• Mika Hirvensalo
Part of the Natural Computing Series book series (NCS)


In connection to computational complexity, it could be stated that the theory of quantum computation was launched in the beginning of the 1980s. A most famous physicist, Nobel Prize winner Richard P. Feynman, proposed in his article [30] which appeared in 1982 that a quantum physical system of R particles cannot be simulated by an ordinary computer without an exponential slowdown in the efficiency of the simulation. However, a system of R particles in classical physics can be simulated well with only a polynomial slowdown. The main reason for this is that the description size of a particle system is linear in R in classical physics,1 but exponential in R according to quantum physics (In Section 1.4 we will learn about the quantum physics description). Feynman himself expressed:

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. [30]

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 [30], 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.


Tensor Product Quantum System Mixed State Classical Physic Auxiliary System 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Mika Hirvensalo
    • 1
  1. 1.Department of MathematicsUniversity of TurkuTurkuFinland

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