# Global perspectives

# # Global perspectives

- Quantum computation and quantum information is the study of the information processing tasks that can be accomplished using quantum mechanical systems.

## # History of quantum computation and quantum information

*Quantum Mechanics*is a mathematical framework or set of rules for the construction of physical theories.- [?] What is a physical theory?
- Their relationship is rather like the relationship of a computerâ€™s operating system to specific application software.
- Much like how an operating system specifies some basic set of operations which can then be used by the application software to perform certain tasks.

- The rules of
*Quantum Mechanics*are simple, but**==counterintuitive==**. - One of the goals of quantum computation and quantum information is to develop tools which sharpen our intuition about
*quantum mechanics*, and make its predictions more transparent to human minds. - If cloning were possible in
*Quantum Mechanics*, then it wouldâ€™ve been possible to signal faster than light using quantum effects. - The desire to obtain
*complete control over quantum systems*also contributed to the development of quantum computation/information.- [i] Since the $1970s$, many techniques have been developed for this purpose.
- [?] Why desire complete control over quantum systems?
- Because this will allow us to explore untouched regimes of Nature in the hope of discovering new and unexpected phenomena.
- Often the most profound insights in science come when we develop a method for probing a new regime of Nature.
- Moreover, it is essential for quantum computation/information, otherwise, we wonâ€™t be able to manipulate/control our experiments.

- The modern
*Computer Science*was announced by*Alan Turing*in his remarkable $1936$ paper.- He developed the
*Turing machine*, which is a model for computation. - He showed that there is a
*Universal Turing Machine*that can be used to simulate any other*Turing machine*. - Furthermore, he claimed that the Universal Turing Machine completely captures what it means to perform a task by algorithmic means. This assertion is known as the Church-Turing Thesis.

- He developed the
*John von Neumann*developed a simple theoretical model outlining all the components necessary for a computer to be fully as capable as a*Universal Turing Machine*.*Gordon Moore*codified the growth of computer hardware power in $1965$, known as*Mooreâ€™s Law*, which states that computer power will double for constant cost roughly once every two years.- This law has approximately held true in the decades since, but many believe that itâ€™ll end some time during the first two decades of the twenty-first century.
- As the devices become smaller and smaller, quantum effects are beginning to interfere in their functions, which limits their growth and power.

- A possible solution to the eventual failure of the
*Mooreâ€™s Law*is to move to a different computing paradigm, such a Quantum Computation. - Classical computers can’t simulate quantum computers efficiently
- An Efficient algorithm runs in polynomial time while an
*Inefficient algorithm runs in superpolynomial time*. - According to the Strong Church-Turing Thesis, any algorithmic process can be simulated efficiently using a
*Turing machine*.- [i] This implies that the
*Turing machine*can efficiently simulate any type of machine that we use to run our algorithms. So if we want to analyze if a certain computational task can be performed efficiently, we can restrict ourselves to the analysis of the Turing machine model of computation, meaning that there is no need for other computation models/machines like quantum computation. - [f] One class of challenges to this thesis comes from the field of
*Analog Computation*, where many researchers noticed that there are some problems that can be solved by certain types of analog computers which are believed to have no efficient solution on a Turing machine. Unfortunately, when we take the realistic noise into account, their power disappears.

- [i] This implies that the
- [!] The effects of realistic noise must be taken into account when evaluating the efficiency of a computational model.