Our active application of quantum mechanics has previously been constrained by our ability to engineer and control systems at the small scales where quantum effects predominate. This has now changed. Scientists have reached first base on a set of enabling technologies that allow us to routinely manipulate atoms of matter and photons of light at individual level. This has unlocked our ability to create a new generation of devices that deliver unique capabilities directly tied to properties of quantum mechanics such as superposition and entanglement.

1. The second quantum
revolution: the world
beyond binary 0 and 1
Bruno FEDRICI
20/04/18 – Université de Lyon
DU Transformation Numérique

2. The first quantum
revolution

3. First half of the 20th
century, discovery of
fundamental laws of the microscopic realm
Formulation of quantum physics

4. Ground-breaking technologies
such as transistor (1947) and
laser (1960)

5. Based on bulk effects where
many quantum degrees of
freedom are manipulated
at once

6. “The mathematical theory of communication”
C. Shannon, 1947
→ source coding, channel coding, algorithmic complexity
theory, algorithmic information theory, information-
theoretic security, ...
The age of information

7. Gave birth to the semiconductors and to the
telecommunications industries

8. A second quantum
revolution ?

9. Technologies based on the manipulation
of individual quantum systems

10. Technologies based on the manipulation
of individual quantum systems
Make use of quantum properties such as
superposition and entanglement

11. Technologies based on the manipulation
of individual quantum systems
Make use of quantum properties such as
superposition and entanglement
Theoretically secure communications,
ultimate computing power, ultraprecise
sensors

12. Quantum information
processing toolbox

13. Superposition – A quantum
object can be in two or more
states at the same time; only
when a measurement is made
does it fall back into a single
state. If the coherence of the
system is carefully maintained,
superimposed states can
interfere with each other with
measurable consequences. This
key feature enables quantum
computers to go beyond the
power of digital 1 and 0. It is
also the source of the
remarkable sensitivity of
quantum sensors.
1

14. Superposition – A quantum
object can be in two or more
states at the same time; only
when a measurement is made
does it fall back into a single
state. If the coherence of the
system is carefully maintained,
superimposed states can
interfere with each other with
measurable consequences. This
key feature enables quantum
computers to go beyond the
power of digital 1 and 0. It is
also the source of the
remarkable sensitivity of
quantum sensors.
1
Classical bit
0
1

15. Superposition – A quantum
object can be in two or more
states at the same time; only
when a measurement is made
does it fall back into a single
state. If the coherence of the
system is carefully maintained,
superimposed states can
interfere with each other with
measurable consequences. This
key feature enables quantum
computers to go beyond the
power of digital 1 and 0. It is
also the source of the
remarkable sensitivity of
quantum sensors.
1
Classical bit
0
1
Quantum bit (Qubit)
|α |2
+ |β |2
= 1

16. Superposition – A quantum
object can be in two or more
states at the same time; only
when a measurement is made
does it fall back into a single
state. If the coherence of the
system is carefully maintained,
superimposed states can
interfere with each other with
measurable consequences. This
key feature enables quantum
computers to go beyond the
power of digital 1 and 0. It is
also the source of the
remarkable sensitivity of
quantum sensors.
1
Classical bit
0
1
Quantum bit (Qubit)
P(0) = |α |2
P(1) = |β |2
|α |2
+ |β |2
= 1

17. Superposition – A quantum
object can be in two or more
states at the same time; only
when a measurement is made
does it fall back into a single
state. If the coherence of the
system is carefully maintained,
superimposed states can
interfere with each other with
measurable consequences. This
key feature enables quantum
computers to go beyond the
power of digital 1 and 0. It is
also the source of the
remarkable sensitivity of
quantum sensors.
1
Blackboard
….

18. Indeterminacy – Quantum
physics is an intrinsically
probabilistic theory. The
uncertainty principle tells us
that it is not possible to
precisely measure all properties
of a quantum system at the
same time; this leads to the No-
Cloning Theorem: it is not
possible to create an identical
copy of a quantum state. This is
central to quantum
cryptography.
2

19. Indeterminacy – Quantum
physics is an intrinsically
probabilistic theory. The
uncertainty principle tells us
that it is not possible to
precisely measure all properties
of a quantum system at the
same time; this leads to the No-
Cloning Theorem: it is not
possible to create an identical
copy of a quantum state. This is
central to quantum
cryptography.
2

20. Indeterminacy – Quantum
physics is an intrinsically
probabilistic theory. The
uncertainty principle tells us
that it is not possible to
precisely measure all properties
of a quantum system at the
same time; this leads to the No-
Cloning Theorem: it is not
possible to create an identical
copy of a quantum state. This is
central to quantum
cryptography.
2
Blackboard
….

21. Entanglement – When two
quantum objects are entangled
they behave as one system. A
measurement on one also
affects the other, even if it is
physically separated. This is
intrinsic to the operation of
quantum computers, and also to
advanced forms of quantum
cryptography.
3

22. Entanglement – When two
quantum objects are entangled
they behave as one system. A
measurement on one also
affects the other, even if it is
physically separated. This is
intrinsic to the operation of
quantum computers, and also to
advanced forms of quantum
cryptography.
3
Single Q-system

23. Entanglement – When two
quantum objects are entangled
they behave as one system. A
measurement on one also
affects the other, even if it is
physically separated. This is
intrinsic to the operation of
quantum computers, and also to
advanced forms of quantum
cryptography.
3
Single Q-system
2 Q-systems
Separable state

24. Entanglement – When two
quantum objects are entangled
they behave as one system. A
measurement on one also
affects the other, even if it is
physically separated. This is
intrinsic to the operation of
quantum computers, and also to
advanced forms of quantum
cryptography.
3
Single Q-system
2 Q-systems
Separable state
2 Q-systems
Entangled state

25. Entanglement – When two
quantum objects are entangled
they behave as one system. A
measurement on one also
affects the other, even if it is
physically separated. This is
intrinsic to the operation of
quantum computers, and also to
advanced forms of quantum
cryptography.
3
Blackboard
….

26. Let's play with that !

27. Quantum Random
Number Generator

28. Applications
→ Cryptography
→ Numerical simulations
→ Statistical sampling
Random Numbers

29. Applications
→ Cryptography
→ Numerical simulations
→ Statistical sampling
Critical that these values be
→ Uniform distribution
→ Independent
Random Numbers

30. Applications
→ Cryptography
→ Numerical simulations
→ Statistical sampling
Critical that these values be
→ Uniform distribution
→ Independent
True random number
generators provide this
Random Numbers

31. Pseudo Random Numbers
Cryptographic applications typically use
algorithms for random number generation
→ Algorithms are deterministic and therefore
produce sequences of numbers that are not
trully random

32. Pseudo Random Numbers
Cryptographic applications typically use
algorithms for random number generation
→ Algorithms are deterministic and therefore
produce sequences of numbers that are not
trully random
Pseudo random numbers are
→ Sequences produced that satisfy statistical
randomness tests
→ Likely to be predictible

33. True vs Pseudo randomness
Conversion
to binary
Deterministic
algorithm
Source of true
randomness Seed
Random
bit stream
Pseudo random
bit stream
TRNG PRNG

34. E.g. true random numbers from single
photons and a 50:50 beam splitter:
TRNG by quantum means

35. Single Photon
Source
E.g. true random numbers from single
photons and a 50:50 beam splitter:
TRNG by quantum means

36. Single Photon
Source
“1”
E.g. true random numbers from single
photons and a 50:50 beam splitter:
TRNG by quantum means

37. Single Photon
Source
“0”
“1”
1 0 0 1 1 0 1 0 1 0 0
E.g. true random numbers from single
photons and a 50:50 beam splitter:
TRNG by quantum means

38. Single Photon
Source
“0”
“1”
1 0 0 1 1 0 1 0 1 0 0
E.g. true random numbers from single
photons and a 50:50 beam splitter:
QRNG are already
commercially available
→ See for instance ID Quantique,
Quintessence Labs, ...
State of the art QRNG ~ 100 Gb/s
TRNG by quantum means

39. https://qrng.anu.edu.au/RainBin.php
To download true random numbers from
quantum fluctuations of the vacuum field:
TRNG by quantum means

40. Quantum Computing

41. Moore's law

42. R. Feynman, “Simulating physics with computers”,
International Journal of Theoretical Physics, vol. 21, no. 6,
pp. 467–488, 1982.
D. Deutsch, “Quantum theory, the Church-Turing principle
and the universal quantum computer”, Proc. R. Soc. A, vol.
400, no. 1818, pp. 97–117, 1985.
Quantum
Speedup

43. R. Feynman, “Simulating physics with computers”,
International Journal of Theoretical Physics, vol. 21, no. 6,
pp. 467–488, 1982.
D. Deutsch, “Quantum theory, the Church-Turing principle
and the universal quantum computer”, Proc. R. Soc. A, vol.
400, no. 1818, pp. 97–117, 1985.
Quantum
Speedup
Conventional computing
One out of 2N
permutations
→ Sequential computation

44. R. Feynman, “Simulating physics with computers”,
International Journal of Theoretical Physics, vol. 21, no. 6,
pp. 467–488, 1982.
D. Deutsch, “Quantum theory, the Church-Turing principle
and the universal quantum computer”, Proc. R. Soc. A, vol.
400, no. 1818, pp. 97–117, 1985.
Quantum
Speedup
Conventional computing
One out of 2N
permutations
→ Sequential computation
Quantum computing
All of 2N
possible permutations
→ Parallel computation

45. R. Feynman, “Simulating physics with computers”,
International Journal of Theoretical Physics, vol. 21, no. 6,
pp. 467–488, 1982.
D. Deutsch, “Quantum theory, the Church-Turing principle
and the universal quantum computer”, Proc. R. Soc. A, vol.
400, no. 1818, pp. 97–117, 1985.
Quantum
Speedup
Conventional computing:
→ Classical bits + Logic gates (AND, OR, XOR, ...)

46. R. Feynman, “Simulating physics with computers”,
International Journal of Theoretical Physics, vol. 21, no. 6,
pp. 467–488, 1982.
D. Deutsch, “Quantum theory, the Church-Turing principle
and the universal quantum computer”, Proc. R. Soc. A, vol.
400, no. 1818, pp. 97–117, 1985.
Quantum
Speedup
Conventional computing:
→ Classical bits + Logic gates (AND, OR, XOR, ...)
Quantum computing:
→ Quantum bits + Quantum logic gates

47. R. Feynman, “Simulating physics with computers”,
International Journal of Theoretical Physics, vol. 21, no. 6,
pp. 467–488, 1982.
D. Deutsch, “Quantum theory, the Church-Turing principle
and the universal quantum computer”, Proc. R. Soc. A, vol.
400, no. 1818, pp. 97–117, 1985.
Quantum
Speedup
Blackboard
….

48. R. Feynman, “Simulating physics with computers”,
International Journal of Theoretical Physics, vol. 21, no. 6,
pp. 467–488, 1982.
D. Deutsch, “Quantum theory, the Church-Turing principle
and the universal quantum computer”, Proc. R. Soc. A, vol.
400, no. 1818, pp. 97–117, 1985.
Quantum
Speedup

49. Quantum
Speedup
R. Feynman, “Simulating physics with computers”,
International Journal of Theoretical Physics, vol. 21, no. 6,
pp. 467–488, 1982.
D. Deutsch, “Quantum theory, the Church-Turing principle
and the universal quantum computer”, Proc. R. Soc. A, vol.
400, no. 1818, pp. 97–117, 1985.

50. Quantum
Speedup
→ 50-60 qubits for quantum advantage
R. Feynman, “Simulating physics with computers”,
International Journal of Theoretical Physics, vol. 21, no. 6,
pp. 467–488, 1982.
D. Deutsch, “Quantum theory, the Church-Turing principle
and the universal quantum computer”, Proc. R. Soc. A, vol.
400, no. 1818, pp. 97–117, 1985.

51. Quantum
Speedup
→ 50-60 qubits for quantum advantage
→ 100-150 qubits to tackle calculations in
quantum chemistry
R. Feynman, “Simulating physics with computers”,
International Journal of Theoretical Physics, vol. 21, no. 6,
pp. 467–488, 1982.
D. Deutsch, “Quantum theory, the Church-Turing principle
and the universal quantum computer”, Proc. R. Soc. A, vol.
400, no. 1818, pp. 97–117, 1985.

52. Quantum
Speedup
→ 50-60 qubits for quantum advantage
→ 100-150 qubits to tackle calculations in
quantum chemistry
→ 4000 qubits and more to break existing
public key encryption standard (2048-bit RSA
keys)
R. Feynman, “Simulating physics with computers”,
International Journal of Theoretical Physics, vol. 21, no. 6,
pp. 467–488, 1982.
D. Deutsch, “Quantum theory, the Church-Turing principle
and the universal quantum computer”, Proc. R. Soc. A, vol.
400, no. 1818, pp. 97–117, 1985.

53. Quantum
Speedup
→ 50-60 qubits for quantum advantage
→ 100-150 qubits to tackle calculations in
quantum chemistry
→ 4000 qubits and more to break existing
public key encryption standard (2048-bit RSA
keys)
Are these qubits the same as the ones
often mentioned in press releases?
R. Feynman, “Simulating physics with computers”,
International Journal of Theoretical Physics, vol. 21, no. 6,
pp. 467–488, 1982.
D. Deutsch, “Quantum theory, the Church-Turing principle
and the universal quantum computer”, Proc. R. Soc. A, vol.
400, no. 1818, pp. 97–117, 1985.

54. Fault Tolerance
Exposure to heat and radiation makes qubits
prone to errors (decoherence):
→ Bit flip errors
→ Phase flip errors

55. Fault Tolerance
Exposure to heat and radiation makes qubits
prone to errors (decoherence):
→ Bit flip errors
→ Phase flip errors
Press releases often refer to “physical” qubits

56. Fault Tolerance
Exposure to heat and radiation makes qubits
prone to errors (decoherence):
→ Bit flip errors
→ Phase flip errors
Press releases often refer to “physical” qubits
We need auxiliary qubits to implement error
correcting codes (e.g. surface codes):
→ Physical-to-Logical qubit ratio
→ Physical qubit fidelity threeshold

57. Fault Tolerance

58. The DiVicenzo Criteria
1. A scalable physical system with well
characterized qubits.
2. The ability to initialize the state of the qubits
to a simple fiducial state, such as .
3. Long relevant decoherence times, much
longer than the gate operation time.
4. A “universal” set of quantum gates.
5. A qubit-specific measurement capability.
DiVincenzo's
Criteria
David P. DiVincenzo, "The Physical
Implementation of Quantum
Computation", Fortschritte der
Physik. 48: 771–783, 2000.

59. The DiVicenzo CriteriaPhysical implementation
Behold the mighty qubit:
https://www.youtube.com/wa
tch?v=_P7K8jUbLU0
A Tour of an IBM Q Lab:
https://www.youtube.com/wa
tch?v=KZf4BSmgdO4
Running an experiment in the
IBM Quantum Experience:
https://www.youtube.com/wa
tch?v=pYD6bvKLI_c

60. The DiVicenzo CriteriaPhysical implementation
→ Superconducting qubits (IBM ~50 qubits, Intel
~50 qubits, Google ~70 qubits ?, …)
+ Fast gate times, Fabrication
- Coherence, Cryogenic T°

61. The DiVicenzo CriteriaPhysical implementation
→ Superconducting qubits (IBM ~50 qubits, Intel
~50 qubits, Google ~70 qubits ?, …)
+ Fast gate times, Fabrication
- Coherence, Cryogenic T°
But also:
→ Trapped ions
→ Spin qubits in silicon
→ All optical
→ NV center in diamond
→ ...

62. Post Quantum
Cryptography

63. Private key
Ciphered
message
transmission
2
Private key
Ciphering with
private key
Unciphering with
private key
3
1
Symmetric-key algorithms

64. Public key
transmission
Public key
transmission
Ciphering with
public key
Unciphering with
private key
4
1
3
2
Ciphered
message
transmission
Asymmetric-key algorithms

65. Types of cryptography

66. Types of cryptography
Q-computing provides
an exponential speedup

67. Types of cryptography
Q-computing provides
an exponential speedup
Q-computing (only) provides
a quadratic speedup

68. Quantum attacks on Bitcoin

69. Quantum Key Distribution

70. Cybersecurity Requirements meet Quantum Cryptography
Practical (no physical meeting)
Information-theoretic security based on no-cloning theorem and Heisenberg's
uncertainty relations
Basic principle

71. BB84 QKD protocol

72. BB84 QKD protocol

73. BB84 QKD protocol

74. BB84 QKD protocol

75. BB84 QKD protocol

76. BB84 QKD protocol

77. BB84 QKD protocol
0 1

78. “No-cloning theorem: No quantum operation exists that can
duplicate perfectly an arbitrary quantum state.”
Valerio Scarani, Sofyan Iblisdir, Nicolas Gisin, and Antonio Acín
Rev. Mod. Phys. 77, 1225 – Published 8 November 2005
Achievable distance

79. “No-cloning theorem: No quantum operation exists that can
duplicate perfectly an arbitrary quantum state.”
Valerio Scarani, Sofyan Iblisdir, Nicolas Gisin, and Antonio Acín
Rev. Mod. Phys. 77, 1225 – Published 8 November 2005
“No-cloning theorem: No quantum operation exists that can
duplicate perfectly an arbitrary quantum state.”
W.K. Wootters and W.H. Zurek, “A Single Quantum Cannot be
Cloned”, Nature 299 (1982), pp. 802-803

80. “No-cloning theorem: No quantum operation exists that can
duplicate perfectly an arbitrary quantum state.”
Valerio Scarani, Sofyan Iblisdir, Nicolas Gisin, and Antonio Acín
Rev. Mod. Phys. 77, 1225 – Published 8 November 2005
SPS: Single Photon Source EPPS: Entangled Photon Pair Source
BSM: Bell State Measurement
“No-cloning theorem: No quantum operation exists that can
duplicate perfectly an arbitrary quantum state.”
W.K. Wootters and W.H. Zurek, “A Single Quantum Cannot be
Cloned”, Nature 299 (1982), pp. 802-803

81. “No-cloning theorem: No quantum operation exists that can
duplicate perfectly an arbitrary quantum state.”
Valerio Scarani, Sofyan Iblisdir, Nicolas Gisin, and Antonio Acín
Rev. Mod. Phys. 77, 1225 – Published 8 November 2005
SPS: Single Photon Source EPPS: Entangled Photon Pair Source
BSM: Bell State Measurement
“No-cloning theorem: No quantum operation exists that can
duplicate perfectly an arbitrary quantum state.”
W.K. Wootters and W.H. Zurek, “A Single Quantum Cannot be
Cloned”, Nature 299 (1982), pp. 802-803

82. SPS: Single Photon Source EPPS: Entangled Photon Pair Source
BSM: Bell State Measurement
“No-cloning theorem: No quantum operation exists that can
duplicate perfectly an arbitrary quantum state.”
W.K. Wootters and W.H. Zurek, “A Single Quantum Cannot be
Cloned”, Nature 299 (1982), pp. 802-803

83. DelayCoincidences
SPS: Single Photon Source EPPS: Entangled Photon Pair Source
BSM: Bell State Measurement
D1 D2

84. DelayCoincidences
SPS: Single Photon Source EPPS: Entangled Photon Pair Source
BSM: Bell State Measurement
SYNCHRONIZATION REQUIRED
D1 D2

85. Satellite QKD
https://www.youtube.com/watch?v=4QlcKuxDGrs
Quantum satellite achieves 'spooky action' at
record distance (China QKD network):

86. Quantum Internet

87. European flagship on
quantum technologies

88. Quantum Manifesto was handed over to
the European Commission in May 2016
→ More than 3600 supporters from academia and
industry
1b€ investment by the EU over 10 years