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From Feynman's 1982 talk on quantum computing: "[N]ature isn't classical, dammit, and if you want to make a simulation of nature, you'd better make it quantum

From Feynman's 1982 talk on quantum computing: "[N]ature isn't classical, dammit, and if you want to make a simulation of nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem, because it doesn't look so easy." 0. https://s2.smu.edu/~mitch/class/5395/papers/feynman-quantum-1981.pdf https://s2.smu.edu/~mitch/class/5395/papers/feynman-quantum-...

fooker 3y ago
You can simulate quantum mechanics with classical computers pretty well, as long as you stick to the copenhagen interpretation.
- DiogenesKynikos 3y ago
  Feynman's lecture explains why classical computers are terrible at simulating quantum systems. The basic problem is that the number of states grows exponentially with the size of the system. You very quickly have to start making approximations, and it takes an enormous amount of classical computing power and memory to handle even relatively small systems.
  - eru 3y ago
    Yes, you have to make approximations and deal with (estimates of) errors. However, quantum computers also have to deal with noise and errors. So far, that's not very different. (If we manage to build error-correcting quantum computers, that might change.)
    - DiogenesKynikos 3y ago
      The approximations don't just introduce small errors. To simulate quantum systems classically, you need to make drastic assumptions that fundamentally change the nature of the system. This is very different from, say, an approximation that adds in a small amount of noise that you can estimate. The approximations in simulating quantum systems classically can radically change the behavior of the system, in ways that you might not understand or be able to easily estimate.
- amelius 3y ago
  We currently can't even simulate a hydrogen atom.
  - fsh 3y ago
    We can absolutely simulate the hydrogen atom. This paper lists the equations and fundamental constants that allow calculating the hydrogen energy levels with around 13 digits of accuracy: https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.93.025010 https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.93....
    - tsimionescu 3y ago
      We know how to simulate it, but we can't do it. Those equations though require too much computation if you solve them with any known classical algorithm.
      - fsh 3y ago
        This is completely wrong. My laptop can solve the equations in fractions of a second. I believe that with some optimizations it should be trivial to do the calculations on a 1960s mainframe.
        adrian_b 3y ago
        That is not true. You can solve such equations in fractions of a second only for very low precisions, much lower than the precision that can be reached in measurements. For higher precision in quantum electrodynamics computations, you need to include an exponentially increasing number of terms in the equations, which come from higher order loops that are neglected when doing low precision computations. When computing the energy levels of the spectrum of a hydrogen atom with the same precision as the experimental results (which exceed by a lot the precision of FP64 numbers, so you need to use an extended precision arithmetic library, not simple hardware instructions), you need either a very long time or a supercomputer. I am not sure how much faster can that be done today, e.g. by using a GPU cluster, but some years ago it was not unusual for the comparisons between experiments and quantum electrodynamics to take some months (but I presume that the physicists doing the computations where not experts in optimizations, so perhaps it would have been possible to accelerate the computations by some factor).
- eru 3y ago
  Huh? Your simulation doesn't care about your interpretation. All interpretations of quantum mechanics make the same predictions.
- throwaway63467 3y ago
  No even simulation of pure quantum states scales exponentially with the number of degrees of freedom, that’s irrespective of any interpretation or invoking of non-unitary evolution like measurements, just pure simulation of the Schrödinger equation. If you simulate an environment to e.g. incorporate wave function collapse or measurement operations you’ll work with a master equation that also grows linearly with the complexity of the density matrix simulation.
constantcrying 3y ago
>and if you want to make a simulation of nature, you'd better make it quantum mechanical That is an absurd claim, if taken by itself. Most of nature relevant to us behaves classically. If you want to do simulations of a building or a car or an earthquake or the climate, modeling it as a quantum system would be absurd.
- DiogenesKynikos 3y ago
  He's obviously talking about the nonclassical regime, where the fundamental quantum nature of reality matters.

fooker 3y ago

You can simulate quantum mechanics with classical computers pretty well, as long as you stick to the copenhagen interpretation.

DiogenesKynikos 3y ago
Feynman's lecture explains why classical computers are terrible at simulating quantum systems. The basic problem is that the number of states grows exponentially with the size of the system. You very quickly have to start making approximations, and it takes an enormous amount of classical computing power and memory to handle even relatively small systems.
- eru 3y ago
  Yes, you have to make approximations and deal with (estimates of) errors. However, quantum computers also have to deal with noise and errors. So far, that's not very different. (If we manage to build error-correcting quantum computers, that might change.)
  - DiogenesKynikos 3y ago
    The approximations don't just introduce small errors. To simulate quantum systems classically, you need to make drastic assumptions that fundamentally change the nature of the system. This is very different from, say, an approximation that adds in a small amount of noise that you can estimate. The approximations in simulating quantum systems classically can radically change the behavior of the system, in ways that you might not understand or be able to easily estimate.
amelius 3y ago
We currently can't even simulate a hydrogen atom.
- fsh 3y ago
  We can absolutely simulate the hydrogen atom. This paper lists the equations and fundamental constants that allow calculating the hydrogen energy levels with around 13 digits of accuracy: https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.93.025010 https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.93....
  - tsimionescu 3y ago
    We know how to simulate it, but we can't do it. Those equations though require too much computation if you solve them with any known classical algorithm.
    - fsh 3y ago
      This is completely wrong. My laptop can solve the equations in fractions of a second. I believe that with some optimizations it should be trivial to do the calculations on a 1960s mainframe.
      - adrian_b 3y ago
        That is not true. You can solve such equations in fractions of a second only for very low precisions, much lower than the precision that can be reached in measurements. For higher precision in quantum electrodynamics computations, you need to include an exponentially increasing number of terms in the equations, which come from higher order loops that are neglected when doing low precision computations. When computing the energy levels of the spectrum of a hydrogen atom with the same precision as the experimental results (which exceed by a lot the precision of FP64 numbers, so you need to use an extended precision arithmetic library, not simple hardware instructions), you need either a very long time or a supercomputer. I am not sure how much faster can that be done today, e.g. by using a GPU cluster, but some years ago it was not unusual for the comparisons between experiments and quantum electrodynamics to take some months (but I presume that the physicists doing the computations where not experts in optimizations, so perhaps it would have been possible to accelerate the computations by some factor).
eru 3y ago
Huh? Your simulation doesn't care about your interpretation. All interpretations of quantum mechanics make the same predictions.
throwaway63467 3y ago
No even simulation of pure quantum states scales exponentially with the number of degrees of freedom, that’s irrespective of any interpretation or invoking of non-unitary evolution like measurements, just pure simulation of the Schrödinger equation. If you simulate an environment to e.g. incorporate wave function collapse or measurement operations you’ll work with a master equation that also grows linearly with the complexity of the density matrix simulation.

constantcrying 3y ago

>and if you want to make a simulation of nature, you'd better make it quantum mechanical That is an absurd claim, if taken by itself. Most of nature relevant to us behaves classically. If you want to do simulations of a building or a car or an earthquake or the climate, modeling it as a quantum system would be absurd.

DiogenesKynikos 3y ago
He's obviously talking about the nonclassical regime, where the fundamental quantum nature of reality matters.