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A quantum computer is just a computer. Yes, a turing machine can simulate a QC. A QC doesnt use any special quantum properties in its computation. The "quantum"

A quantum computer is just a computer. Yes, a turing machine can simulate a QC. A QC doesnt use any special quantum properties in its computation. The "quantum" part should really be read more about its storage system than its computation, ie., its mostly about how its input states are prepared. That's neither here nor there though. A myriad of other issues exist. The uncertainty principle precludes "in any world", infinitely precise measurement. Thus chaotic systems, at least of a large time horizon, arent deterministic. A chaotic system is one in which "insignificant digits" in the input determine "significant digits" in the output. You need very very very low digit precession in inputs the longer the time horizon. This gets beyond the uncertainty principal. You can run as many turing machines as you like (necessarily, uncountably many to be consistent with QM). But you cannot escape the problem. The best theories of physics are extremely far away from "effective computation". They are phrased actively hostile to it. And you have to completely revise physics to make it even half-plausible. It's a project which is barely stated, and a long way from finished. It seems, indeed, a little doomed to failure. Properties that physics uses day-in-day-out posses the trivial infinities of geometry; and the trivial randomness of uncountable ensembles etc. -- to claim that physics states that reality is a computer is bizarre.

tsimionescu 5y ago
A QC absolutely uses quantum properties in its probabilistic computation (the complex-valued probabilities of its qbits and their entanglement). A QC can also perfectly represent the state of a quantum system (until you want to measure its output, of course). The laws of physics are known to be computable. Quantum Mechanics is one of the easiest to prove this for, since it is based on simple linear transforms! (Thermodynamics and GR are more complex, but still computable). I have no idea why you believe differently. A chaotic system requires arbitrary precision in the input measurements to be able to predict arbitrarily precisely its state after arbitrarily many steps. But, crucially, it does not require infinite precision in the input unless you want to predict its state with infinite precision (non-goal) or after infinite time (also a non-goal). The uncertainty principle is also irrelevant. The uncertainty principle has to do with measurement of classical properties. Conversely, the wave function of a system is precise, not fuzzy. It's only in measuring properties of the wave function that we reach uncertainty or probability at all. So, a computer can precisely compute the simple linear evolution of the wave function, according to the Schrodinger equation, which is what the universe itself is doing. The result of this computation is a complex value. You can then apply the Born rule to this result to get the probability of your system being in a particular state after following the simulated evolution, just as you would for a real quantum mechanical system. We do this kind of quantum simulation every day with great success, with a countable number of classical computers (typically 1), though it is only tractable for very very simple systems. The results don't typically differ in any perceivable way from the actual experiment.

tsimionescu 5y ago

A QC absolutely uses quantum properties in its probabilistic computation (the complex-valued probabilities of its qbits and their entanglement). A QC can also perfectly represent the state of a quantum system (until you want to measure its output, of course). The laws of physics are known to be computable. Quantum Mechanics is one of the easiest to prove this for, since it is based on simple linear transforms! (Thermodynamics and GR are more complex, but still computable). I have no idea why you believe differently. A chaotic system requires arbitrary precision in the input measurements to be able to predict arbitrarily precisely its state after arbitrarily many steps. But, crucially, it does not require infinite precision in the input unless you want to predict its state with infinite precision (non-goal) or after infinite time (also a non-goal). The uncertainty principle is also irrelevant. The uncertainty principle has to do with measurement of classical properties. Conversely, the wave function of a system is precise, not fuzzy. It's only in measuring properties of the wave function that we reach uncertainty or probability at all. So, a computer can precisely compute the simple linear evolution of the wave function, according to the Schrodinger equation, which is what the universe itself is doing. The result of this computation is a complex value. You can then apply the Born rule to this result to get the probability of your system being in a particular state after following the simulated evolution, just as you would for a real quantum mechanical system. We do this kind of quantum simulation every day with great success, with a countable number of classical computers (typically 1), though it is only tractable for very very simple systems. The results don't typically differ in any perceivable way from the actual experiment.