Introduction

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 [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 x_i,..., 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.