Quantum Computing Quantum Internet 2020_unit 1 By: Prof. Lili Saghafi

1
UNIT 1
By : Professor Lili Saghafi
proflilisaghafi@gmail.com
https://professorlilisaghafiquantumcomputing.wordpres
s.com
Quantum Computing
First Course
Quantum internet
Introduction
@Lili_PLS

2
Unit 1
• When was the first message sent over the
classical internet?
• What is the greatest technological achievement
of mankind?
• We will take you back in time and place the
recent developments of quantum computing and
quantum communication in perspective.
• After this we will introduce you to the bizarre
laws of quantum mechanics, and how these can
be used to create the technology of the future:
the quantum computer and the quantum
internet.

3
Introducing the quantum
computer
• From manipulating one electron and manipulating its
quantum state to scaling it up to a large-scale system.
The biggest challenge for quantum computing is going
from one qubit to a large-scale system.
• Quantum computers can find many applications, such as
computing the behaviour of molecules and materials, for
designing new medications, energy storage and
transport.
• A quantum computer is a complex system constructed
out of many hardware and software components, that all
have their challenges and need to be integrated.

5
Introducing the quantum internet
• The quantum internet is now in a similar
stage as the classical internet in the
1960's.
• In half a decade the internet gained a
huge role in our daily life.
• It is not a matter of science anymore: a
large community has been and still is
working on how we can use the internet in
our daily communication.

6
Quantum node network
• Bringing a scientific concept from universities to society
requires effort from academia and industry and now we
see the first footsteps being made.
• In 2020 it is aiming to have a small quantum node
network, which might become the first quantum internet
on earth.
• A quantum internet enables us to send qubits from one
node to another.
• This allows us to create entanglement between any two
points.
• Entanglement is inherently private.

8
Simulation of quantum systems
• Simulation of quantum systems is a
natural application of quantum computers
• Though quantum computers are thought to
be able to solve many problems more
efficiently than classical computers, there
are already classical algorithms for
multiplication which are as fast as
possible, even comparing to a quantum
computer.

9
Early days of the classical (and
quantum) internet
• In 2018, there are over 3 billion internet
users, and many more devices connected
to the network, making it one of the largest
and most complex machines ever created
by humanity.
• It's sometimes hard to imagine that it all
started with a small and unreliable network
called ARPANET

10
ARPANET
• The Advanced Research Projects
Administration (ARPANET) was an early
packet switching network and the first
network to implement the protocol suite
TCP/IP.

11
ARPANET
• Both technologies became the technical
foundation of the Internet.
• The ARPANET was initially funded by the
Advanced Research Projects Agency
(ARPA) of the United States Department
of Defence

13
In Quantum Internet
• Which property of entanglement is useful
for making communication secure?
• Inherent privacy: If an eavesdropper
measures part of an entangled state while
listening in on Alice and Bob, this leaves
evidence which Alice and Bob can detect
before they try to communicate

14
WORD CLOUD
Which industry get the most out of
Quantum Internet

Before we start with Quantum
Internet

16
Four commonly used definitions
in quantum
world
• Quantum mechanics is different from everything
we know in the classical world.
• It is completely counterintuitive! Even Einstein
spoke about “spooky action at a distance”
referring to the quantum principle of
entanglement.
• 4 commonly used definitions in quantum world:
– Qubit
– Superposition
– Entanglement
– Teleportation

17
Qubit
• A qubit is an essential element in In quantum
computing and quantum internet. It is a unit of
quantum information, and the quantum
counterpart of the classical bit.
• A qubit can be zero and one at the same time,
which is called a superposition of states.
• Qubits have some very peculiar properties; it is
not possible to copy qubits.
• Wave Particle Duality
https://www.youtube.com/watch?time_continue=
1&v=qCmtegdqOOA

19
Classical Bit VS Quantum Bit
• classical bit: a classical bit can in two states, it can be
either zero or it can be one.
• A quantum bit or qubit however can be sort of in zero
and one at the same time.
• This is called a superposition of states.
• Qubits have some very peculiar properties.
• For instance it is not possible to make copies of qubits.
• This is sometimes very useful, such as when you want
to keep information private.
• But it is also sometimes very annoying, because you
can imagine that if you cannot copy a qubit you
cannot use this copying mechanism as a means to
overcome errors.
• A qubit can be 0 and 1 at the same time.

20
Superposition
Schrödinger's cat paradox
• Can something be dead and alive at the same
time? Or here and there? Or active and quiet?
Learn here about the principle of superposition!
• Schrödinger's cat is a thought experiment,
sometimes described as a paradox, devised by
Austrian physicist Erwin Schrödinger in 1935,
though the idea originated from Albert Einstein.
It illustrates what he saw as the problem of the
Copenhagen interpretation of quantum
mechanics applied to everyday objects.

21
Schrödinger's cat paradox
• The scenario presents a
hypothetical cat that may be
simultaneously both alive and dead.
• a state known as a quantum
superposition, as a result of being linked to
a random subatomic event that may or
may not occur.
• Schrödinger's cat paradox

22
Superposition
• Superposition is a fundamental principle of
quantum mechanics.
• Quantum states can be added together –
superposed - to yield a new valid quantum state.
• Every quantum state can be seen as a linear
combination, a sum of other distinct quantum
states.
• Superposition can be visualized by an
experiment, where you shoot quantum particles
through two slits.
• Wave Particle Duality

23
Superposition
• Superposition is a fundamental principle of
quantum mechanics.
• It states that, much like waves in classical
physics, quantum states can be added
together- superposed - to yield a new valid
quantum state; and conversely, that every
quantum state can be seen as a linear
combination, a sum of other distinct
quantum states.
•

24
Quiz
• Mr. C and Mr. Q are our two protagonists.
• Mr. C likes to work in the classical domain,
while Mr.Q wants to try explore the
quantum domain.
• Mr. C's computer stores bits as a state in
his classical computer. What is the state?

25
Answer
• Mr. C's computer stores bits as a state in
his classical computer. What is the state?
– This state can be either 0 or 1 at a given
instance.

26
Question
• Mr. Q's computer stores qubits as a state
in his quantum computer. What is the
state?

27
Answer
• Mr. Q's computer stores qubits as a state
in his quantum computer. What is the
state?
– This state can be either 0 or 1 at a given
instance.
– This state can be both 0 and 1 at a given
instance.

28
Superposition on screen Video
• In the double slit experiment a classical bit
chooses either one of the openings.
• The qubit can be put in a superposition of
both paths.

29
• One of the ways superposition can be visualized is by
shooting quantum particles at two narrow slits.
• A classical particle will always pass either through the
top slit or through the bottom slit.
• But a quantum particle, if properly prepared, can be
put in a superposition of two paths.
• One path that passes through the top slit and one
path that passes through the bottom slit.
• This superposition leaves a mark in the form of
interference fringes
• when we later measure the particles position.

30
• Consider the following two experiments for a
double slit experiment:
• Experiment 1: A lot of photons (light particles)
are shot at the double slit at the same time. They
will go through the slits and end up on the
screen.
• Experiment 2: The same amount of photons are
shot at the slits, but only one at a time. They will
go through the slits and end up on the screen.
• After the two experiments the two screens are
compared. How do the two screens differ from
each other?

31
Both screens show the same interference
pattern. All photons go through both slits,
then interfere with themselves correct

33
Videos
• Wave-Particle Duality Animation
• Quantum superposition of states and
decoherence

34
Entanglement
• It’s almost romantic to think that two
particles can be entangled even when they
are millions of kilometres apart.
• How is Entanglement generated and
what are the implications?

36
Entanglement
• Quantum entanglement is a special
connection between two qubits.
• When qubits are entangled, they can be
moved arbitrarily far apart from each other
and they will remain entangled.
• When entangled qubits are measured,
they will always yield zero or one perfectly
at random, but they will always yield the
same outcome.

37
Entanglement
• Entanglement has two very special properties:
entanglement is inherently private and allows
maximal coordination.
• Coordination can be interpreted as follows:
Imagine some entangled state.
• Now it is actually possible to change the full
state (global state) by only changing
parameters (=doing operations) in the setup of
one qubit.
• Quantum Entanglement & Spooky Action at a
Distance

39
Entanglement
• Imagine we have 2 particles: we have particle
A and particle B.
• And these particles can be either full, which
is the filled have here, empty, or a
superposition of the two.
• Now let’s say that particle A and B are
entangled.
• The weird thing about this entanglement is that
when we would measure one of the particles,
say we’d like to measure particle A, and we get
the outcome/result full.

40
Entanglement
• Instantaneously the particle at B collapses into the full
state as well.
• This happens instantaneously, so even faster than the
speed of light.
• However, particle B, or an observer at particle B would
never know if Alice, the observer at A has already
measured her particle.
• In order for him to know if Alice measured her particle,
Alice needs to send a signal
• over a classical internet, which cannot exceed the speed
of light, to notify Bob,
• who is at particle B, if the particle has been measured.

41
Entanglement
• Only then they can compare their results and see if their
particles were indeed entangled.
• The particles can also be entangled in a different way.
• So, this corresponds to when the particle A would be full
when we measure it,
• particle B would be empty, and vice versa: if A would
result in empty, B would result in full.
• If we do not know beforehand which kind of
entanglement we have, we can also not know what the
state of B will be after measuring A.
• Entanglement can be generated in different ways.

42
Entanglement
• This difference will manifest itself in the
outcome statistics when performing
measurements.
• In this example you can see an
entangled pair of qubits that always
produces the opposite answers,rather
than the same answers as we saw
before.

44
Question
• Consider that qubits A and B are
maximally entangled with each other in
such a way that they have
perfect correlation with each other.
• If qubit A gives outcome 0 on
measurement, what is the outcome of
qubit B's measurement?

45
Answer
qubit B's measurement? 0 zero

46
Question
• Consider that qubits A and B are
maximally entangled with each other in
such a way that they have perfect anti-
correlation with each other.
qubit B's measurement?

47
Answer
qubit B's measurement? 0 zero

48
Entanglement
• When discussing entanglement, it is
sometimes convenient to ignore the type
of entanglement that is being created.
• This is sometimes permitted, because
correlated entanglement can be
transformed into anti-correlated
entanglement using local operations
affecting only one of the two entangled
qubits.

49
Controllable qubit
• Many systems in nature have attributes that would
make them good qubits.
• These attributes include well defined energy levels or
isolation from the environment
• but the most important quality that a qubit must have
• in order to be a good qubit that is actually useful in
computation is controllability.
• This means that we can take the state of the qubit and
change it to any other desired state by external means
such as for instance manipulating a magnetic field.
•

51
Question
• In terms of applicability of a good qubit,
which of the following attributes is the
most important?

52
Answer
• In terms of applicability of a good qubit,
which of the following attributes is the
most important? Controllability

53
Measurement
• Let's see how we transform the quantum information in
a qubit to classical information.
• Measurement is the act of observing a quantum
state.
• This observation will yield classical information such as
a bit.
• It is important to note that this measurement process
will change the quantum state.
• For instance if the state is in superposition, this
measurement will ‘collapse’ it into a classical state;
zero or one.
• This collapse process happens randomly.

54
Measurement
• Before we do the measurement we have no way
of knowing what the outcome will be.
• What we can do however is to calculate the
probability of each outcome.
• This probability is a prediction about the
quantum state, a prediction that we can test by
preparing the state many times, measuring it
and then counting the fraction of each outcome.
• Quantum Entanglement & Spooky Action at a
Distance

57
Quiz
• Mr. C and Mr. Q are our two protagonists.
Mr. C likes to work in the classical domain,
while Mr.Q wants to try explore the
quantum domain.
• Mr. C wants to read the contents of a bit
stored in his classical computer. What will
the content of the read out be?

58
Answer
• Mr. C wants to read the contents of a bit
stored in his classical computer. What will
the content of the read out be?
The read out content will always be either
a 0 or a 1 depending on the state
contained in the cell

59
Question
• Mr. Q wants to read the contents of a qubit
stored in his quantum computer in the
computational basis.
• What will the content of the read out be?

60
Answer
• What will the content of the read out be?
The read out content will always be either
a 0 or a 1 depending on the state
contained in the cell ,since A
measurement in the computational basis
destroys the superposition. We say that
the state collapses to either a 0 or a 1.

61
Question
• Is the state of the bit in the memory of Mr.
C always the same before and after
reading out?

62
Answer
• Is the state of the bit in the memory of Mr.
C always the same before and after
reading out?
– Yes, A classical bit does not change its value
when read out.

63
Question
• Is the state of the qubit in the quantum
memory of Mr. Q always the same before
and after reading out?

64
Answer
• Is the state of the qubit in the quantum memory of Mr. Q
always the same before and after reading out?
– No, When reading out, or measuring, the qubit collapses to the
state that you measure.
– So if you for example measure a qubit whose state is in equal
superposition between a 0 and 1, then you can either measure a
0 or a 1.
– If you measure a 0, the new state of the qubit is now 0.
– If you measure a 1, the new state of the qubit is now 1.
– So it has changed from a superposition of 0 and 1, to either a 0
or a 1.

65
Measurement in superposition
• When performing measurement we do not necessarily
have to collapse into the zero or the one state.
• We can also choose to collapse into a pair of
superposition states.
• This has important consequences when measuring
entangled pairs.
• When both parties perform the same type of
measurement the outcomes will always agree.
• But if one party performs one type and the other party
performs the other type the answers will no longer
agree.In fact they will be completely uncorrelated.

66
When both parties perform the same type
of measurement the outcomes will
always agree.

67
But if one party performs one type and the other party
performs the other type the answers will no longer agree. In
fact they will be completely uncorrelated.

68
• Consider that maximally entangled qubits A and
B are both measured, but with a different type of
measurement: Qubit A is measured 'vertically',
causing the state to collapse to either to 0 or 1;
and qubit B is measured 'horizontally', causing
the state to collapse to some equal
superposition of 0 and 1.
• Then the measurement outcomes for qubits A
and B are: uncorrelated.

69
• Perfect correlation or anti-correlation results
when both the entangled qubits are measured in
the same basis, i.e. in a way such that both the
qubits collapse to the same outcomes.
• If B measures first, both qubit A and B collapse
to a equal superposition of 0 and 1.
• If A then measures her qubit, she will measure a
zero with 50% probability, or a one with 50%
probability, independent on the measurement
result of B.
• Hence the results of A and B are uncorrelated.

70
The maze
Video
• Another experiment that shows the power
of a quantum computer is the maze.
• What is the advantage of superposition
compared to a classical way of
computing?
• Quantum computers are good at solving
search tasks.
• The maze Quantum computers:
Computing the impossible

71
The maze
• How can a quantum computer help us
solve a maze?
• Quantum computers can be used to
solve search problems, such as
finding the correct path in a maze,
• faster than classical computers can.
• However, contrary to popular thought,
they do not do this by trying every
possible path at the same time.

72
• This would be a much more powerful
device.
• What we can do however is put different
paths in superposition and then compute
with that superposition.
• This gives quantum computers a
considerable, but not magical advantage
over classical computers.

73
Question
• Mr. C and Mr. Q are our two protagonists. Mr. C
likes to work in the classical domain, while Mr.Q
wants to try explore the quantum domain.
• Mr. C wants to search for his name in a
database. He uses a classical approach to
search for his name.
• If while searching the database with names, Mr.
C's name is encountered at the very end, then
how many times does the computer have to
access the database?

74
Answer
• If while searching the database
with names, Mr. C's name is encountered
at the very end, then how many times
does the computer have to access the
database? N, Mr. C will begin a new
search operation for each entry in the
database and will end up cross-checking
each of the entries till he finally encounters
his name in the last entry.

75
Scenario
• Mr. Q wants to search for his name in a database. He
uses a quantum approach to search for his name.
• If while searching the database with n names, Mr. Q's
name is encountered at the very end, then the number of
times the computer does have to look into the database
is proportional to:
(Hint: think about question 1 and remember that
quantum computers can solve certain problems faster
than the classical computer.)
• Quantum computers can solve certain problems faster
than classical computers.
• The problem here refers to Grover’s algorithm and this
algorithm allows to solve problems in a quadratic time
faster.

76
Maze search
• Note that this scenario is analogous to the maze
solving scenario.
• Searching the database for an entry is similar to
searching for the right way out of the maze.
• To extrapolate in lines with this concept,
Grover's search algorithm is a quantum search
algorithm that utilizes the advantage offered by
superposition of quantum states.

77
Grover's algorithm
• Grover's algorithm is a quantum
algorithm that finds with high probability
the unique input to a black box function
that produces a particular output value,
using just evaluations of the function,
where is the size of the
function's domain. It was devised by Lov
Grover in 1996.

78
Teleportation
• “A transporter is a fictional teleportation
machine used in the Star Trek universe.
Transporters convert a person or object
into an energy, then "beam" it to a target,
where it is converted into matter.”
• What is and isn't possible with quantum
teleportation?

79
Teleportation
• Can we teleport a human or send
information faster than light?
• Quantum teleportation exploits the most
fundamental principles of quantum
mechanics and has far reaching
consequences.
• However, in order to teleport a classical
channel must be made.

80
Teleportation
• Quantum teleportation is a method to send
qubits using entanglement.
• Quantum teleportation can transmit a qubit
without really using a physical carrier.
• It does not allow for faster than light
communication.

81
Teleportation works as follows:
• First Alice and Bob need to establish an
entangled pair of qubits between them.
• Alice then takes the qubit that she wants
to send and the qubit that is entangled
with Bob’s qubit
• and performs a measurement on them.
• This measurement collapses the qubits
and destroys the entanglement,
• .

82
• but gives her two classical outcomes in the
form of two classical bits.
• She takes this two classical bits and sends
them over the classical internet to Bob.
• Bob then applies a correction operation
that depends on these two classical bits to
his qubit

83
• This allows him to recover the qubit that
was originally in Alice’s possession.
• Note that we have now transmitted a qubit
without really using a physical carrier that
is capable of transmitting qubits.
• But of course you already need
entanglement to do this.

84
• It is also important to note that quantum
teleportation does not allow for faster than
light communication.
• This is so because Bob cannot make
sense of the qubit in her possession
before he gets the classical measurement
outcomes from Alice.
• These classical measurement outcomes
must take a certain amount of time to be
transmitted.
• And this time is lower bounded by the
speed of light.

85
Teleportation further explained
• So we’ve talked a lot about entanglement, but
now we will see how we can use this
entanglement to teleport a certain quantum
state.
• So let’s take a look at how this works.
• First, we have two stations: we have station
Alice and we have station Bob.

86
• Alice and Bob share an entangled state, which
means Bob has one qubit of the entangled state
• and Alice has the other one of the entangled
state.
• What Alice also has is another qubit which is not
entangled with any of those which has a state A.
• Alice and Bob’s goal is to teleport Alice’s state A
to Bob’s qubit.
• The first thing they do is to perform some
operations which we again denote as a black
box.

87
• After the operations have been done, Alice will
measure her qubits.
• Since Alice has 2 qubits the total outcome can
be 4 different situations.
• For example: both the qubits could be measured
into the state empty,
• the first qubit might have been full and the
second empty and vice versa.
• And there is also the situation where both of the
qubits are measured to be full.

88
• And these four situation also results in 4 different states
for Bob.
• So in the empty-empty case we get the full state A back,
but as you can see
• not all the measurement outcomes result in this nice
state A.
• They do resemble A, but they are rotated or flipped a bit.
• So Bob needs to do something in order to correctly
retrieve the state A.
• And for this he needs Alice’s help.
• What does Alice do?

89
• Alice uses her information she had on the
measured qubits to send Bob instructions.
• If her first bit was measured to be full, she says
to Bob: rotate your qubit 180 degrees clockwise.
• If it’s empty, do nothing.
• Almost the same goes for the second qubit, only
now the rotation is 90 degrees clockwise.
• So if it’s full, Bob has to rotate the bit, if it’s
empty Bob has to do nothing.
• So let’s take a look at what this would result in.

90
• So let’s take a look at the first case: Alice
measured empty-empty.
• She knows now: I measured empty-empty,
and because of my clever operations in
the black box
• I know that Bob must already be in the
state A.
• So I order him to do nothing.

91
• She sends Bob this information over a classical
internet,
• so she cannot exceed the speed of light on this
one.
• Then we go to the second possibility, so she
measured full on the first qubit and empty on the
second qubit.
• Remember: the instruction on this one was:
rotate your qubit 180 degrees clockwise.
• So let’s take a look.

92
• We see we have an A upside down here,
and we have to rotate it 180 degrees.
• And we see that we get the correct state
A.
• So it works for this outcome.
• But now we take a look at what happened
for the third possibility.
• What is the first qubit was empty and the
second qubit was full.

93
• This corresponds to a 90 degrees clockwise rotation.
• So she sends this information to Bob, and Bob says: OK,
right, 90 degrees, I can do this!
• So we see we have this sort of flipped A here, and were
going to rotate it 90 degrees clockwise,
• again resulting in the state A.
• And you can already a little bit check for the final case,
when both the qubits are full,
• we have to rotate 180 degrees clockwise and also rotate
90 degrees clockwise.
• So this would again result in:
• first the 180 degrees clockwise...

94
• ..and now the 90 degrees clockwise,
• which is again the state A.
• So if Bob follows the orders of Alice
correctly, and Alice of course sends the
correct information,
• Bob will always retrieve the quantum state
A that Alice initially had.
• So the quantum state has been teleported
from Alice’s lab to Bob’s lab.

95
Teleportation-video
• Transporters and Quantum Teleportation

96
Questions / Scenario
• Mr. C and Mr. Q are our two protagonists. Mr. C
likes to work in the classical domain, while Mr.Q
wants to try explore the quantum domain.
• Mr. C and Mr. Q are now planning to
communicate with their respective peers. Mr. C
wants to send one classical bit of information to
his peer over the network. Mr. Q wants to send
one quantum bit of information to his peer with
whom he shares an entangled pair of qubit (with
each party holding one qubit).

97
Question 1: Teleportation
• While it is quite straightforward that if Mr. C has
a classical channel and Mr. Q has a quantum
channel at his disposal, then both have to
communicate just one classical and quantum bit
respectively.
• But let's say that Mr. Q's quantum channel is not
available for communication after the distribution
of the entangled qubits.
• Is it possible for Mr. Q to send a quantum bit to
his peer using the classical channel and the
already established entangled qubit pair?

98
Answer
• Is it possible for Mr. Q to send a quantum
bit to his peer using the classical channel
and the already established entangled
qubit pair? yes

99
Question
• How many classical bits of information will
have to be communicated by Mr. Q to be
able to send his qubit across, over the
classical channel?

100
Answer
• How many classical bits of information will
have to be communicated by Mr. Q to be
able to send his qubit across, over the
classical channel? 2

101
more
• Mr. Q got the bits from partially measuring
his qubit. This measurement destroys the
qubit Mr. Q wants to send (cloning is not
possible), and due to entanglement
collapses the qubit on the peers side.
• The peer doesn't know how it has
collapsed however, but the two bits tell
him which corrections he should do on his
qubit to get Mr. Q's original qubit.

102
Unit 1 -First Course
By : Professor Lili Saghafi
https://professorlilisaghafiquantumcomputing.wordpres
s.com
@Lili_PLS
Quantum Computing
First Course
Quantum internet
Introduction

Quantum Computing Quantum Internet 2020_unit 1 By: Prof. Lili Saghafi

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