Quantum Computing pp 1-11 | Cite as

# Introduction

Chapter

## Abstract

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 [38] 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

Rparticles is given by a function,ψ(x_{1},x_{2},...,x_{ R },t) which we call the amplitude to find the particlesx_{1},...,x_{ R }, and therefore, because it has too many variables, itcannot be simulatedwith a normal computer with a number of elements proportional toRor proportional toN. [38]

## Keywords

Tensor Product Quantum System Mixed State Classical Physic Auxiliary System
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© Springer-Verlag Berlin Heidelberg 2004