Comprehensive Research Paper: Quantum Computing and its Applications

This research paper delves into the fascinating realm of quantum computing, examining its foundational concepts and technological advancements. The paper begins with an introduction to quantum computing, contrasting it with classical computing and highlighting its potential to solve complex computational problems more efficiently. It then explores key elements such as Quantum Finite Automata (QFA), Qubits, and Superposition, providing detailed explanations of their roles and significance in quantum systems. The paper also discusses Measure Once Automata and concludes with an overview of the IBM Q Experience, an initiative aimed at making quantum computing accessible. The literature review provides the findings of the research on the QFA, Automata and Quantum Computing, and Technical Roadmap for Fault-Tolerant Quantum Computing. The paper highlights the advantages of quantum computing over conventional methods, emphasizing its potential to revolutionize various fields. This paper is a resource for students seeking to understand the fundamentals and applications of quantum computing.

Running head: RESEARCH PAPER
Research Paper
Topic: Quantum Computing
Name of the Student
Name of the University
Author Note

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Table of Contents
Chapter 1: Introduction..............................................................................................................2
Background Information about Quantum Computing...........................................................2
Quantum Finite Automata......................................................................................................3
Qubits.....................................................................................................................................5
Superposition..........................................................................................................................5
Measure Once Automata........................................................................................................6
Explanation about IBM Q Experience...................................................................................7
Chapter 2: Literature Review.....................................................................................................8
Introduction............................................................................................................................8
Findings of the Literature.......................................................................................................9
Quantum Finite Automata......................................................................................................9
Automata and Quantum Computing....................................................................................11
Technical Roadmap for Fault-Tolerant Quantum Computing.............................................13
A gap in the Literature.........................................................................................................14
Chapter Summary.................................................................................................................15
References................................................................................................................................18

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Chapter 1: Introduction
Background Information about Quantum Computing
Quantum Computing is the latest era of computer science technology that combines
the theories of computer science and quantum computing. This is established with the
implementation and detailed study of the computational modes in quantum physics which is
somewhat different from the conventional study of physics. Mostly, the knowledge gathered
through this study evaluates into developing and manufacturing the quantum devices for
implementing these models (Zheng, Qiu and Gruska 2017). Through this study, when a
quantum computer is built, it is identified that the model and the device is able to solve the
computational problems even faster than the conventional computer models.
The idea behind the quantum computing development had started in the 1980s at the
time when the likes of Richard Feynman and Yuri Manin wanted to implement the concept of
quantum computing since they believed that this new technology would have the potential for
stimulating issues that the conventional computing models could not solve. The conventional
models are capable of manipulating the individual bits and further store the information in the
binary state of 0 and 1. For displaying particular information, it takes the working of millions
of bits together for processing and acting on the information (Das and De 2016). On the other
hand, for the same purpose, the Quantum Computing devices leverage the physical
phenomenon of a different kind as the likes of superposition, interference and entanglement
for manipulating the information. These added advantages to the technology of computer
science that adds significant value to the reason behind computing and this are the reason
why the idea was developed to invent the theory of quantum computing and manufacture the
devices utilising the concept.

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However, it was not a unified idea, and there have been many theories developed
behind the idea of manufacturing a computing device by amalgamating the ideas for
computer science and quantum physics (Ambainis and Yakaryılmaz 2015). The latest times
have witnessed the reduction in the size of the devices used for the communication and other
functions of the computing devices. It was found that the more the computers have reduced in
size, the more it has become powerful enough to handle massive information management
and simulation (Piccinini 2019). The implementation of this particular technology has made it
easier for paper to differentiate between conventional computing and quantum computing.
The way by which the conventional computers used work utilized two specific tricks
under which the information was stored, and theories were implemented to synthesize or
make them work according to the requirement of the user (Yang et al. 2016). On the other
hand, the Quantum Computing theories use the quantum-mechanical phenomenon including
the likes of entanglement and superposition for performing simple computation. Various
theories are still under research that needs to be implemented in the development of the
theories that are utilized for the manufacturing of Quantum Computers. The research is thus
required to research through the various theories used for the development of Quantum
Computers to understand the mechanism and idea behind the development. The next sections
would hold the analysis and descriptions of different Quantum Computers like the sorts of
Quantum Finite Automata, Qubits, Superposition, Measure Once Automata, and the
description of the experience about the IBM Q.
Quantum Finite Automata
Quantum Finite Automata of QFA helps in forming the specific and descriptive
amount of the pedagogical basis of the introduction of the quantum computational computers
to the computer scientists because of its relatively simple nature (Ahmad et al. 2016).

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Previously the QFA models were found to be extremely problematic as it did not exhibit the
practical potential that the theoretical base of quantum physics as it proved to be implying. It
was found that there were also several specific areas of the initial and classical computational
counterpart that were found to be quite confusing and the quantum machine was found to be
leading to even confusing results and have not been able to stimulate any computational
theory (Wiesner 2018). Thus, there have been several pieces of research based on the
Quantum Finite Automata that would help in solving the problems and at the same time
would prove to be putting the quantum computing above the theories of the classical
computation.
There have been several theories presented that uses the QFA theory to prove that
Quantum Computing is far superior to the traditional or conventional ways of computing.
This is because the mechanism under which the QFA works makes use of the quantum state
machines that mostly is the quantum analogue of either the probabilistic automata or the
Markov Decision Process (Ardesi et al. 2018). The research processes use various strategies
to describe the technology that is based upon the QFA and most of these researches being
with the representation of the deterministic finite automata or DFA and its graph theoretic
interpretation. The researchers also enunciate how the DFA can also be represented in the
form of a different form of computing than conventional computing techniques. Researchers
have presented numerous examples in which the quantum finite automata utilised for
outperforming the traditional counterparts which were inferred that the QFA model could be
used for the simple technique of introducing the quantum computation concepts in the
standard computer use (Siccardi and Adamatzky 2015). There have been various researches
describing the modern quantum finite automata model that involves superoperators for
stimulating the classical finite automaton variants.

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Qubits
The introduction of Quantum Computing also clears out the needs of creating the
ideas into which the various aspects of the structural quantum computing features are
imbibed. Qubits are also regarded as one of the basic features of quantum computing; this is
regarded as the basic unit of quantum information (Bisio, D’Ariano and Tosini 2015). This is
also regarded as Qubit, and it is the basic quantum version of what is regarded as the
traditional computing unit, the binary bits. The only difference is that it is a two-state system
in quantum mechanics. The main features of Qubit are that it represents the peculiarity that
the quantum mechanics hold. There have been numerous researches done for this system that
decides the basic unit of the quantum computers as Qubit. The research has been performed
into various quanta computing field, and it has been found through researches that the basic
unit of the quantum computing field is capable of delivering the technical road map that
would be feasible enough to explain all the involved concepts about the fault-tolerant
quantum computing. To describe this idea, the researchers wanted to go deep within the ideas
of fault-tolerant quantum computing. There are also a few pieces of research that are based
upon the conduction of the number of Qubits that is required for small sized computer
applications.
Superposition
Amongst the several theories that have been developed in response to quantum
computing, there has been another inclusion of theory, known as the quantum superposition.
This theory has been developed by various researchers that feasibly describe the idea behind
the entire development of the superposition theory and how it can be encapsulated into the
quantum computing theory (Stephen et al. 2018). The features also put up the contrasts
between the various traditional forms of the computing systems and the ways by which

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quantum theory needs to be implemented in the base of the computing systems. The
researches describe how both the regular bits, which are 0 and 1, are capable of staying in
superposition with both 1 and 0 as Qubits (Angizi et al. 2015). The result can either be more
than both 0 and 1; however, it can also be a ratio lying in between them. Superposition
describes how the Qubit is utilized within the initial set up of the quantum theory in
computers as it depends on the functionality of the Qubit within the computational system.
Therefore, superposition is regarded as one of the primary functionalities or feature of a
Qubit. This original feature of a Qubit describes how the unit is regarded as an arrow which
can point at any given direction within the 3D space. Based on this feature, when the pointer
remains up, it is called the 0 , and when it is pointed at the downwards direction, it is called
the 1 state. When the Qubit points at any other direction in the 3D space, it is regarded as the
combination of both the 0 states and the 1 state (Bisio, D’Ariano and Perinotti 2016). Then,
then, the position of the Qubit can also describe the state of the Qubit and not just the
position. The angle rotation in two directions characterizes this, one is the up-down direction,
and the other is the left-right direction. The state where the Qubit is at an angle of up-down
direction describes that there is a probability that the Qubit can be found in 0 or 1 direction
(Farazkish and Khodaparast 2015). On the other hand, there is a possibility that the Qubits
can also be found in the left-right direction as well. At that point of time, the state is purely
regarded as the quantum property called phase of the Qubit.
Measure Once Automata
This theory behind the Quantum Finite Automata has been introduced first by Chris
Moore and James P. Crutchfield. The formal definition of the Measure Once Automata can
be defined as the finite automation for which the quantum automation is considered to have N
possible internal states, which would be represented in any particular case by the N-state

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Qubit. The possible state at which it can be represented is the N-state Qubit (Farazkish 2015).
This is the way by which the N-state Qubit can also be regarded as the N-dimensional
complex projective space, and these also carry a personal product, which is the Fubini-Study
Metric.
There is also an acceptance state in the measure once automata which are specified by
the implementation of the NXN matrix projection (Tsukerblat et al. 2018). The language that
is accepted by this automation state is found to be of a maximum one probability. It is almost
identical to the regular language of a classical DFA when consulted at a regular stage, and the
regular expressions give it.
Explanation about IBM Q Experience
IBM Q or IBM Quantum experience is regarded as the first initiative by the industry
for building the universal quantum computers are probably utilised for science and business
(Centrone et al. 2018). It is a cross-disciplinary team put together for the development of a
scalable amount of quantum systems two potentially make them applicable for a technology
that is available to everybody in recent times. IBM Q makes the quantum devices accessible
through a Qiskit, which is an open source programming framework and also modular. There
has been a report that over a worldwide network of the fortune 500 companies, startups and
other academic institutions are right now using the IBM Q Technology and collaborates with
the researchers by IBM for advancing the technology of quantum computing (Harneit 2017).
To put it simply, this is an online platform that IBM has tried to implement for
providing the users with general public access to the prototype quantum processor that IBM
has put together with the help of cloud computing implementation systems. IBM tried to
implement this for providing the users with general public access to the prototype quantum

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processor that IBM has put together with the help of cloud computing implementation
systems. Decision online internet forum that discusses the relevant topics for quantum
computing professes the tutorials over the quantum computing devices and how IBM is
trying to program them into the organisational used and other educational material regarding
the technology of computing through the quantum technology. Since May 2018, there have
been three processors built by IBM for the quantum experience (Gruska, Qiu and Zheng
2015). These are two 5-Qubit processors and a 16-Qubit processor. The services are probably
used with the help of algorithms to run the experiments. The tutorials are explored and
simulated to find out the main factor and technology of quantum computing. The website also
provides the easily discoverable list of the research papers that have been established
concerning various researches is published with the help of the IBM Q experience used for
the experimentation as a platform. IBM developed the quantum processor are usually made
up of superconducting transom Qubits which are located in a particular delusion refrigerator
within the headquarters of IBM research, which is the Thomas J. Watson Research Centre.
The users feasibly interact with the quantum processor with a quantum circuit model for
computation. For this purpose, it is required that the quantum gates are applied on the Qubits
with the help of a graphical user interface known as a quantum composer, which is used for
writing the quantum assembly language code through Qiskit.
Chapter 2: Literature Review
Introduction
A literature review is mostly conducted to go through all the researchers that have
been done in the previous times by various analysis and researchers over a chosen topic.
Secondary data collection techniques characterize this. Throughout the entire digitations, this
chapter is the most important one where the base of the primary data collection forms. Since

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the information gathered through the review of pieces of literature in this chapter is based on
the information gathered by a different source, this kind of data collection techniques through
literature review is known as secondary data collection. Through the findings of this
particular section, the primary data collection techniques should be formulated. The findings
food from the base of the questions that would be asked for the interview or survey conducted
for the primary data collection techniques. In this particular topic, there would be several
reviewed articles published on the subject of this particular dissertation, which is quantum
computing. The chosen articles in this section talk about several subjects like; the quantum
finite automata, the automata and quantum computing and the technical roadmap for fault-
tolerant quantum computing. Various theories are still under research that needs to be
implemented in the development of the theories that are utilized for the manufacturing of
Quantum Computers. The research is thus required to research through the various theories
used for the development of Quantum Computers to understand the mechanism and idea
behind the development. This section would also from the base of the several researchers
including a description about what researchers have gathered for the IBM Q experience
(Gheorghiu, Kashefi and Wallden 2015). At the end of the entire literature review, a critical
analysis would be based on the findings of the literature and what the pieces of literature
could not convey about the topic which has been gathered from other sources than the articles
reviewed in this section. In the end, the summary of the entire chapter would be provided as
per the conducted literature review.
Findings of the Literature
Quantum Finite Automata
The quantum finite automata are presented as a simple relative method for a sound
pedagogical basis of introducing the concept of quantum computation to the computer

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scientists. According to Douce et al. (2017), in previous times the quantum fine and automata
models have been extremely problematic since they did not have the embodiment of full
power as provided due to the quantum physics. This later to a much confusing result since the
accounted machine was not going to stimulate a classical counterpart. There are several paper
where it has been presented that the quantum finite automata algorithms have been presented
in several simple forms which helps in demonstrating the purity of the quantum computation
for the classical competition techniques. There have been several researchers that have been
constructed over the systematic development of general quantum finite automata model
which would in future be able to stimulate the quantum finite automata techniques and also
include the classical variants of the finite automaton (Takeda and Furusawa 2017).
According to various researchers, the basics of the quantum computation have been
amalgamated with the five quantum finite automata-based examples where the quantum
computation techniques can beat the classical form of computation. According to Lamata et
al. (2016), formal quantum finite automata can recognise tally languages for more easily and
efficiently with the use of cut point theories. There are also non-deterministic finite automata
that can recognise the languages which are, Quantum no determinism can also be defined as a
form of recognition of languages with cut point zero. In several cases, it has been found that
the real time nondeterministic finite automata can only define the regular languages.
According to Weiss and Saffman (2017), they have been a various practical point of
views that made sure how these algorithms can be used for classifying the input strings
without any error and succinct exact solution for the promised problems. Quantum finite
automata algorithms used in this purpose are capable of at least producing a high probability
of correctness of the solutions. The quantum finite automata are exactly much more succinct
than the real time DFA in case of any language detection that needs to be exact. On the other

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hand, these are also characterized by concise the bounded error language recognition. This
means that the gap between quantum finite automata and PFA is not exponential in any case
of bounded error language recognition. This is bound with the tight, simple model of
quantum finite automata and is employed by the unitary utility transformations only.
Last but not least, it can also be said that the quantum finite automata has the structure
of bounded error recognition on non-regular languages in polynomial time (Mohseni et al.
2017). This specifies the example of quantum finite automata in being a two-way automaton,
which has the ability to move the tape head over the input string in a back and forth motion
and for which it is established that the runtime forms an issue. This also means that the two-
way PFAs are unable to recognise the non-regular languages with rounding error in the
expected polynomial time.
Automata and Quantum Computing
The authors have established the fact that quantum computing has found the new
model of computation which is extremely in a client on the theories developed in quantum
physics. It is established that quantum computers have the ability to be exponentially factor
than that of the traditional computers that are being used in the latest times for the problems
like factoring (Ruoff 2018). There are various models of quantum computers rather than the
full-scale computers utilising quantum computing anthologies. There are various restricted
models like the quantum versions of finite automata which have been studied by various
researchers based on this particular topic. The researchers have found out various models of
quantum finite automata according to their properties, and there are also open questions
offered by them that would lead the technology into new directions for other researchers as
well.