Feynman also suggested that this slowdown could be avoided by using a computer running according to the laws of quantum physics. This idea suggests, at least implicitly, that a quantum computer could operate exponentially faster than a deterministic classical one. In , Feynman also addressed the problem of simulating a quantum physical system with a probabilistic computer but due to interference phenomena, it appears to be a difficult problem.
But the full description of quantum mechanics for a large system with R particles is given by a function ψ (x l, x2, ... , x R , t) which we call the amplitude to find the particles xi,..., xR, and therefore, because it has too many variables, it cannot be simulated with a normal computer with a number of elements proportional to R or proportional to N. 
KeywordsTensor Product Quantum System Mixed State Classical Physic Auxiliary System
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