University Report: Function and Computing in IT - Discrete Mathematics

This report delves into the realm of function and computing within Information Technology, emphasizing its significance and practical applications. It begins by defining the role of function and computing in IT, highlighting the use of computers for data storage, manipulation, and transmission. The report then focuses on quantum computing, discussing its potential in solving complex problems and its relevance in the context of discrete mathematics. It includes a flowchart and algorithm for implementing an application, specifically addressing Shor's algorithm for finding divisors. The report analyzes the algorithm's functionality, providing inputs and demonstrating how it solves a problem. In conclusion, the report presents a comprehensive overview of the application of quantum computing in IT, illustrating the intersection of discrete mathematics and technological advancements.

Running head: FUNCTION AND COMPUTING FOR INFORMATION TECHNOLOGY
FUNCTION AND COMPUTING FOR INFORMATION TECHNOLOGY
Name of the Student
Name of the University
Author Note

FUNCTION AND COMPUTING FOR INFORMATION TECHNOLOGY 1
Table of Contents
Introduction:...............................................................................................................................2
Function and Computing in IT:..................................................................................................2
Description of why students choose this application and why students omit other application:
....................................................................................................................................................3
Give a complete plane to implement the application in to a computer program with use of
flowchart:...................................................................................................................................3
Algorithm:..................................................................................................................................4
Inputs:.........................................................................................................................................5
Conclusion:................................................................................................................................6
References:.................................................................................................................................8

2FUNCTION AND COMPUTING FOR INFORMATION TECHNOLOGY
Introduction:
The purpose of this paper is to discuss about function and computing in Information
technology. The information technology is basically the use of any computer, networking as
well as some of the other physical devices, infrastructure and processes is for creating
processing, securing, storing as well as for exchanging all of the forms related to the
electronic data. In this paper an application will be also provided for function and computing
in IT (McCarty, 2014). The information technology is typically used in the context of the
organisational operations as opposed to entertainment technologies or for personal purpose.
Function and Computing in IT:
The information technology is basically the utilization of the computers for storing,
retrieving, manipulating as well as transmitting information and data. The electric based data
storage that is utilized in the modern PCs, the 1st practical app was the mercury delay line
(Raykova and Boev, 2018). The computing and function is able to be referred to as one of the
activity which utilizes the computers for managing, processing, communicating as well as for
arranging the important and useful information. The growth and development of both
hardware and software are included in function and computing. The computing is basically an
activity which utilized the computer PCs for managing, processing, and communicating
information. It is very much critical as well as integral component for the present industrial
industry (Soomro, Z.A., Shah and Ahmed, 2016). The computing also has been defined as
one of the branch of engineering which can deal with the system wise study of algorithmic
procedures that are utilized for describing and transforming information.

3FUNCTION AND COMPUTING FOR INFORMATION TECHNOLOGY
Description of why students choose this application and why students omit
other application:
The function and computing is having an application in information technology in the
form of quantum computing such as the traits of the qubits that are known as quantum
entanglement. This is the major thought of the quantum computing that gives allowance to
the quantum computers that they can execute the equations of big scale they often utilize for
(Svensson, 2016). Let there is a problem “Let’s say I decided to entangle 256 of these
electrons together, what would that equate to? To simulate 250 cubits of information it would
be ten to the eighty classical bits, which is approximately the number of atoms in the
universe.” For solving this problem the modern computer PCs might take billions of years for
finding the prime factors but the quantum computers have contained 256 cubits that will help
the QC to solve the problem in 100 seconds only. So, the students need to choose this
application and omit other application. The quantum computing a very useful area of the
research that bring various discipline together for the information theory (Dumitrescu et al.,
2018). This is found that the conventional computing can operate over the binary system of
ones and zeros.
Give a complete plane to implement the application in to a computer
program with use of flowchart:
The schematic flowchart of the recursive quantum algorithm that is utilized for the
computing, the square free part of the of an odd integer N that is arbitrary. The possible
outcome after applying the Ω on the odd integer N that is arbitrary, either ensure that the
arbitrary number is square free number or else it returns a factor c with the square free part
when r’s value is equal to N. If the factor c>1 will be returned along with N is tested to be not

4FUNCTION AND COMPUTING FOR INFORMATION TECHNOLOGY
square free then the issues will be broken into 2 smaller sub problems for N / cD and c / d. d
is the gcd of N/c or c.
Algorithm:
The problem is, given that a composite no N for finding a non trivial divisor of N.
Before making the attempt for finding such a divisor, one can utilize quick primarily testing
that is quick for verifying that N is a composite (Preskill, 2018). It is needed to be checked
that there is no integer roots,

5FUNCTION AND COMPUTING FOR INFORMATION TECHNOLOGY
For solving the problem shor’s algorithm is there. It is consisting of two parts.
 A reduction that can be done on the computer that is classical. Of the factoring
problem to the issue of finding order.
 A quantum algo for solving the order finding issue.
Algorithm:
Step 1: pick a number a < N randomly.
Step 2: computer the gcd of a and N. the greatest common divisor of N and a. It can be done
by utilizing thee algorithm of Euclidean.
Step 3: if the GCD if a and N is not equal to 2, the number is a non trivial factor of N. So, it is
proved.
Step 4: Otherwise. Utilize the quantum period finding subroutine for finding r, that is denote
the period of the function as follows:
f (x) = a^x * mod N.
This is the order of r of a in the group (Zn)x that is the tiny most positive integer r for that f ( x
+ r ) = f (x) or f (x + r ) = a ^ (x + r) mod N = a ^ x mod N. By theorem of Eular, it can be
said that r divides , where is denoting the toilet function of Euler.
Step 5: if r is odd then get back to step number 1.
Step 6: if a ^ (r/2) = 1 (mod N) then go back to step 1.
Step 7: otherwise, at least one of the gcd ( a^(r/2) + 1 , N ) is a non trivial factor of N. So, it it
proved.

6FUNCTION AND COMPUTING FOR INFORMATION TECHNOLOGY
Inputs:
1.
Given that N = 15, a = 7 and r = 4, the gcd of (7^2 +- 1, 15) = gcd (49 +- , 1,15) where the
gcd (48 , 15 ) = 3 and the gcd (50, 15) = 5. For N that is the product of p and q that are two
distinct prime, the value of is N – p – q + 1, that for N = 15 is 8 and r divides 8.
r N
? 0
15 8
2.
Given that N = 24, a = 8 and r = 4, the gcd of (8^2 +- 1 , 24) = gcd (64 +- , 1,24) where the
gcd (64 , 24 ) = 4. For N that is the product of p and q that are two distinct prime, the value of
is N – p – q + 1, that for N = 24 is 8 and r divides 8.
N a
? 0
24 8

7FUNCTION AND COMPUTING FOR INFORMATION TECHNOLOGY
Conclusion:
Thus, it can be concluded from the entire report that it has successfully developed an
algorithm for the application of quantum computing. The various perspectives of utilizing the
discrete mathematics to evolve the information technology have been successfully discussed
in this report. The inputs are also given in the paper for the given algorithm. As the
technologies of modern computing such as cloud computing is using the functions of DM as
well as the computing tactics to make the humanity and businesses growth more efficient. It
is very much useful for being utilized the computer PCs for managing, processing, and
communicating information.

8FUNCTION AND COMPUTING FOR INFORMATION TECHNOLOGY
References:
Dumitrescu, E.F., McCaskey, A.J., Hagen, G., Jansen, G.R., Morris, T.D., Papenbrock, T.,
Pooser, R.C., Dean, D.J. and Lougovski, P., 2018. Cloud quantum computing of an atomic
nucleus. Physical review letters, 120(21), p.210501.
McCarty, W., 2014. Humanities computing. UK: Palgrave Macmillan.
Preskill, J., 2018. Quantum Computing in the NISQ era and beyond. Quantum, 2, p.79.
Raykova, M. and Boev, S., 2018. How to improve teaching in discrete mathematics via
programming and vice versa. Computer Science and Education in Computer Science, pp.211-
228.
Soomro, Z.A., Shah, M.H. and Ahmed, J., 2016. Information security management needs
more holistic approach: A literature review. International Journal of Information
Management, 36(2), pp.215-225.
Svensson, P., 2016. Humanities computing as digital humanities. In Defining Digital
Humanities (pp. 175-202). Routledge.