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This might be a matter of semantics. When I say "superposition," I mean the view that all we could possibly know about a system is represented in its wave func

This might be a matter of semantics. When I say "superposition," I mean the view that all we could possibly know about a system is represented in its wave function. This implies an ontological superposition of states until the wave function is collapsed, as is famously embodied in Schroedinger's cat. It is this ontological superposition of states which the QC scenario depends on for massive parallelism: If Schroedinger's cat was the input to your QC function, you would get to run the function with an alive-cat and a dead-cat input at the same time. Of course, you only get to see the output for the state the cat's in when the wave function is collapsed, and a key aspect of search algorithms like Shor's QC factorization scheme is to make sure that all the other states cancel out. (Shor's algorithm basically tries all possible divisors of the target number at the same time, through a superposition scheme.) But if the probabilistic component of the QM wave function instead merely represents our degree of ignorance about the entire system, rather than some such magical superposition, then the QC system is actually only in one of the many states on which the computation is supposed to be run simultaneously, and the promised massive parallelism is just a fantasy. (Yes, I think a hidden-variables explanation is more likely than the Copenhagen interpretation. Yes, I know about the EPR experiment.)

gjm11 16y ago
It sounds to me as if what you don't believe in is not the Copenhagen interpretation but quantum mechanics. The things on which quantum computation depends, and that you are being skeptical about, are common to all interpretations of QM. (Which is just as well, because all interpretations make the same predictions about our observations -- aside perhaps from some funny "anthropic" things -- and whether quantum computation works or not is, at least once the necessary engineering has been done, eminently observable.)
- Estragon 16y ago
  > The things on which quantum computation depends, and > that you are being skeptical about, are common to all > interpretations of QM. I disagree: http://en.wikipedia.org/wiki/Hidden_variable_theory http://en.wikipedia.org/wiki/Hidden_variable_theory (The "Motivation" section is particularly relevant to this discussion.) This is not the standard QM, but to the best of my knowledge it is consistent with the results of all the standard QM experiments.
  - gjm11 16y ago
    Quantum computation works just fine in Bohmian QM. (The pilot wave contains all the same structure you get in a conventional wavefunction, including the "parallel worlds".)
    - Estragon 16y ago
      That's exactly my point. Not only does QC work "just fine" in Bohmian QM, it critically depends on the Bohmian interpretation of the wave function probabilities to achieve the massive parallelism it promises. To the best of my knowledge, there is no empirical basis to that interpretation, and there are effective QM models which don't need it.
      - gjm11 16y ago
        Are you perhaps confusing Born with Bohm? There is no possible sense in which QC critically depends on anything to do with Bohm. Neither does it depend on very much about exactly what those Born probabilities mean. All that matters is that, e.g., when one of them is very close to 1 and the others very close to 0, you will almost always find yourself observing an outcome corresponding to the nearly-1 probability. Again: if you disbelieve that -- which is what you'd need to disbelieve to have a problem with QC here -- then what you are rejecting is not any particular interpretation, but quantum mechanics itself as a description of what the universe does.
        Estragon 16y ago
        > Are you perhaps confusing Born with Bohm? Sorry for my misunderstanding. I thought you were using "Bohmian" to refer to the standard interpretation. (I'd forgotten about that reference in the "Motivation" section of the wikipedia article.) I wasn't referring to the Bohmian interpretation two comments back, I was referring more to the kind of hidden variable Einstein had in mind. (I realize it would have to be non-local.) > All that matters is that, e.g., when one of them is > very close to 1 and the others very close to 0 That's just begging the question. The "nearly-1 probability" comes from the assumption that the initial state in the algorithm is a superposition over a large number of classical states. > what you are rejecting is not any particular > interpretation, but quantum mechanics itself as a > description of what the universe does. No, I accept that the probabilities which come out of the QM formalism accurately describe the frequencies observed in QM systems in the aggregate over many observations. I don't accept that those probabilities tell the whole story in one particular instance.

gjm11 16y ago

It sounds to me as if what you don't believe in is not the Copenhagen interpretation but quantum mechanics. The things on which quantum computation depends, and that you are being skeptical about, are common to all interpretations of QM. (Which is just as well, because all interpretations make the same predictions about our observations -- aside perhaps from some funny "anthropic" things -- and whether quantum computation works or not is, at least once the necessary engineering has been done, eminently observable.)

Estragon 16y ago
> The things on which quantum computation depends, and > that you are being skeptical about, are common to all > interpretations of QM. I disagree: http://en.wikipedia.org/wiki/Hidden_variable_theory http://en.wikipedia.org/wiki/Hidden_variable_theory (The "Motivation" section is particularly relevant to this discussion.) This is not the standard QM, but to the best of my knowledge it is consistent with the results of all the standard QM experiments.
- gjm11 16y ago
  Quantum computation works just fine in Bohmian QM. (The pilot wave contains all the same structure you get in a conventional wavefunction, including the "parallel worlds".)
  - Estragon 16y ago
    That's exactly my point. Not only does QC work "just fine" in Bohmian QM, it critically depends on the Bohmian interpretation of the wave function probabilities to achieve the massive parallelism it promises. To the best of my knowledge, there is no empirical basis to that interpretation, and there are effective QM models which don't need it.
    - gjm11 16y ago
      Are you perhaps confusing Born with Bohm? There is no possible sense in which QC critically depends on anything to do with Bohm. Neither does it depend on very much about exactly what those Born probabilities mean. All that matters is that, e.g., when one of them is very close to 1 and the others very close to 0, you will almost always find yourself observing an outcome corresponding to the nearly-1 probability. Again: if you disbelieve that -- which is what you'd need to disbelieve to have a problem with QC here -- then what you are rejecting is not any particular interpretation, but quantum mechanics itself as a description of what the universe does.
      - Estragon 16y ago
        > Are you perhaps confusing Born with Bohm? Sorry for my misunderstanding. I thought you were using "Bohmian" to refer to the standard interpretation. (I'd forgotten about that reference in the "Motivation" section of the wikipedia article.) I wasn't referring to the Bohmian interpretation two comments back, I was referring more to the kind of hidden variable Einstein had in mind. (I realize it would have to be non-local.) > All that matters is that, e.g., when one of them is > very close to 1 and the others very close to 0 That's just begging the question. The "nearly-1 probability" comes from the assumption that the initial state in the algorithm is a superposition over a large number of classical states. > what you are rejecting is not any particular > interpretation, but quantum mechanics itself as a > description of what the universe does. No, I accept that the probabilities which come out of the QM formalism accurately describe the frequencies observed in QM systems in the aggregate over many observations. I don't accept that those probabilities tell the whole story in one particular instance.