. > Is there any Complexity Theory work published about continuous variable models? "Complexity and Real Computation". > And photonic systems do not magically fix the noise issue. Noise grows in a fast non-linear fashion with the size of the system, so the "constant factor" noise suppression you gain from switching to photonic systems is quickly washed away. Is there anything published on the fact that this cannot be overcome?
- krastanov 8y ago
  Just looking at the wiki pages for Real Computation is enough to see it is not a physically realizable model. For more detailed discussion of the problem you can see the essay "NP-complete Problems and Physical Reality". To quote from it "The problem, of course, is that unlimited-precision real numbers would violate the holographic entropy bound". At every level of physics there is a bound on precision, from boring things like classical macroscopic thermodynamics and noise, to quantum noise, to bounds that emerge in speculative theoretical physics. Basically, anything capable of encoding an infinitely precise real number in a finite amount of space will collapse and form a black hole. In case this is not convincing enough, to your question about how this noise can not be overcome: if there was a method that can overcome the noise asymptotically in photonic systems, then that method would work in electric systems too. And there is actually such a method: turning the computer into a digital computer thanks to error correction codes. The claim that Real Computation can be realized in our universe is comparable to the claim one can construct a perpetual motion machine or some other generator of free energy. They are both preposterous given our understanding of physics. And yes, I would celebrate if either of one turns out to actually be possible, but incredible claims require incredible evidence.
  - adamnemecek 8y ago
    > Just looking at the wiki pages for Real Computation is enough to see it is not a physically realizable model. This computer is literally at the physical limit reality can take. This number is actually quite high, although not unlimited. If you could make a computer faster by 10^30, ok I might not need unlimited. What if this number could be 10^300? Furthermore, and this is important, this computer allows for a fundamentally different type of computation. > At every level of physics there is a bound on precision, from boring things like classical macroscopic thermodynamics and noise, to quantum noise, to bounds that emerge in speculative theoretical physics. Correct, this can be accounted for. Don't press on details, you won't be satisfied with the answers. Can we talk about would be possible if this computer were possible and work backwards? As a mental exercise. Also what if I'm fundamentally more interested in probabilistic computation and this error can actually be a foundation of my computation. > then that method would work in electric systems too. Electricity is fundamentally more "unstable". This error compounds. This of the difference in attenuation rate in electric vs optical media. Where does this attenuation come from? > And there is actually such a method: turning the computer into a digital computer thanks to error correction codes. Nope. Think of it as averaging unstable signals. The result is very much continuous. You are getting too hung-up on the infinity aspect. Let's talk more about what sort of programming model this would allow for. A Turing machine technically has a tape of infinite length, while current computers don't. Does that mean that no Turing machine has ever been constructed? Does the answer to this question matter? Also, and this is important, compared with a normal computer, this computer would not heat up. Current CPU's can't get much larger because they can't dissipate heat fast enough. What if you could have a CPU of the size of a cube of the volume of one cubic meter?
    - krastanov 8y ago
      > Can we talk about would be possible if this computer were possible and work backwards? As a mental exercise. Certainly! This type of thought experiments is how much of physics progresses. But their results should be contemplated seriously. Assuming it is possible to prepare a system that works like your computer, it will immediately collapse into a black hole, because it breaks the holographic principle (and plenty of other bounds). Similarly we can imagine what happens if FTL was possible: time paradoxes. Or if we could measure both position and momentum: UV catastrophe. > You are getting too hung-up on the infinity aspect. The infinity aspect is what makes Real Computation more powerful than other types of computation. It is also what makes it impossible in our universe. It has absolutely nothing to do with the type of (countable) infinity that is the length of a Turing machine tape. You can make asymptotic statements that are useful about Turing machines or logic circuits. The only useful thing you get out of Real Computation is strictly after you take the limit to infinity. Otherwise you have old boring less-powerful analog computers (which are nonetheless marvels of engineering and their creators deserve praise). > Electricity is fundamentally more "unstable". This is just nonsense. By the way, the majority of continuous variable hardware is actually in the microwave regime, which is closer to the fields of electrical and radio engineering, than to the fields of lasers or THz systems. Lastly, yes, I completely agree that such hardware might be interesting in many cases. But claiming that Real Computation is possible (as oppossed to just admitting that small analog computers are occasionally useful) is far fetched. Claiming that such hardware can be built when it flies in the face of everything we know about physics is like claiming you can build a perpetual motion generator. As I said, extraordinary claims require extraordinary evidence. Please believe me, it is extremely rewarding to learn the details of these arguments, much more rewarding than the existence of Real Computation. In comparison with the real world, "Real Computation" is a boring cop-out. The last strip here describes the idea well: http://calamitiesofnature.com/ http://calamitiesofnature.com/

adamnemecek 8y ago

> Especially given that most uses of the continuous variable systems is to encode discrete qubits Current uses, maybe. > Is there any Complexity Theory work published about continuous variable models? "Complexity and Real Computation". > And photonic systems do not magically fix the noise issue. Noise grows in a fast non-linear fashion with the size of the system, so the "constant factor" noise suppression you gain from switching to photonic systems is quickly washed away. Is there anything published on the fact that this cannot be overcome?

krastanov 8y ago
Just looking at the wiki pages for Real Computation is enough to see it is not a physically realizable model. For more detailed discussion of the problem you can see the essay "NP-complete Problems and Physical Reality". To quote from it "The problem, of course, is that unlimited-precision real numbers would violate the holographic entropy bound". At every level of physics there is a bound on precision, from boring things like classical macroscopic thermodynamics and noise, to quantum noise, to bounds that emerge in speculative theoretical physics. Basically, anything capable of encoding an infinitely precise real number in a finite amount of space will collapse and form a black hole. In case this is not convincing enough, to your question about how this noise can not be overcome: if there was a method that can overcome the noise asymptotically in photonic systems, then that method would work in electric systems too. And there is actually such a method: turning the computer into a digital computer thanks to error correction codes. The claim that Real Computation can be realized in our universe is comparable to the claim one can construct a perpetual motion machine or some other generator of free energy. They are both preposterous given our understanding of physics. And yes, I would celebrate if either of one turns out to actually be possible, but incredible claims require incredible evidence.
- adamnemecek 8y ago
  > Just looking at the wiki pages for Real Computation is enough to see it is not a physically realizable model. This computer is literally at the physical limit reality can take. This number is actually quite high, although not unlimited. If you could make a computer faster by 10^30, ok I might not need unlimited. What if this number could be 10^300? Furthermore, and this is important, this computer allows for a fundamentally different type of computation. > At every level of physics there is a bound on precision, from boring things like classical macroscopic thermodynamics and noise, to quantum noise, to bounds that emerge in speculative theoretical physics. Correct, this can be accounted for. Don't press on details, you won't be satisfied with the answers. Can we talk about would be possible if this computer were possible and work backwards? As a mental exercise. Also what if I'm fundamentally more interested in probabilistic computation and this error can actually be a foundation of my computation. > then that method would work in electric systems too. Electricity is fundamentally more "unstable". This error compounds. This of the difference in attenuation rate in electric vs optical media. Where does this attenuation come from? > And there is actually such a method: turning the computer into a digital computer thanks to error correction codes. Nope. Think of it as averaging unstable signals. The result is very much continuous. You are getting too hung-up on the infinity aspect. Let's talk more about what sort of programming model this would allow for. A Turing machine technically has a tape of infinite length, while current computers don't. Does that mean that no Turing machine has ever been constructed? Does the answer to this question matter? Also, and this is important, compared with a normal computer, this computer would not heat up. Current CPU's can't get much larger because they can't dissipate heat fast enough. What if you could have a CPU of the size of a cube of the volume of one cubic meter?
  - krastanov 8y ago
    > Can we talk about would be possible if this computer were possible and work backwards? As a mental exercise. Certainly! This type of thought experiments is how much of physics progresses. But their results should be contemplated seriously. Assuming it is possible to prepare a system that works like your computer, it will immediately collapse into a black hole, because it breaks the holographic principle (and plenty of other bounds). Similarly we can imagine what happens if FTL was possible: time paradoxes. Or if we could measure both position and momentum: UV catastrophe. > You are getting too hung-up on the infinity aspect. The infinity aspect is what makes Real Computation more powerful than other types of computation. It is also what makes it impossible in our universe. It has absolutely nothing to do with the type of (countable) infinity that is the length of a Turing machine tape. You can make asymptotic statements that are useful about Turing machines or logic circuits. The only useful thing you get out of Real Computation is strictly after you take the limit to infinity. Otherwise you have old boring less-powerful analog computers (which are nonetheless marvels of engineering and their creators deserve praise). > Electricity is fundamentally more "unstable". This is just nonsense. By the way, the majority of continuous variable hardware is actually in the microwave regime, which is closer to the fields of electrical and radio engineering, than to the fields of lasers or THz systems. Lastly, yes, I completely agree that such hardware might be interesting in many cases. But claiming that Real Computation is possible (as oppossed to just admitting that small analog computers are occasionally useful) is far fetched. Claiming that such hardware can be built when it flies in the face of everything we know about physics is like claiming you can build a perpetual motion generator. As I said, extraordinary claims require extraordinary evidence. Please believe me, it is extremely rewarding to learn the details of these arguments, much more rewarding than the existence of Real Computation. In comparison with the real world, "Real Computation" is a boring cop-out. The last strip here describes the idea well: http://calamitiesofnature.com/ http://calamitiesofnature.com/