4 ms·

> Quantum mechanics can be simulated classically with an exponential slowdown. This is actually quite subtle. For example, I don't see how you can "simulate" b

> Quantum mechanics can be simulated classically with an exponential slowdown. This is actually quite subtle. For example, I don't see how you can "simulate" bell non-locality. Is it even possible to define the word "simulate" here? The whole status of quantum randomness is unsettled, I don't think it can be settled, but anyway it is not as straightforward as you suggest. Scott Aaronson has a nice paper where he discusses related ideas: https://arxiv.org/abs/1306.0159 https://arxiv.org/abs/1306.0159

danbruc 7y ago
One of the axioms of quantum mechanics is that the wave function completely describes a physical system. Therefore all you have to do in order to simulate a quantum system is to compute the evolution of the wave function which is pretty straight forward given an initial state and the Hamiltonian of the system - you just evaluate the Schrödinger equation. It is however computationally intensive for systems of non-trivial size. Also the evolution of the wave function is unitary, i.e. it is completely deterministic forward and backward in time and there is no randomness involved at all. Quantum non-locality can not be simulated classically if you distribute your computations just as the simulated system is distributed and if you do not allow for communication between the computers. This is however not an issue if you perform the simulation in one place or allow for communication between the computers. An example may help. Take the classical experiment of producing two spins with opposite orientations in one place, then separating them by a large distance, and finally measuring them at those distant locations. You can easily simulate that with one classical computer, but you can not use two classical computers - one to simulate each spin and the measurement of that spin at the distant location - without allowing the two computers to communicate even after the time the spins have been separated [in the simulation]. This especially highlights that quantum mechanics can not be described by a local hidden variable theory, or maybe it is better to think about it the other way round, such an simulation is not possible because quantum mechanics can not be explained by a local hidden variable theory as predicted by the Bell inequality and demonstrated by Bell test experiments. You can not write an algorithm that generates some hidden state while the two spins respectively the two computers are not yet separated and can therefore still communicate with each other and that then reproduces the results of all possible measurement experiments after the separation and without further communication.

danbruc 7y ago

One of the axioms of quantum mechanics is that the wave function completely describes a physical system. Therefore all you have to do in order to simulate a quantum system is to compute the evolution of the wave function which is pretty straight forward given an initial state and the Hamiltonian of the system - you just evaluate the Schrödinger equation. It is however computationally intensive for systems of non-trivial size. Also the evolution of the wave function is unitary, i.e. it is completely deterministic forward and backward in time and there is no randomness involved at all. Quantum non-locality can not be simulated classically if you distribute your computations just as the simulated system is distributed and if you do not allow for communication between the computers. This is however not an issue if you perform the simulation in one place or allow for communication between the computers. An example may help. Take the classical experiment of producing two spins with opposite orientations in one place, then separating them by a large distance, and finally measuring them at those distant locations. You can easily simulate that with one classical computer, but you can not use two classical computers - one to simulate each spin and the measurement of that spin at the distant location - without allowing the two computers to communicate even after the time the spins have been separated [in the simulation]. This especially highlights that quantum mechanics can not be described by a local hidden variable theory, or maybe it is better to think about it the other way round, such an simulation is not possible because quantum mechanics can not be explained by a local hidden variable theory as predicted by the Bell inequality and demonstrated by Bell test experiments. You can not write an algorithm that generates some hidden state while the two spins respectively the two computers are not yet separated and can therefore still communicate with each other and that then reproduces the results of all possible measurement experiments after the separation and without further communication.