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The Standard Model of physics (the mathematical model which predicts the Higg's boson) is, as far as I understand, our most complete model of the universe. That is to say, it is the best description of the mathematical game to be played to make predictions on the outcome of experiments performed in our Universe.

As I understand it, quantum physics, used to create models of quantum computation (as used, for example, in the construction of Shor's algorithm) is a mathematical game contained within the Standard Model. Thus, in this sense the Standard Model is a generalization of quantum physics.

Is it at all conceivable that the Standard Model can allow for the construction of more general Standard Model computers? Or is there an obvious reason why quantum physics extracts all the benefit modern physics brings over classical models of computation and thus computer scientists should only reason according to quantum physics? Has any fundamental work been done on this? Is my question even well posed? Supposing that a Standard Model of physics computer could be a well-posed mathematical object more general than quantum computers, is there any reason at all to think that there could be any use to reasoning about that? Has there been any work done related to this question?

More informally, you might think of this question as something of the form "could we make a 'Higg's Boson' computer?" a rather natural justification for research in particle physics. Note that I know very little of the Standard Model (but a good deal about quantum physics) so this question might be ill posed, and if so, knowing that would be a clarification of my understanding.

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If quantum computers can simulate in polynomial time the Standard Model, which is a quite complicated quantum field theory, then probably the Standard Model does not provide any extra computational power beyond BQP. Simulating quantum field theories with a quantum computer is not an easy task, but a start has been made by this paper by Jordan, Lee, and Preskill, which shows how to simulate in polynomial time a much simpler quantum field theory than the Standard Model.

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  • $\begingroup$ Is your statement "probably the Standard Model does not provide any extra computational power" really implied by a quantum polynomial time algorithm to simulate the Standard Model? Certainly the distinction between "exponential time" and "polynomial time" is a significant one. That does not imply, however, that there can be no gain at all from a more general computation, it just means that the gain could at most be a polynomial factor. Is there any intuitive reason at all to assume more general computers cannot provide any such gain over a quantum computer? $\endgroup$ – Chris Blake Jun 1 '15 at 13:18
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    $\begingroup$ There is probably going to be a polynomial factor involved. If the problem the computer is solving is; what happens when I do this physics experiment? then the computer is going to require some overhead to simulate it, while the universe does not. But even different architectures for quantum computers require polynomial factors when simulating each other (and different architectures for classical computers require at least logarithmic factors when simulating each other). $\endgroup$ – Peter Shor Jun 1 '15 at 13:28
  • $\begingroup$ It seems like a more general computer can likely simulate its own physics faster than a more restricted computer, if only by a polynomial factor. Of course, as we know by Shor's algorithm, sometimes a generalization of a computer allows for the creation of a more efficient algorithm for a problem unrelated to the simulation problem. Could there conceivably be a physics experiment whose outcome, when measured, allows us, for example, to factor an integer more efficiently than a corresponding quantum algorithm, even if only by say, a loglog n factor? $\endgroup$ – Chris Blake Jun 1 '15 at 13:41
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    $\begingroup$ @Chris: all quantum computers are really physics experiments (or at least, can be viewed as ones), and so if your quantum computer has architecture A, and your physics experiment is really a quantum computer with architecture B, and architecture B can factor slightly faster than architecture A, then yes. $\endgroup$ – Peter Shor Jun 1 '15 at 16:58
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    $\begingroup$ @Chris: Where did you get $O(n^{1000})$ from in your last comment? There's going to be some polynomial penalty for simulating quantum field theory, but I very much doubt it is $O(n^{1000})$. And nothing is proved for the Standard Model; just for much simpler quantum field theories. $\endgroup$ – Peter Shor Jun 1 '15 at 19:50

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