A Simple Introduction to Quantum Computers

7/24/2019 A Simple Introduction to Quantum Computers

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Chapter 1: Introduction

1.1Introduction

Research into the quantum-mechanical phenomena has existed since the beginning of the

interest of quantum physics over classical (Newtonian) physics. It is the science behind

matter, atoms, subatomic particles and their interactions with energy. Many of the

phenomena that occurs at the quantum level, cannot be explained with classical physics. Thus

even in the modern age, physicists are bewildered by the somewhat paradoxical and self-

contradicting properties of matter. Can we make use of some of these properties in our

technology? Quantum computing theory was introduced as a possibility by Yuri Manin and

Richard Feynman in 1982. It has in some sense become a reality now.

1.2Motivation

Modern or classical computers, including personal computers, mainframes, distributed

computing systems and supercomputers work on the same principle. They use transistors to

transmit binary code via small lines of semiconducting devices. The transistor count used in

systems have increased and technologies making use of these have advanced, but the basic

functioning of all these types of computers has not changed for the past 60 years. We can say


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the microprocessor has been optimized, upgraded and refined over the years, but it still uses

the basic principles of classical computing.

Quantum Computers are a revolutionary step towards parallel processing of complex discrete

problems. Their use is still in its infancy as of 2015. However theoretically, many problems

that have bewildered man till date can be solved using quantum computers. A recent use of

quantum computers is the D-wave QC bought by Google, with an up-gradation from 25Q-

bit to a 2Q-bit system which sparked an interest into this discussion of quantum

computing.

1.3Organization of the Report

The report begins with a basic introduction of classical computing. The limitations of

classical computing, and the areas where the Quantum computer can be brought into use. A

brief overview of quantum mechanics, as the principle of operation of a quantum computer

will be covered. Realization of Quantum bits, technologies used to achieve such machines

will be covered also. Finally an application regarding Quantum computing in the real life

scenario will also be discussed.


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Chapter 2: Background Theory

2.1Moores law

An observation by Gordon Moore, a co-founder of Intel, in 1965, was that the transistor

count in processors will continue to increase exponentially every year. This law has set

the pace of modern computation. Today we are using more than 10 billion transistors on a

single chip. In the current manufacturing techniques we are able to achieve a 22nm size.

This is the length of the transistor from the drain to the source. I.e. this is about 50 atoms

across.

Figure 2.1.1 Graph of processors conforming to Moore's law

We expect the transistor follow Moores law until around 2025, as show in the figure.

After this point of time, the transistor is known to display quantum effects. This is due to


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the fact that transistors will be so small that the distance between the drain and source

regions (channel length) is approximately 3 atoms across. However when we achieve this

size, we would start to see quantum effects, like quantum tunnelling between the source

and drain despite the signal at the gate.

Figure 2.1.2 Effect of Quantum Tunnelling

Quantum tunnelling is the ability of an electron to pass through a barrier/wall despite no

physical tunnelling happening. This is much clearer when we consider the wave like

characteristics of matter. The transmission is much like a wave, with some waves going

around the barrier while most of it is deflected. A finite probability is considered with

respect to tunnelling. I.e. Heisenbergs Uncertainty principle.


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Thus to further decrease the size of a transistor (for higher density packaging), taller

barriers need to be placed on the transistor. Otherwise interference would occur. This

method of reducing the size of the transistor is somewhat impractical.

Figure 2.1.3 Diagram of a transistor (MOSFET)

Thus we venture into the atomic size. I.e. transistors the size of atoms, which are

approximately 0.1nm in size.

However Quantum computing is completely different from classical computing

techniques. This means that it does not even conform to the conditions set by Moores

law, and thus it is an entirely new topic of discussion . The description of Moores law and

transistor scaling gave perspective to the limits of computers, and transistors. It is used

only as a measure to the potential of Quantum computing in the foreseeable future.


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2.2 Qubits

Entering the domain of Quantum computation. We make use of Quantum Mechanics and

the interesting effects of matter at the microscopic scale. These properties are used in the

design of the Qubit/Q-bit, also known as quantum bit, are the descriptors of data in a

Quantum Machine. An electron or any particle that has a quantum spin can be used as a

Qubit.

The Qubit is similar to the normal bits used in classical computers. It has both the high

and low state, similar to normal bits. However unlike the normal bits, Qubits can also

have an intermediate state. The state of the Qubit is determined by its spin (orientation). A

Qubit can be an electron or the nucleus of an atom. The spin of the bit is determined by

the magnetic field applied to it. This works similar to the principle of a compass needle.

Figure 2.2.1Classical bit versus Quantum Bit


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A magnetic field is applied in practical conditions, by a superconducting solenoid. The

magnetic dipole of the field aligns the Qubit in the direction of the field. This is called the

spin down state, or 0 state. It requires the least energy to be aligned in this direction.

Whereas in a spin up state (antiparallel to the field), or 1 state, some energy is required to

be aligned in this direction. Thus this is its highest energy state. If the nucleus of the atom

is used instead of the electron, it would require less energy to rotate towards spin up or

spin down. The Qubit displays a natural probability of being in spin up orientation 67%

percent of the time, whereas in spin down 33% of the time. This is when no other fields,

and decoherence (interference) doesnt upset the system.

The spin of a Qubit can be controlled by pulse of microwaves of a specific (resonant)

frequency of the atom.

Before the Qubit is measured, it will be present in either spin up (1) or spin down (0),

however when we measure it, the Qubit will be in a condition known as quantum

superposition. This is essentially the ability of the quantum system to have multiple

states at the same time. These do not only include up and down, it can be in any direction.

Another property to be considered is quantum entanglement. Entanglement is the

extremely strong correlation displayed by quantum particles even when separated by


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large distances, like the opposite ends of the universe. Both superposition and

entanglement are two parameters which explain the working of Qubits.

2.3 Dirac Notation

Figure 2.3.1 Illustration of Single Qubit States, up (1) and down (0)

Quantum states are described using a convention known as Dirac notation, also known as

bra-ket notation. The | sign describes the starting of the notation, and the > sign

indicates the ending. It is similar to the Cartesian coordinate system representation.

| > = |> + |> + |> = (

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)

Where e are the unit vectors that describe the direction of the system. A are the

constants that describe the magnitude of each vector.

We use vectors to describe the states of a Qubit, because it also considers a superposition

state. The Qubit can be in both a state of spin up and spin down at the same time. Vectors

are useful when we take into account more than 1 Qubit. An event called entanglement


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occurs, which increases the complexity of the system. This will be discussed in the

following.

2.4 Two Qubit System and Entanglement

When we consider more than 1 Qubits, we see the usefulness of Qubits in computing. The

complexity of the system also increases. However at the same time we are able to solve

computational problems that correspond to an increase in the order of complexity as well.

In this case we will take into consideration the two Qubit system.

In a classical two bit system, we require two pieces of information, the state of the first bit

and the state of the second bit. In a two Qubit system this is not so the case. The state

called entanglement will come into play and four pieces of data are required to represent

the two Qubit system, , , and , which are also constants.

Figure 2.4.1 States for two Qubits


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We keep the two particles on the same axis with respect to each other. The states for a two

Qubit system take the natural up-up and down-down, which is simple. However we cannot

obtain up-down or down-up like in classical bits. We get two states called the entangled states

instead.

In the entangled states, the direction of one Qubit is in antiparallel with respect to the other

Qubit, but it can have any orientation (not only up or down). Thus the quantum state of one

particle cannot be described individually, but has to include a description of the other. I.e.

One particle knows the information regarding the other. The particles have a strong

correlation, and this correlation describes the information regarding the bits rather than the

individual bits. This property of the Qubits is what gives the Quantum computer an edge over

classical computing in very specific tasks.


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Figure 2.4.2 Comparison of information used in Quantum bits (green) to classical bits (blue) with respect to N information

In a classical computer, we use N bit data to represent information, whereas in a quantum

computer we can achieve 2information. To put this in perspective, if we build a quantum

computer with 23information, we are using more information than the number of atoms in

the observable universe. With quantum computers we can use a lot more data than normal

computers. However for a 23 bit quantum computer, we need just as much information

which might not be available. It would be specifically designed to compute for 23

information. This problem in quantum computers are a matter to leave for future discussions

and will not be further considered in this report. For general description, if more number of

Qubits are used, then the problem which we wish to solve will be more complex.


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Quantum registers hold quantum bits, much similar to classical registers. In classical

registers, we require some amount of time to change the data. However in a quantum register,

since bits occupy superimposed states, we can change the data within a very short time, and

the register can hold more than one number at a time. If we use,

(|0 > +|1 >)

(|0 > +|1 >)

(|0 > +|1 >)

to represent a 3 Qubit system, an equivalent representation in binary of this superposed

information would be:

000+ 001+ 010+ 011+ 100+ 101+ 110+ 111

However due to entanglement, the change of one bit of data in a quantum register can affect

all the other bits of the register. Again this will not be a topic for discussion as of now.


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Chapter 3: Methodology

3.1 Transistors for reading spin

We can use normal silicon transistors (MOSFETS), made from silicon-28 rather than silicon-

29 for the creation of the Qubit. Silicon-28 has almost no spin, thus does not affect the Qubit

directly. A Phosphorous atom placed in the base of a transistor can be used to create a Qubit.

The extra electron on the valence shell of phosphorous has a higher energy state. This higher

energy electron is in spin up state. This electron will jump into a sea of other electrons, thus

leaving behind a positively charged phosphorous ion. This positive charge can act as a gate

activation for the flow of electricity between the source and drain rather than the actual gate

of the transistor.

This transistor model using phosphorous indicates whether the electron is in spin up state or

not. If the current between source and drain of a transistor is accelerated, we can conclude the

electron was in spin up state. The state of the Qubit is controlled using microwave pulses of

resonant frequency to the electron and the magnetic field produced by the solenoid

(superconductor). The temperature surrounding such a device would need to be near zero

Kelvin.


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3.2 Diamonds for reading spin

Diamonds can be used in alternative to Transistors. We need a slightly impure diamond to

store the electrons (Qubits). These defects are specifically called Nitrogen Vacancy (NV)

centres of diamonds. These NV centres trap electrons.

NV centres include a nitrogen atom within the diamond lattice, its nearby neighbour is a

vacancy (I.e. no atom). The advantage of using diamonds over other methods, is that

electrons in diamonds have a longer coherence time. They are stored in the same state for

longer. Diamonds have strong carbon bonds, thus unlike other material there will be less

lattice vibrations. Such disturbances would have affected the Qubit.

Figure 3.2.1 Representation of NV centre in Diamond

Light directed onto the diamond by a laser enables us to see these NV centres. The light

exiting the diamond is measured using spectroscopy indicating this vacancy. If we shine light


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onto a Qubit stored in the diamonds NV centre, the electron goes to an excited state.

Eventually this electron will dissipate energy, as when moving from a high energy state to a

lower one. Fluorescence is present during dissipation. This is used to define the spin down

state.

Another state can be arrived by using the original NV centre diamond, with an electron in its

vacancy. If we apply microwaves, the electron reaches a slightly higher energy state. The

spin of the electron is also changed due to these waves. After this laser light is applied to the

diamond, the electron goes to an even excited state. However this time when dissipating its

energy, the electron reaches an intermediate level before going back to its ground state. Upon

dissipation, there is no detectable light, unlike spin down. This is representative of the spin up

state, or any superposition between spin up and spin down. This is indicated below in the

diagram.

Figure 3.2.2 a) For Spin down b) For spin up or any quantum superposition


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Such diamonds are not available by nature, and require manufacturing. We cannot use the

standard method of HPHT diamonds, as the diamond would also have high quantities of

nitrogen and would not be suitable for a Qubits environment. The diamonds used for

Quantum computers have to be built carbon stacked on carbon, with NV centres separated.

+

+ 4 + 3

The 3is deposited on a diamond or silicon substrate to form the diamonds. This is done by

applying a large amount of heat by a plasma cannon (Microwave plasma reactor) with

hydrogen being constantly fed into the machine. The hydrogen is require to produce the 3

radical and acts as a medium to etch the excess of graphite which will also be formed. It also

introduces stability of the growth surface and a means for termination.


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This is done using 99% Hydrogen, 1% Methane at 200mBar at 800C and can take up to 5

days to form a suitable size diamond.

3.3 Quantum Cooling

One of the issues of a Quantum computer is cooling. We require near absolute zero

temperatures to prevent the Qubits from changing their spin due to the surroundings. At room

temperatures the spin is constantly changed between spin up and spin down, so it would not

provide reliable information. One can draw parallels to Quazistability in a classical

computing bit.

However even in absolute zero (0 K) particles still can have a tendency to move due to the

Heisenberg uncertainty principle. This is a property we use to control the state of the Qubit.

Figure 3.2.3Simple diagram of how to make diamond

using Hot Filament, same can be done using microwave

lasma reactor


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The absolute zero temperatures are achieved by using helium-4 and helium-3. Particles have

a tendency to vibrate, and helium-3 vibrates more that helium-4 due to its lesser mass. The

helium-3 is slightly more attracted to helium-4 than another helium-3 (Van der Waals). We

exploit these properties to achieve the cooling. When mixed together, about 6.3% of helium-3

is dissolved in the helium-4 and the rest remains floating on the surface of the helium-4.

Helium-3 also has a lower boiling point than helium-4.

The Helium-3 (LHS) and Helium-4 (RHS) are placed in a U tube. The 6.3% of helium-3

dissolved in the helium-4 is vaporised upon heating. This creates an osmotic difference

between the helium-3 on the left side to the helium-4 which is depleted of dissolved helium-3

on the right side. The helium-3 travels to the helium-4 side and begins taking away heat. The

Qubit device (quantum computers processor) is placed in the interface between helium -3 and

helium-4 to remove heat and reach the absolute 0 K temperature necessary for operation.


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Chapter 4: Applications

4.1 Abstract applications

Quantum computing is known for calculation of complex algorithms for the solving of

discrete optimization problems. These are problems like the travelling salesman problem as

shown in the figure below.

For the optimal routes a travelling salesman to go between 28 cities, a classical computer

solves for it in time which would take longer than the lifespan of the universe. This can be

solved in minutes for a Quantum computer. This example of an optimization problem can be

used for applications such as space travel.

Figure 4.1.1 Brute force: classical computer 1 Ghz (10^9 operations/sec)


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4.2 Cryptography

One of the theorized applications of Quantum computers in our everyday life is in the field of

cryptography. Cryptography includes encryption and decryption of important information for

security purposes. The best algorithm for decrypting a message without a key is to go for all

permutations of code.

There are two types of cryptography, symmetric and asymmetric. In symmetric cryptography

we used the same code for encryption of data and decryption of data. It is relatively simple

and just requires prior communication between two parties before the message is

communicated, in a secure environment. In asymmetric cryptography, it is much harder as

both the codes for decryption and encryption are different. This is much more advantageous,

since information can be transmitted privately even on tapped lines.

The standard RSA encryption can be easily hacked, whether it is using 128 bit or 256 bit

encryption scheme, if one can calculate the prime factors of large numbers. This is very hard

and tedious for a classical computer. However for a Quantum computer this is very easy,

since all the prime factors can be calculated in a short amount of time using the superposition

property of quantum matter.


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Conclusion

Quantum computers as stated earlier are in a stage of infancy. Many studies by NSA, Google,

Microsoft and other government organizations are going on to discover an alternate to their

huge mainframes and supercomputers. Recently developments in quantum computing is the

D-wave quantum computer bought by Google for research and development. Previously

stated to have 512 Qubits, it has been upgraded to 1000 Qubits. However there are

controversies surrounding the D-wave quantum computers, with some arguments one the fact

that the D-wave is not a true quantum computer. It uses Quantum mechanisms and can solve

certain tasks, however it is a cry from a true Quantum computer.

Quantum computing will be without a doubt used to fuel the requirements of our growing

populations and the resource constraints that come with it. Its applications in research and

theory are still the frame of focus now however.


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REFERENCES

Journal / Conference Papers

[1] Nicolar Woehrl and Volker Buck, Process Control of CVD Deposition ofNanocrystalline Diamond Films by Plasma Diagnostics, Zeitschrift fur Physikalische

Chemie, 225(11-12), 2011, 1279-1291

Reference / Hand Books

[1] Yuhua Cheng, Chenming Hu, MOSFET Modelling & BSIM3 Users Guide, Kluwer

Academic Publishers, Edition 1, ISBN 0-306-47050-0

[2] N. David Mermin, Quantum Computer Science: An Introduction, Cambridge

University Press, 2007, ISBN 978-0-511-34258-5

Web

[1] Quantum Uncertainty,http://www.physicsoftheuniverse.com/

[2] Quantum Computing the Qubits,http://radicalnews.in/

[3] News: Quantum Entanglement and Quantum Computing,http://www.caltech.edu/

[4] Basic Concepts Quantum Computation, http://www.quantiki.org/

[5] Quantum computers end Cryptography, http://www.makeuseof.com/
http://www.physicsoftheuniverse.com/http://www.physicsoftheuniverse.com/http://www.physicsoftheuniverse.com/http://radicalnews.in/http://radicalnews.in/http://radicalnews.in/http://www.caltech.edu/http://www.caltech.edu/http://www.caltech.edu/http://www.caltech.edu/http://radicalnews.in/http://www.physicsoftheuniverse.com/

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A Simple Introduction to Quantum Computers