A Study on the basics of Quantum Computing

A Study on the basics of Quantum Computing

Prashant

Department d¡¯Informatique et de recherch¨¦ operationnelle,

Universite de Montreal, Montreal. Canada.

{prashant}@iro.umontreal.ca



Abstract

Quantum theory is one of the most successful theories that have influenced the course of

scientific progress during the twentieth century. It has presented a new line of scientific

thought, predicted entirely inconceivable situations and influenced several domains of

modern technologies. There are many different ways for expressing laws of science in

general and laws of physics in particular. Similar to physical laws of nature, information

can also be expressed in different ways. The fact that information can be expressed in

different ways without losing its essential nature, leads for the possibility of the automatic

manipulation of information.

All ways of expressing information use physical system, spoken words are

conveyed by air pressure fluctuations: ¡°No information without physical representation¡±.

The fact that information is insensitive to exactly how it is expressed and can be freely

translated from one form to another, makes it an obvious candidate for fundamentally

important role in physics, like interaction, energy, momentum and other such abstractors.

This is a project report on the general attributes of Quantum Computing and Information

Processing from a layman¡¯s point of view.

Keywords: computation, EPR,

transformation, decoherence.

quantum

mechanics,

superposition,

unitary

TABLE OF CONTENTS

Abstract

Chapter 1: Introduction

Chapter 2: Literature Survey

2.1 A Brief History of Quantum Computing

2.2

Limitations of Classical Computers and birth of art of Quantum Computing

2.2.1 Public key Cryptography and Classical factoring of big integers.

2.2.2 Quantum Factoring

2.2.3 Searching of an item with desired property.

2.2.4 Simulation of quantum system by classical computer.

2.3

Quantum Computing: A whole new concept in Parallelism

2.4

Quantum Superposition and Quantum Interference: Conceptual

visualization of Quantum Computer.

2.5

Quantum Entanglement

2.5.1 Bertleman¡¯s Socks

2.5.2 EPR situation, Hidden Variables and Bell Theorem

2.5.2.1 An EPR situation

2.5.2.2 Bell Inequalities.

2.6

Quantum Teleportation and Quantum Theory of Information

2.7

Thermodynamics of Quantum Computation

2.8

Experimental Realization of Quantum Computer

2.8.1 Heteropolymers

2.8.2 Ion Traps

2.8.3 Quantum Electrodynamics Cavity

2.8.4 Nuclear Magnetic Resonance

2.8.5 Quantum Dots

2.8.5.1 Josephson Junctions

2.8.5.2 The Kane Computer

2.8.6

2.9

Topological Quantum Computer

Future Directions of Quantum Computing

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Chapter 3: A New outlook to the Principle of Linear Superposition

3.1 Modification of Wave function as a requirement of Quantum

Teleportation

3.2 Introduction of EPR correlation term in Expansion Theorem

3.2.1 Suitability of Quantum bits for Quantum Computation

3.3 An alternative interpretation of Quantum No Cloning Theorem.

Chapter 4: Experimental realization of Quantum Computers

4.1 Materials of Low dimensionality-Quantum Dot a promising

candidate.

4.2 Need for Modified Coulomb Potential and its analysis

4.3 Analysis of Quantum Dots using Modified Coulomb Potential.

4.4 Study of Quantum Wires using Modified Coulomb Potential

4.5 Visit to Nano Technology Lab in Barkatullah University, Bhopal

Chapter 5: Future Directions of Research

5.1 Explanation of Measurement Problem by Symmetry breaking

5.2 EPR Correlation: Interacting Hamiltonian Vs Non linear wave

function

5.3 Possibility of third paradigm in Quantum Mechanics

5.4 Conclusion and Future Scope

References

3

List of Figures:

Fig 1: Showing number of dopant impurities involved in logic in bipolar transistors with year.

Fig 2: Beam splitting of light

Fig3: Example to show wave particle duality of light

Fig 4: EPR paradox description using He atom

Fig 5: Graphical description of the EPR situation

Fig 6: Quantum Dots

Fig 7: Quantum Teleportation using Entanglement

Fig 8: The graphical representation of the Modified Coulomb potential

Fig 9: Plot of Wave Function Vs. distance in a Quantum Dot

Fig 10: Quantum Wire as a 1-D system

Fig 11: Quantum Dots as seen from an Atomic Force Microscope

Fig 12: The tip of the Scanning Tunneling Microscope

Fig 13: AFM Plots of Quantum Dots prepared in laboratory.

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CHAPTER 1

1.0 INTRODUCTION

With the development of science and technology, leading to the advancement of

civilization, new ways were discovered exploiting various physical resources such as

materials, forces and energies. The history of computer development represents the

culmination of years of technological advancements beginning with the early ideas of

Charles Babbage and eventual creation of the first computer by German engineer Konard

Zeise in 1941. The whole process involved a sequence of changes from one type of

physical realization to another from gears to relays to valves to transistors to integrated

circuits to chip and so on. Surprisingly however, the high speed modern computer is

fundamentally no different from its gargantuan 30 ton ancestors which were equipped

with some 18000 vacuum tubes and 500 miles of wiring. Although computers have

become more compact and considerably faster in performing their task, the task remains

the same: to manipulate and interpret an encoding of binary bits into a useful

computational result.

The number of atoms needed to represent a bit of memory has been decreasing

exponentially since 1950. An observation by Gordon Moore in 1965 laid the foundations

for what came to be known as ¡°Moore¡¯s Law¡± ¨C that computer processing power doubles

every eighteen months. If Moore¡¯s Law is extrapolated naively to the future, it is learnt

that sooner or later, each bit of information should be encoded by a physical system of

subatomic size. As a matter of fact this point is substantiated by the survey made by

Keyes in 1988 as shown in fig. 1. This plot shows the number of electrons required to

store a single bit of information. An extrapolation of the plot suggests that we might be

within the reach of atomic scale computations with in a decade or so at the atomic scale

however.

1014

1012

1010

No. Of

Impurities

108

106

104

102

1

1950

1970

1980 1990 2000

Year

2010

Fig 1: Showing number of dopant impurities in logic in bipolar transistors with year.

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