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A tale of quantum computers Alexandru Gheorghiu - - PowerPoint PPT Presentation

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A tale of quantum computers Alexandru Gheorghiu gheorghiuandru@gmail.com The University of Edinburgh I V N E U R S E I H T Y T O H F G R E U D B I N A long time ago in a galaxy not so far away... Quantum Mechanics

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A tale of quantum computers

Alexandru Gheorghiu gheorghiuandru@gmail.com

The University of Edinburgh

T H E U N I V E R S I T Y O F E D I N B U R G H

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A long time ago in a galaxy not so far away...

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Quantum Mechanics

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Quantum Mechanics

1900s-1930s Inception of Quantum Mechanics

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Quantum Mechanics

1900s-1930s Inception of Quantum Mechanics

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Quantum Mechanics

1900s-1930s Inception of Quantum Mechanics Extremely successful theory leading to many many discoveries...

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Quantum Computation

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Quantum Computation

While highly accurate, quantum systems are extremely complex

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SLIDE 9

Quantum Computation

While highly accurate, quantum systems are extremely complex Polarizations for system of 100 photons → 2100 variables!

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SLIDE 10

Quantum Computation

While highly accurate, quantum systems are extremely complex Polarizations for system of 100 photons → 2100 variables!

  • “What kind of computer are we

going to use to simulate physics?” Richard Feynman (1981)

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SLIDE 11

Quantum Computation

While highly accurate, quantum systems are extremely complex Polarizations for system of 100 photons → 2100 variables!

  • “What kind of computer are we

going to use to simulate physics?” Richard Feynman (1981)

  • Simulate physics = simulate QM
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SLIDE 12

Quantum Computation

While highly accurate, quantum systems are extremely complex Polarizations for system of 100 photons → 2100 variables!

  • “What kind of computer are we

going to use to simulate physics?” Richard Feynman (1981)

  • Simulate physics = simulate QM
  • Exponential overhead for classical

computers

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SLIDE 13

Quantum Computation

While highly accurate, quantum systems are extremely complex Polarizations for system of 100 photons → 2100 variables!

  • “What kind of computer are we

going to use to simulate physics?” Richard Feynman (1981)

  • Simulate physics = simulate QM
  • Exponential overhead for classical

computers

  • A task for super-computers
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SLIDE 14

Quantum Computation

While highly accurate, quantum systems are extremely complex Polarizations for system of 100 photons → 2100 variables!

  • “What kind of computer are we

going to use to simulate physics?” Richard Feynman (1981)

  • Simulate physics = simulate QM
  • Exponential overhead for classical

computers

  • A task for super-computers

Feynman’s idea: Make a computer with quantum computing elements!

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SLIDE 15

Brief history

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SLIDE 16

Brief history

  • 1980s Idea of quantum computation. Paul Benioff, Yuri

Manin, Richard Feynman, David Deutsch

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SLIDE 17

Brief history

  • 1980s Idea of quantum computation. Paul Benioff, Yuri

Manin, Richard Feynman, David Deutsch

  • 1990s Theory of efficient quantum simulation. Seth Lloyd
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SLIDE 18

Brief history

  • 1980s Idea of quantum computation. Paul Benioff, Yuri

Manin, Richard Feynman, David Deutsch

  • 1990s Theory of efficient quantum simulation. Seth Lloyd
  • 1994 Peter Shor’s algorithms for factoring and discrete log.

Quantum computers can break RSA, Diffie-Hellman, El Gamal, Elliptic Curve Cryptography and others

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SLIDE 19

Brief history

  • 1980s Idea of quantum computation. Paul Benioff, Yuri

Manin, Richard Feynman, David Deutsch

  • 1990s Theory of efficient quantum simulation. Seth Lloyd
  • 1994 Peter Shor’s algorithms for factoring and discrete log.

Quantum computers can break RSA, Diffie-Hellman, El Gamal, Elliptic Curve Cryptography and others

  • 2001 Experiment factors 15 using Shor’s algorithm
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SLIDE 20

Brief history

  • 1980s Idea of quantum computation. Paul Benioff, Yuri

Manin, Richard Feynman, David Deutsch

  • 1990s Theory of efficient quantum simulation. Seth Lloyd
  • 1994 Peter Shor’s algorithms for factoring and discrete log.

Quantum computers can break RSA, Diffie-Hellman, El Gamal, Elliptic Curve Cryptography and others

  • 2001 Experiment factors 15 using Shor’s algorithm
  • 2010s D-Wave, Google, IBM, NQIT and various universities

work on developing quantum computers

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Brief history

  • 1980s Idea of quantum computation. Paul Benioff, Yuri

Manin, Richard Feynman, David Deutsch

  • 1990s Theory of efficient quantum simulation. Seth Lloyd
  • 1994 Peter Shor’s algorithms for factoring and discrete log.

Quantum computers can break RSA, Diffie-Hellman, El Gamal, Elliptic Curve Cryptography and others

  • 2001 Experiment factors 15 using Shor’s algorithm
  • 2010s D-Wave, Google, IBM, NQIT and various universities

work on developing quantum computers How serious is the involvement in quantum computation?

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Who invests in Quantum Computing?

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Development and current status

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Other applications

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Other applications

  • Data mining and efficient unstructured querying
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Other applications

  • Data mining and efficient unstructured querying
  • Machine learning and quantum machine learning
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SLIDE 27

Other applications

  • Data mining and efficient unstructured querying
  • Machine learning and quantum machine learning
  • Efficient distributed computation
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SLIDE 28

Other applications

  • Data mining and efficient unstructured querying
  • Machine learning and quantum machine learning
  • Efficient distributed computation
  • Efficient communication
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SLIDE 29

Other applications

  • Data mining and efficient unstructured querying
  • Machine learning and quantum machine learning
  • Efficient distributed computation
  • Efficient communication
  • Data compression
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SLIDE 30

Other applications

  • Data mining and efficient unstructured querying
  • Machine learning and quantum machine learning
  • Efficient distributed computation
  • Efficient communication
  • Data compression
  • Quantum cryptography (more on that later)
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Other applications

  • Data mining and efficient unstructured querying
  • Machine learning and quantum machine learning
  • Efficient distributed computation
  • Efficient communication
  • Data compression
  • Quantum cryptography (more on that later)

“For me, the single most important application of a quantum computer is disproving the people who said it’s impossible. The rest is just icing on the cake” Scott Aaronson

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Misconceptions

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Misconceptions

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How do they work?

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How do they work?

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How do they work?

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How do they work?

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How do they work?

Bits: 0, 1 Qubits: |0, |1

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How do they work?

Bits: 0, 1 Qubits: |0, |1 General qubit: |ψ = α |0 + β |1

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How do they work?

Bits: 0, 1 Qubits: |0, |1 General qubit: |ψ = α |0 + β |1 α, β are amplitudes (complex numbers)

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How do they work?

Bits: 0, 1 Qubits: |0, |1 General qubit: |ψ = α |0 + β |1 α, β are amplitudes (complex numbers) |α|2 probability of observing |0, |β|2 probability of observing |1 |α|2 + |β|2 = 1

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How to make them?

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How to make them?

  • Atom energy levels +

magnetic fields

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How to make them?

  • Atom energy levels +

magnetic fields

  • Photon polarization +

crystals

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SLIDE 45

How to make them?

  • Atom energy levels +

magnetic fields

  • Photon polarization +

crystals

  • Photon paths + mirrors and

crystals

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SLIDE 46

How to make them?

  • Atom energy levels +

magnetic fields

  • Photon polarization +

crystals

  • Photon paths + mirrors and

crystals

  • Electron spin + magnetic

fields

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SLIDE 47

How to make them?

  • Atom energy levels +

magnetic fields

  • Photon polarization +

crystals

  • Photon paths + mirrors and

crystals

  • Electron spin + magnetic

fields

  • Hybrid systems and others...
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SLIDE 48

Summary

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Summary

  • State

Classical

  • Bits (0, 1)

Quantum

  • Qubits (α |0 + β |1)
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Summary

  • State
  • Computation

process Classical

  • Bits (0, 1)
  • Logical (AND, OR,

NAND) Quantum

  • Qubits (α |0 + β |1)
  • Unitary

(interference)

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Summary

  • State
  • Computation

process

  • Realization

Classical

  • Bits (0, 1)
  • Logical (AND, OR,

NAND)

  • Voltage, light

intensity etc Quantum

  • Qubits (α |0 + β |1)
  • Unitary

(interference)

  • Atomic energy levels,

polarization etc

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How will they look?

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Challenges

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Challenges

  • Maintaining superposition

states (coherence)

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Challenges

  • Maintaining superposition

states (coherence)

  • Interaction with the

environment → decoherence

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SLIDE 56

Challenges

  • Maintaining superposition

states (coherence)

  • Interaction with the

environment → decoherence

  • Noise
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SLIDE 57

Challenges

  • Maintaining superposition

states (coherence)

  • Interaction with the

environment → decoherence

  • Noise
  • Fault tolerance
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Challenges

  • Maintaining superposition

states (coherence)

  • Interaction with the

environment → decoherence

  • Noise
  • Fault tolerance
  • Scalability
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Challenges

  • Maintaining superposition

states (coherence)

  • Interaction with the

environment → decoherence

  • Noise
  • Fault tolerance
  • Scalability
  • Only technological

limitations

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State of the art

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State of the art

  • 2001 Shor’s algorithm factors 15 on 7 qubits
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State of the art

  • 2001 Shor’s algorithm factors 15 on 7 qubits
  • 2011 Shor’s algorithm factors 21
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SLIDE 63

State of the art

  • 2001 Shor’s algorithm factors 15 on 7 qubits
  • 2011 Shor’s algorithm factors 21
  • 2012 Universal quantum computation on 2 fault tolerant

qubits

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State of the art

  • 2001 Shor’s algorithm factors 15 on 7 qubits
  • 2011 Shor’s algorithm factors 21
  • 2012 Universal quantum computation on 2 fault tolerant

qubits

  • 2014-2015 Qubits and gates in silicon chips
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State of the art

  • 2001 Shor’s algorithm factors 15 on 7 qubits
  • 2011 Shor’s algorithm factors 21
  • 2012 Universal quantum computation on 2 fault tolerant

qubits

  • 2014-2015 Qubits and gates in silicon chips
  • 2015 D-Wave 2X, 1000 qubits, optimization problems, no

fault tolerance

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State of the art

  • 2001 Shor’s algorithm factors 15 on 7 qubits
  • 2011 Shor’s algorithm factors 21
  • 2012 Universal quantum computation on 2 fault tolerant

qubits

  • 2014-2015 Qubits and gates in silicon chips
  • 2015 D-Wave 2X, 1000 qubits, optimization problems, no

fault tolerance

  • 2020 NQIT, Q20:20, fault tolerant (20 qubits), scalable
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State of the art

  • 2001 Shor’s algorithm factors 15 on 7 qubits
  • 2011 Shor’s algorithm factors 21
  • 2012 Universal quantum computation on 2 fault tolerant

qubits

  • 2014-2015 Qubits and gates in silicon chips
  • 2015 D-Wave 2X, 1000 qubits, optimization problems, no

fault tolerance

  • 2020 NQIT, Q20:20, fault tolerant (20 qubits), scalable
  • And others...
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Towards quantum secure cryptography

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Towards quantum secure cryptography

Will quantum computers pose a threat to cryptography?

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Towards quantum secure cryptography

Will quantum computers pose a threat to cryptography? Existing crypto based on unproven hard problems (factoring, discrete log etc)

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Towards quantum secure cryptography

Will quantum computers pose a threat to cryptography? Existing crypto based on unproven hard problems (factoring, discrete log etc) How long do you want your data to stay secure? (∼ 20 years)

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Towards quantum secure cryptography

Will quantum computers pose a threat to cryptography? Existing crypto based on unproven hard problems (factoring, discrete log etc) How long do you want your data to stay secure? (∼ 20 years) How long to make the Internet quantum secure? (∼ 20 years)

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Towards quantum secure cryptography

Will quantum computers pose a threat to cryptography? Existing crypto based on unproven hard problems (factoring, discrete log etc) How long do you want your data to stay secure? (∼ 20 years) How long to make the Internet quantum secure? (∼ 20 years) What about problems that are hard for quantum computers?

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SLIDE 74

Towards quantum secure cryptography

Will quantum computers pose a threat to cryptography? Existing crypto based on unproven hard problems (factoring, discrete log etc) How long do you want your data to stay secure? (∼ 20 years) How long to make the Internet quantum secure? (∼ 20 years) What about problems that are hard for quantum computers? “Even if a classical protocol is proven secure based on the hardness

  • f some problem, and that problem is hard even for quantum

computers, we have no guarantee that the protocol is secure against quantum computers.” Dominique Unruh

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Quantum Cryptography

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Quantum Cryptography

  • Idea: do not base security
  • n computational problems,

but on the laws of physics

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Quantum Cryptography

  • Idea: do not base security
  • n computational problems,

but on the laws of physics

  • Assuming quantum

mechanics is correct, unconditional security

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SLIDE 78

Quantum Cryptography

  • Idea: do not base security
  • n computational problems,

but on the laws of physics

  • Assuming quantum

mechanics is correct, unconditional security

  • Adversary with unlimited

power cannot break the encryption

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SLIDE 79

Quantum Cryptography

  • Idea: do not base security
  • n computational problems,

but on the laws of physics

  • Assuming quantum

mechanics is correct, unconditional security

  • Adversary with unlimited

power cannot break the encryption

  • First development: quantum

money scheme

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SLIDE 80

Quantum Cryptography

  • Idea: do not base security
  • n computational problems,

but on the laws of physics

  • Assuming quantum

mechanics is correct, unconditional security

  • Adversary with unlimited

power cannot break the encryption

  • First development: quantum

money scheme

  • Quantum key distribution
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SLIDE 81

Quantum Cryptography

  • Idea: do not base security
  • n computational problems,

but on the laws of physics

  • Assuming quantum

mechanics is correct, unconditional security

  • Adversary with unlimited

power cannot break the encryption

  • First development: quantum

money scheme

  • Quantum key distribution
  • Uses one-time pad
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SLIDE 82

One-time pad

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One-time pad

M1

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One-time pad

M1 ⊕ Key

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One-time pad

M1 ⊕ Key = C1

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SLIDE 86

One-time pad

M1 ⊕ Key = C1 C1 ⊕ Key = M1

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One-time pad

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One-time pad

M2 ⊕ Key = C2

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SLIDE 89

One-time pad

M2 ⊕ Key = C2 C1 ⊕ C2 = M1 ⊕ M2

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SLIDE 90

Quantum Key Distribution (QKD)

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SLIDE 91

Quantum Key Distribution (QKD)

Make two parties share a random secret key

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SLIDE 92

Quantum Key Distribution (QKD)

Make two parties share a random secret key Arbitrary size key → arbitrary number of messages

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SLIDE 93

Quantum Key Distribution (QKD)

Make two parties share a random secret key Arbitrary size key → arbitrary number of messages Communication bandwidth limited by key rate

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SLIDE 94

Quantum Key Distribution (QKD)

Make two parties share a random secret key Arbitrary size key → arbitrary number of messages Communication bandwidth limited by key rate

  • BB84
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SLIDE 95

Quantum Key Distribution (QKD)

Make two parties share a random secret key Arbitrary size key → arbitrary number of messages Communication bandwidth limited by key rate

  • BB84
  • Uncertainty

principle

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SLIDE 96

Quantum Key Distribution (QKD)

Make two parties share a random secret key Arbitrary size key → arbitrary number of messages Communication bandwidth limited by key rate

  • BB84
  • Uncertainty

principle

  • No cloning
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SLIDE 97

Quantum Key Distribution (QKD)

Make two parties share a random secret key Arbitrary size key → arbitrary number of messages Communication bandwidth limited by key rate

  • BB84
  • Uncertainty

principle

  • No cloning
  • Unconditional

security (based

  • n QM)
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SLIDE 98

Quantum Key Distribution (QKD)

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SLIDE 99

Quantum Key Distribution (QKD)

What about exploiting the implementation?

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SLIDE 100

Quantum Key Distribution (QKD)

What about exploiting the implementation? Not a problem!

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SLIDE 101

Quantum Key Distribution (QKD)

What about exploiting the implementation? Not a problem!

  • Device

independence

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SLIDE 102

Quantum Key Distribution (QKD)

What about exploiting the implementation? Not a problem!

  • Device

independence

  • QKD with

untrusted devices

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SLIDE 103

Quantum Key Distribution (QKD)

What about exploiting the implementation? Not a problem!

  • Device

independence

  • QKD with

untrusted devices

  • Quantum

entanglement

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SLIDE 104

Quantum Key Distribution (QKD)

What about exploiting the implementation? Not a problem!

  • Device

independence

  • QKD with

untrusted devices

  • Quantum

entanglement

  • Testing for

correlations

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SLIDE 105

Quantum Key Distribution (QKD)

What about exploiting the implementation? Not a problem!

  • Device

independence

  • QKD with

untrusted devices

  • Quantum

entanglement

  • Testing for

correlations

  • Difficult to

realize

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SLIDE 106

What you can buy today

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SLIDE 107

What you can buy today

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SLIDE 108

State of the art

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SLIDE 109

State of the art

  • QKD backbone
  • To be completed 2016
  • QuantumCTek
  • Commercial and government

use

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SLIDE 110

State of the art

  • QKD backbone
  • To be completed 2016
  • QuantumCTek
  • Commercial and government

use

  • QKD network
  • To be completed
  • Battelle and ID Quantique
  • Commercial and government

use

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SLIDE 111

Other uses of Quantum Cryptography

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SLIDE 112

Other uses of Quantum Cryptography

  • Secure authentication
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SLIDE 113

Other uses of Quantum Cryptography

  • Secure authentication
  • Digital signatures
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SLIDE 114

Other uses of Quantum Cryptography

  • Secure authentication
  • Digital signatures
  • Quantum money
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SLIDE 115

Other uses of Quantum Cryptography

  • Secure authentication
  • Digital signatures
  • Quantum money
  • Secure delegated (quantum) computation
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SLIDE 116

Other uses of Quantum Cryptography

  • Secure authentication
  • Digital signatures
  • Quantum money
  • Secure delegated (quantum) computation
  • Secure multi-party (quantum) computation
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SLIDE 117

Other uses of Quantum Cryptography

  • Secure authentication
  • Digital signatures
  • Quantum money
  • Secure delegated (quantum) computation
  • Secure multi-party (quantum) computation
  • Relativistic quantum cryptography
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SLIDE 118

Other uses of Quantum Cryptography

  • Secure authentication
  • Digital signatures
  • Quantum money
  • Secure delegated (quantum) computation
  • Secure multi-party (quantum) computation
  • Relativistic quantum cryptography

“In the next 6-24 months, organizations without a well articulated quantum risk management plan will loose business to organizations that do” Michele Mosca (October 2015)

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SLIDE 119

Recommended reading

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SLIDE 120

Recommended technical reading

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SLIDE 121

Conclusions

  • Quantum computers would be extremely useful
  • They can solve problems efficiently using interference
  • Recently, lots of investments and interest
  • Poses a risk to existing cryptography
  • Quantum cryptography to the rescue
  • Unconditional security and device independence
  • Commercial systems already exist
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SLIDE 122

Conclusions

  • Quantum computers would be extremely useful
  • They can solve problems efficiently using interference
  • Recently, lots of investments and interest
  • Poses a risk to existing cryptography
  • Quantum cryptography to the rescue
  • Unconditional security and device independence
  • Commercial systems already exist

There’s still a lot of work to be done...

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SLIDE 123

Conclusions

  • Quantum computers would be extremely useful
  • They can solve problems efficiently using interference
  • Recently, lots of investments and interest
  • Poses a risk to existing cryptography
  • Quantum cryptography to the rescue
  • Unconditional security and device independence
  • Commercial systems already exist

There’s still a lot of work to be done... “I don’t pretend we have all the answers. But the questions are certainly worth thinking about.” Arthur C. Clarke

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SLIDE 124

Thank you!

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SLIDE 125

Reading material and references

  • Quantum Computing since Democritus -

http://www.scottaaronson.com/democritus/

  • Quantum Computation and Quantum Information -

http://www.amazon.com/ Quantum-Computation-Information-Anniversary-Edition/ dp/1107002176

  • Scott Aaronson’s blog -

http://www.scottaaronson.com/blog/

  • Michael Nielsen’s blog -

http://michaelnielsen.org/blog/

  • Nice paper on quantum crypto - http://www.nature.com/

nature/journal/v507/n7493/full/nature13132.html

  • Quantum Computing for Computer Scientists -

http://www.amazon.co.uk/ Quantum-Computing-Computer-Scientists-Yanofsky/ dp/0521879965/ref=sr_1_1?ie=UTF8&qid=1451928677& sr=8-1&keywords=quantum+computing+for+computer+ scientists

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SLIDE 126

References

  • Feynman’s original paper on QC - https://www.cs.

berkeley.edu/~christos/classics/Feynman.pdf

  • Efficient quantum simulation, Seth Lloyd - https://www.

sciencemag.org/content/273/5278/1073.abstract

  • Experiment to factor 15 - http://www.nature.com/

nature/journal/v414/n6866/full/414883a.html

  • Experiment to factor 21 - http://www.nature.com/

nphoton/journal/v6/n11/full/nphoton.2012.259.html

  • Universal QC with 2 qubits - http://www.nature.com/

nature/journal/v484/n7392/abs/nature10900.html

  • QC in silicon - http://www.nature.com/nature/journal/

v526/n7573/full/nature15263.html

  • NQIT and Q20:20 - http://nqit.ox.ac.uk/technologies
  • D-Wave - http://www.dwavesys.com/
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SLIDE 127

References

  • Source for Dominique Unruh’s quote on slide 19 -

https://eprint.iacr.org/2010/212.pdf

  • Michele Mosca on the quantum risk to cryptography -

https://www.youtube.com/watch?v=eEn8LT119bY

  • Review of quantum cryptography - http://journals.aps.
  • rg/rmp/abstract/10.1103/RevModPhys.74.145
  • Device independence - https:

//www.icfo.eu/images/publications/J07-045.pdf

  • Quantum machine learning -

http://www.scottaaronson.com/papers/qml.pdf

  • List of existing quantum algorithms -

http://math.nist.gov/quantum/zoo/

  • Workshop on quantum computation - http:

//workshop.rosedu.org/2015/sesiuni/quantum-comp

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SLIDE 128

References

  • Image on slide 3 (Solvay conference) -

https://en.wikipedia.org/wiki/File: Solvay_conference_1927.jpg

  • Image on slide 4 (Richard P. Feynman) -

https://upload.wikimedia.org/wikipedia/en/4/42/ Richard_Feynman_Nobel.jpg

  • Image on slide 7 (development ladder) - M.H. Devoret, R.J.

Schoelkopf, Superconducting Circuits for Quantum Information: An Outlook, Science 8 March 2013, Vol. 339,

  • no. 6124, pp. 1169-1174, DOI:10.1126/science.1231930
  • Image on slide 9 (SMBC comic) -

http://www.smbc-comics.com/?id=1623

  • Image on slide 11 (comparison) -

http://download2.cerimes.fr/canalu/documents/ fuscia/quantum.turing.test_13249/kashefi.pdf

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SLIDE 129

References

  • Image on slide 12 (atom energy levels) - https:

//dr282zn36sxxg.cloudfront.net/datastreams/f-d% 3A96a9d2797f6e33d4a10187aeef0abdb52be51b8602c4fda58fa9768d% 2BIMAGE_THUMB_POSTCARD%2BIMAGE_THUMB_POSTCARD.1

  • Image on slide 12 (photon polarization) -

https://physics.aps.org/articles/v5/86

  • Image on slide 12 (optical paths) -

https://www.quora.com/ What-is-a-physical-example-of-a-unitary-operator-in-quantum- answer/Bingjie-Wang-2

  • Image on slide

14 (D-Wave chip) - http://www.aboutai.com/2014/07/11/ how-d-wave-built-quantum-computing-hardware-for-the-next-

  • Image on slide 14 (Optics) -

http://www.ichf.edu.pl/res/CL/research_en.html

  • Image on slide 14 (Optical chip) - http://www.bristol.ac.

uk/news/2015/april/photonic-chip.html

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SLIDE 130

References

  • Image on slide 14 (Ion trap top) - http://jqi.umd.edu/

sites/default/files/images/razoriontrap-001.jpg

  • Image on slide 14 (Ion trap bottom) - http://www.nist.

gov/pml/div688/microwave-quantum-081011.cfm

  • Image on slide 18 (Huge atom) -

http://www.economist.com/node/6877077

  • Image on slide 18 (quantum money) - https://a248.e.

akamai.net/f/1097/1823/7m/deliveryimages.acm.org/ 10.1145/2250000/2240258/figs/f2.jpg

  • Image on slide 19 (Death star) -

https://techrepublic-a.akamaihd.net/hub/i/2015/ 05/07/7663b419-f49c-11e4-940f-14feb5cc3d2a/death_ star_schematic.gif

  • Image on slide 20 (Lightsaber) -

http://vignette3.wikia.nocookie.net/starwars/ images/4/41/KunLightsaberSchematic.jpg/revision/ latest?cb=20110717211606

slide-131
SLIDE 131

References

  • Image on slide 21 (BB84) - http:

//swissquantum.idquantique.com/IMG/jpg/bb84.jpg

  • Image on slide 22 (Device independence) -

https://physics.aps.org/articles/v7/99

  • Image on slide 23 (idquantique website) -

http://www.idquantique.com/quantum-safe-crypto/

  • Image on slide 24 (QKD rack) - http://www.vad1.com/

photo/stock/a299-3-boxes-labeled.pdf

  • Image on slide 25 (China network) - http:

//2014.qcrypt.net/wp-content/uploads/Zhao.pdf

  • Image on slide 25 (US network) -

http://www.theverge.com/2014/11/18/7214483/ quantum-networks-expand-across-three-continents