Brief Historical Survey and Perspectives

Another breakthrough paper appeared twelve years afterwards, in 1948, again by Claude Shannon A mathematical theory of communication [2]. On this paper. Shannon defined the unit of information, the binary digit, or bit, and established the theory which tells us the amount of information (i.e., the number of bits) which can be sent per unit time through a communication channel, and how this information can be fully recovered, even in the presence of noise in the channel. This work founded the Theory of Information. 

The computation and information technologies have developed very close to each other, in an astonishingly rapidly pace, for the last 50 years. Nowadays, a few square centimeters computer chip possesses hundreds of millions of electronic constituents, and a hairy thin optical fibre can transmit and maintain millions of conversations simultaneously  

After Benioff, in the year of 1985, David Deutsch gave a decisively important step towards quantum computers presenting the first example of a quantum algorithm [6]. The Deutsch algorithm shows how quantum superposition can be used to speed up computational processes. Another influent name is Richard Feynman, who was involved about the same time in the discussions of the viability of quantum computers and their use for quantum systems simulations [7]. 

However, it was in 1994 that a main breakthrough happened, calling the attention of the scientific community for the potential practical importance of quantum computation and its possible consequences for modem society. Peter Shor discovered a quantum algorithm capable of factorizing large numbers in polynomial time [8]. Classical factorization is a kind of problem considered by computation scientists to be of exponential complexity. 

This basically means that the amount of time required to factorize a number N bits long, increases exponentially with N. In contrast, a quantum computer running Shor algorithm would require an amount of time which would be a polynomial function of N. This is a huge difference To give an example, if IV = 1024 bits, a classical algorithm would take about 100 thousand years to factorize the number, whereas Shor algorithm would accomplish the task in a few minutes  

---