Quantum computers consist of qubits that can be in superposition and entangled with each other. The quantum internet is still in early stages, similar to the classical internet in the 1960s. Efforts are being made to build small quantum networks that could become the first quantum internet. Quantum teleportation allows transmitting qubits using entanglement, but does not enable faster-than-light communication. Building a large-scale quantum computer faces challenges of developing sophisticated hardware and software to control and operate many qubits.

1. Quantum Computers
Lesson 2
By: Professor Lili Saghafi
proflilisaghafi@gmail.com
@Lili_PLS
1

2. Intro
● 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.
● Just like a classical internet a quantum internet consists of computers attached to
an internet. In the case of a quantum internet these are naturally quantum
computers.
● 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 QuTech is aiming to have a small quantum node network, which might
become the first quantum internet on earth.
2

3. Quantum Internet
● 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.
● 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
● The quantum manifesto is a €1 billion initiative, aiming to kick-start the
quantum industry in Europe.
● The efforts of Google to achieve quantum supremacy with their latest 72 qubit
processor.
3

4. ARPANET
● The Advanced Research Projects Agency Network
(ARPANET) was an early packet switching network and
the first network to implement the protocol suite TCP/IP.
● 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 Defense.
4

5. 5

6. Layers in a working quantum computer
4 components listed below are layers in a working quantum
computer
1. Qubits - to store quantum information
2. Compilers - to translate quantum algorithms into a form
that can be reliably executed on the available hardware
3. Software - to give instructions to the computer to perform
operations
4. Quantum algorithm - it's like a recipe: a set of instructions
to create a delicious cake
6

7. Four commonly used definitions in quantum world
● Qubit
● Superposition
● Entanglement
● Teleportation
7

8. Qubit
● 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.
● A qubit can be 0 and 1 at the same time.A qubit is the basic building block of a
quantum computer. A two-level quantum system, A qubit can only be a two-level
quantum system. Where one level will be defined to be zero and the other to be
one. A qubit can be in any superposition of these two levels.
● It is possible for a quantum system to have multiple levels, or states. These
systems are not considered qubits, except if only 2 of the levels are used.
● storing bits as a state in classical computer.This state can be either 0 or 1 at a
given instance.storing qubits as a state in quantum computer.This state can be
either 0 or 1 at a given instance or This state can be both 0 and 1 at a given
8

9. Qubits
In many architectures for quantum computers, it's necessary to distinguish
between physical qubits, which are built in the laboratory, and logical
qubits, in which we encode valuable quantum information.
Physical Qubits
● Physical qubits can be in superposition
● Physical qubits are physically realised qubits
Logical qubits
● Logical qubits can be in superposition
● Logical qubits consist of one or more physical qubits
● Logical qubits have a longer coherence time than physical qubits
9

10. Note
● One important fact about comparing classical and quantum computers is that
everything a quantum computer can do, a classical computer can also do.
However, a lot of classical memory is needed to simulate a small number
of qubits.
● To simulate n qubits on a classical computer, you need 64×2 to the power of
n classical bits (if working with 'double-precision floating point' numbers).
● There are classical supercomputers that have access to about 500 terabytes
(∼5×10 to the power 14 bits) of memory.
● How many logical qubits are needed to perform a computation that cannot be
simulated on such a classical supercomputer? ~50
10

11. Five key criteria
In 2000, David DiVincenzo listed five key criteria in building Quantum
Computers.
1. First, a quantum computer must be scalable.
2. Second, it must be possible to initialize the qubits.
3. Third, good qubits are needed, they need to have a long quantum
coherence to make sure that the quantum state is not lost.
4. It is furthermore required to have what is called a universal set of quantum
gates, meaning that one can do the operations needed to execute a
quantum algorithm.
5. And finally, we need to be able to measure all of those qubits
11

12. A checklist, called the DiVincenzo criteria
When evaluating a design for a new quantum computer, it's helpful to have a checklist of known
requirements that the computer has to fulfil. We have just such a checklist, called the DiVincenzo
criteria.
Following statements are the DiVincenzo criteria for the implementation of quantum computation.
1. Good qubits are needed, the quantum state cannot be lost
2. A quantum system must have a universal set of quantum gates. (A universal set of gates is a
set such that any other possible gate can be rewritten in a sequence of the gates in the
universal set)
3. A quantum system must be scalable, with well-defined qubits
4. It must be possible to perform measurements on a qubit in a quantum system
5. A quantum system must be able to initialize qubits to a fixed state, such as the zero state
12

13. 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.
● 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.
● So Quantum computers are good at solving search tasks.
13

14. Superposition
● in the quantum world superposition can mean something different entirely. At the
quantum scale, particles can also be thought of as waves.
● Particles can exist in different states, for example they can be in different positions, have
different energies or be moving at different speeds. But because quantum mechanics is
weird, instead of thinking about a particle being in one state or changing between a
variety of states, particles are thought of as existing across all the possible states at the
same time.
● It’s a bit like lots of waves overlapping each other. This situation is known as a
superposition of states. If you’re thinking in terms of particles, it means a particle can
be in two places at once. This doesn’t make intuitive sense but it’s one of the weird
realities of quantum physics.However, once a measurement of a particle is made, and
for example its energy or position is known, the superposition is lost and now we have
a particle in one known state.
14

15. Superposition
15

16. Superposition
Consider the following two experiments for a double slit experiment:
● Experiment 1: A lot of photons (light particles, which are also quantum 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.
Both screens show the same interference pattern. All photons go through both slits, then interfere
with themselves.
16

17. (interference pattern made by electrons)
Another image of the patterns created by electrons and protons.
17

18. Watch the video
18

19. In a Double-Slit Experiment, an actual wave completely passes through two slits at the same
time creating an interference pattern. But a particle can only pass through either one of the slits,
and so it should just pass through and hit the region on the wall right behind the slits. We would
expect the particles to create 2 bright regions.
19

20. 20

21. Even if we move the individual particles apart to vast distances in the universe,
they keep behaving like a system in superposition of multiple states.
21

22. Entanglement
Two particles can be entangled even when they are millions of
kilometres apart.
● 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
● Entanglement has two very special properties:
● entanglement is inherently private
and allows maximal coordination.
22

23. Entanglement
● 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.
● Qubit A is in a laboratory on earth and qubit B is in outer space.
● These qubits are maximally entangled with each other and have perfect
correlation.
● These qubits are measured in such a way they collapse to either 0 or 1.
● Statement: Without any communication before the measurement, both
of the qubits will give the same outcomes upon simultaneous
measurement. Which is true. For the mentioned constraints, the qubits
collapse to the same state instantaneously, without any communication, over
an arbitrary distance. 23

24. 24

25. Two very fundamental properties of entanglement
Two properties of entanglement and why they give power to a quantum internet.
The first feature of entanglement is that it allows maximum coordination.
● Two qubits can be entangled even at very long distances.
For example
● I can have a qubit here, which is entangled with a qubit very far away, for
example in China.
● Now if I make a measurement on my qubit here and a friend of mine would
make the same measurement in China, then it will turn out that we will always
get the same outcome.
● You can think of a measurement as asking a question to a qubit. 25

26. For example,
● I might ask the qubit: “Are you pointing left or are you pointing right?”
● Maximum coordination means that if I see the outcome left in here, then
immediately/instantaneously,if my friend in China makes the same
measurement the qubit will also be pointing to the left.
● And if I see it pointing to the right then also in China it will be pointing to the
right,
● even if the answer is not determined ahead of time.
● In fact randomly we will get left-left or right-right, but the point is that the
outcomes will always be the same.
● And the amazing thing about entanglement is that this is true for any
measurement or any question we might ask
26

27. Entanglement
27

28. For example,
● If I were to ask the qubit: “Qubit, are you red or blue?”
● Then we would have always observe maximum
coordination: red-red or blue-blue but never anything else.
So the first feature of entanglement is maximum
coordination and it is this feature that makes
entanglement so suitable for tasks that require
synchronization or coordination.
28

29. 29

30. The second feature of entanglement is that it is inherently
private
● Given that qubits are so powerful allowing this instantaneous maximum
coordination, wouldn’t it be great if many qubits could be entangled?
● Now it turns out that only 2 qubits can be maximally entangled with each other.
● So entanglement is inherently private.
● If I have a qubit here and the qubit that it’s entangled with is somewhere in China,
then you can think of this entanglement as a private connection that nothing else
can have part of.
● It is not possible for any other qubit anywhere, to have any share of this
entanglement between here’s qubit and the qubit in China.It is this feature that
makes quantum communication so fundamentally suitable for tasks that require
30

31. 31

32. Which property of
entanglement is useful for
making communication
secure?
32

33. Answer
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.
33

34. Although quantum computing
has many promising
applications, to build a real
quantum computer several
challenges must be overcome.
The computer architecture and
hardware needed for quantum
computing is very
sophisticated and delicate.
34

35. 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.”
35

36. Teleportation
1. What is and isn't possible with quantum teleportation?
2. 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.
36

37. Teleportation
37

38. Quantum 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.
38

39. 39

40. Example
● 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 a classical
network.
● Mr. Q wants to send one quantum bit of information to his peer with whom he
shares an entangled pair of qubits (with each party holding one qubit).
● 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? YES
40

41. 41
An illustration of a quantum state
being transmitted between the two
Canary Islands, La Palma and
Tenerife. Courtesy of
NOVA/WGBH Boston. Copyright
WGBH Educational Foundation.

42. Quantum Teleportation: A More Secure
Information Processing Platform
“To develop [quantum teleportation] in full scale and allow it to be usable by
everyone, the computer information processing platform needs to be
smaller.” (Xiaosong Ma, Tang lab, Yale’s Nanodevice Laboratory )
42

43. 43
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?

44. 44
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

45. 45

46. From one qubit to many qubits
A future quantum computer will contain many hardware and software components.
We can leverage of classical technology and construct a framework to layout a
vision for a quantum computer. This video will explain the various layers that will
make a quantum computer. First, Menno will introduce the qubit, the basic building
block, and discuss how to go to many qubits. However, many qubits don’t make a
quantum computer and in the second video, Menno will discuss all the elements
that are required for a large-scale quantum computer.
● Creating full working qubits is a huge scientific challenge.
● The five DiVincenzo criteria must be overcome to build a quantum computer.
46

47. From one qubit to many qubits
As DiVincenzo’s five criteria state, many more building blocks are needed to be able to operate the
qubits. Did you know that the water molecules in your glass of water form quantum states that can
be used to define qubits? This means that when you drink you have billions of qubits in your hand!
However, a billion qubits alone does not make a quantum computer. In order to do something
practical with these qubits, we need to be able to control and read them, and all these qubits
need to work in harmony according to your input.
● The scientific interest for quantum computers focuses on the development of working and
scalable qubits.
● On top of the qubit we need a whole new set of layers to actually instruct the qubit.
47

48. Edison thoughts
It is said, that in 1943 Thomas Edison of IBM thought there would be a world
market for maybe 5 computers.
Nowadays, there are billions of computers, in a vast variety of applications and
places, even in your pocket. This development was driven by a variety of
technological advances, such as the silicon transistor, which has allowed for
exponential scaling of the number of transistors on a chip (Moore’s law).
48

49. What is a quantum internet?
Just like a classical internet a quantum internet consists of computers attached to
an internet. In the case of a quantum internet these are naturally quantum
computers.
On a quantum internet we don’t send classical bits, 0’s and 1’s, but we will
transmit qubits.
In the Netherlands they are working on a quantum internet between four hubs:
Delft, Amsterdam, Leiden en The Hague.
49

50. What is a quantum internet?
50

51. What is a quantum internet?
51

52. First element of a Quantum Internet
● The first element of a quantum internet is what we call an end node.
● An end node is basically your computer or laptop or phone that is attached to the internet and that
you use in order to run applications. So you need the end node in order to use the quantum
internet.
● on a quantum internet we will not use normal laptops, cell phones or computers,
● but instead we will use quantum computers.These quantum computers actually don’t need to be
very complicated.It turns out that most applications of a quantum internet only require these end
node quantum computers to be very simple and have less than 10 qubits.In fact for most
applications they only need to have one qubit.The reason why we typically do not need many qubits
is because a quantum internet draws its power from quantum entanglement.And already one
qubit at each end point is sufficient to have entanglement. In contrast on a quantum computer
we always need more qubits than can be simulated on a classical computer in order to do something
new and interesting.
52

53. Second element of a Quantum Internet “quantum repeater”.
● The next element of a quantum internet is that, similar to a classical internet,we have all kinds of
elements that allow us to maximize the use of existing infrastructure.
● On a classical internet, not every computer on the internet has a direct fiber connection to every
other computer on the internet.But instead, fibers run through central points where there are
switches that direct the bits in the right direction.
● If you want to build a quantum internet, then similar to a classical internet, you for example want
switches that are capable of switching single qubits.
● Now ideally we would like to send qubits over very long distances; from any point on earth to any
other point on earth.In order to achieve this we will need something that is capable of sending qubits
over long distances.
● This requires a very special form of repeater called a “quantum repeater”.A quantum repeater
works very differently than the classical repeater.
53

54. Control Traffic
● When realizing a quantum internet, then just like on the classical internet, we
will also need some control traffic.
● Basically next to the quantum communication we will also use classical
communication,for example to direct the qubits in the right destination in the
network.
● This is what a quantum internet looks like.
● quantum internet allows us to solve tasks that are impossible to accomplish
on a classical internet.
54

55. What makes a quantum internet, or what makes the transmission of qubits so much more powerful
than what we have today?
● Qubits have very special features
● They cannot be copied, making them ideal for security applications.
● Two qubits can also be in a very special state: namely an entangled state.
● An entangled state between two qubits is the essence of the power of a
quantum internet.
55

56. Quantum Internet
● A quantum internet is composed of end nodes, switches, repeaters and
control traffic.
● An entangled state between two qubits is the essence of the power of a
quantum internet.
● Qubits can be entangled at a very long distance, but when we make the same
measurement on both qubits, they will give the same outcome. This feature is
called maximum coordination.
● When two qubits are maximally entangled, it is impossible for any other qubit
to have a share of this entanglement, making it inherently private.
56

57. Quantum internet vs classical internet
● Features are possible on a quantum internet, but impossible on a classical
internet are, Secure communication and Secure cloud computing.
● The security of classical communication cannot be guaranteed, as encryption
methods can be broken.
● A quantum internet can be fundamentally secure because of
entanglement.
● While anonymous communication could be implemented on a quantum
internet, this is already widely used on classical internet.
● Cloud computing is possible using a classical internet, but it is impossible to
ensure security.
57

58. Elements of a quantum internet
● End nodes
● Control traffic
● Switches
● Repeaters
Note:
A quantum internet need not be wireless, though it would be very convenient.
A quantum internet will incorporate:
- end nodes, to send and receive information over the network
- control traffic, to relay measurement results and other classical data
- switches, to re-route quantum information towards its intended destination
- repeaters, to extend the range at which we can create entanglement
58

59. Size of an End Node
● a large quantum computer is not necessary in order to have a functioning end
node.
● Why can the quantum computers at the end nodes be very small? Because
one qubit at each end node is enough to have entanglement over the whole
network.
59

60. Features of the entanglement of qubits
entanglement is inherently private and allows maximal coordination
● Measuring one qubit of a pair of maximally entangled qubits is enough to
know the state of the other qubit as well
● Maximal entanglement is inherently private
● Maximum coordination means that measurements on entangled qubits will
give the same outcome.
● When two qubits are maximally entangled, no other qubit can be part of
this entanglement.
60

61. 61

62. Maximum Coordination
entanglement is inherently private and allows maximal coordination
Maximum coordination means that, if measured the same way, two entangled
qubits always give the same outcome
Few-qubit quantum computers
a quantum computer with few (i.e. 5) logical qubits also relevant, because :
● It is useful for scientists and quantum software engineer to test their concepts
● It is already possible to securely communicate with just two end nodes, each
with one qubit
62

63. REVIEW of Five key criteria
In 2000, David DiVincenzo listed five key criteria.
1. First, a quantum computer must be scalable.
2. Second, it must be possible to initialize the qubits.
3. Third, good qubits are needed, they need to have a long quantum
coherence to make sure that the quantum state is not lost.
4. It is furthermore required to have what is called a universal set of quantum
gates, meaning that one can do the operations needed to execute a
quantum algorithm.
5. And finally, we need to be able to measure all of those qubits
63

64. 64

65. Flying qubit
two additional DiVincenzo criteria for quantum communication:
6. The ability to interconvert stationary and flying qubits
7. The ability to faithfully transmit flying qubits between specified locations
● A quantum internet requires flying qubits
● A quantum internet will require qubits which can be transmitted, which is exactly what flying
qubits are.
● While it is correct that photons could be used to implement flying qubits, it is not true that any
photon is a flying qubit. Currently, most proposals for a quantum internet make use of
photons, but other types of qubits could also be used.
● Flying qubits could also interact with other qubits, but these qubits should be at a different
location. Another option is to convert flying to stationary qubits, and have interactions
between stationary qubits only.
● Applying quantum gates is indeed only required for stationary qubits, not for flying qubits. 65

66. Quantum Computers
Lesson 2
By: Professor Lili Saghafi
proflilisaghafi@gmail.com
@Lili_PLS
66