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Grotrian diagram

Quantum vacuum fluctuations

According to quantum field theory and Heisenberg principle, vacuum contains harmonic oscillators with zero-point energy

$$\begin{gathered} E=\frac{1}{2}hv \\ \mathrm{\Delta }E\cdot \mathrm{\Delta }t\ge \frac{h}{2} \end{gathered}$$

with electrons/positrons spontaneously cretaed and annilihating, creating photons

Feynmann diagram

Lamb shift (1947)
Energy shift observed between 2 levels hyperfine structure in hydrogen atom, explained by quantum vacuum fluctations impacting electrons

Casimir effect (1997)

Comparing classical and quantum physics

Quantum myths: History

Einstein was wrong about quantum mechanics

He was a key founder of quantum physics with the photoeletric effect explanation and many other works; he asked the right questions about entanglement in 1935 which are still debated

Werner Heisenberg created his indeterminacy inequality

It was created by Earle Hesse Kennard in 1927 and Hermann Weyl in 1928

Erwin Schrodinger's cat is both dead and alive

He wanted to explain that the wave-particle duality didn't work at macro scale, thus the cat can't be both dead and alive. End of story, but I can elaborate. It's a matter of uncertainty origin.

Richard Feynmann invented the concept of quantum computing

He imagined in 1981 the concept of quantum simulation of quantum physics phenomenon but, before, Yuri Manin invented in 1980 the concept of gate based quantum computing.

Young's slit experiment was done with electrons in 1927

Peux pas lire ptdr

What happened during WWII ?

La bombe atomique

La physique atomique est un champ different de la physique quantique mais on peut expliquer la desintegration du noyau d'uranium par la physique quantique.

Les gens faisant de la physique quantique sont passes sur la physique nucleaire, il y a eu un trou dans la phyisque quantique

Post-WWII

• 1946-1952: Felix Bloc
  • Sphere
• 1947-1956: William Shockley John Bardeen Walter Brattain
  • Transistors
• 1957: John Bardeen, Leon Cooper, John RObert Schrieffer
  • Superconductivity
• 1953
  • 1960: Gordon Gould, Theodore Maiman, Nikolay Basov
  • 1964: Alexander Prokhorov
  • 1964: Charles Hard Townes
• 1962-1973: Brian Josephson
  • Josephson effect
• 1964: John Stewart Bell
  • Bell inaqualities and test
• 1970: Dieter Zeh
  • Quantum decoherence
• 1980: Yuri Manin
  • Quantum computing
• 1980: Tommaso Toffoli
  • Toffoli gate
• 1981: Richard Feynman
  • Quantum simulator
• 1982: Alain Aspect

$1^{st}$ and

$2^{nd}$ quantum revolutions

Manipulating groups of quantum particles (

$1947-\text{*}$)

Photons, electrons and atoms interactions

• Transistors
• Lasers
• GPS
• Photovoltaic cell
• Atom clocks
• Medical imaging
• Digital photography
• LCD TV quantum dots

Manipulating superposition and entanglement and/or individual particles (

$1982-\text{*}$)

• Quantum computing
• Quantum telecommunications
• Quantum cryptography
• Quantum sensing

Second quantum revolution

• 1991: Anton Zellinger
  • Neutrons duality
• 1992: Arthur Ekert
  • QKD
• 1993: Umesh Vazirani
  • Quantum complexity
• 1992:
  • Serge Haroche
    • Quantum decoherence
  • Juan Cirac and Peter Zoller
    • Trapped ions qubits
  • Edward Farhi
    • Adiabatic quantum computing
  • David DiVincenzo
    • Criterium
• 1997: Nicolas Gisin
  • Non locality
• 1997 & 2002: Daniel Esteve
  • Superconducting qubits
• 2001: Hans Briegel
  • MBQC
• 2011: John Preskill
  • Quantum supremacy concept
• 2012: D-Wave One
  • First quantum annealing commercial computer
• 2016: IBM Q
  • First cloud based quantum computer

Quantum sensing

On n'en parlera quasiment pas du tout

• lasers and frequency combs
  • clocks
  • Spectrographs
  • ultra-sound mikes
• entengled photons
  • radars
  • ultra-sensing imaging
• cold atoms

Capteurs quantiques

• Nami
• Entanglement
• iXblue

Classical computing state of the art and limitations

Moore's law: dead or alive ?

C'est un papier ecrit par Gordon Moore. Il fait en observation empirique:

Faire croitre le nombre de transistors dans une puce de maniere exonentielle

Ce n'est pas une loi mathematique ou physique

Cela mettait la pression sur les constructeurs comme Intel.

Elle est applicable aux:

• processeurs
• supercalculateurs
• espaces de stockage

En quoi la loi de Moore s'est arretee ?

La puissance d'horloges n'a pas augmente exponentiellement depuis plus de 15 ans

C'est lie a la fin de l'echelle de Dennard en 2006

L'energie utilisee a explose.

Pourquoi ?

A cause de fuites sur les transistors

Ca a fini sur le dark silicon

A cause de ce mecanisme, on ne peut pas utiliser toute la surface d'un processeur de serveur sinon il va fondre.

Comment on fait pour tout utiliser en entier ?

Avec un isolant ?
Avec un refroidissement ?

CMOS technical challenges

• Extreme ultra violet (EUV)
  • for
    $\le 10$ nm density
• Heat barrier
  • processor clocks

Quantum computing

Promis and use cases

Probleme intractable: probleme dont le temps de calcul va augmenter de maniere exponentielle avec sa taille.

Promesse
Certains problemes intractables vont etre solvable dans un temps humainement raisonable.

• Transports et logisitiques
• Healthcare
• Energy and materials
• Finance and insurance
• Defense

Difference Bits and Qubits

From quantum physics to qubits

• wave function
  • describes particles properties
  • probabilities
• quantization
  • discrete levels of wave functions, like energy, polarity, spin
• superposition
  • linear combination of quantized states
• entanglement
  • quantum objects correlated states, consequence of linear superposition of multiple quantum objects

wave function & quantization: 2 levels of quantum objects

From computing to measurement

• Quantum gates
  • actions on qubits and their superposed states

Computational basis state vector:

$$\begin{array}{cc}\text{complex amplitude}& \text{of all combinations of }0\text{ and }1\\ \left[\begin{array}{c}{\alpha }_1\\ ⋮\\ {\alpha }_{2}N\end{array}\right]& \begin{array}{c}|00\dots 00⟩\\ ⋮\\ |10\dots 01⟩\\ ⋮\\ |11\dots 11⟩\end{array}\end{array}$$

• $N$ qubits registers
  • information in
    $2^N$ superposed state

Qubits can't be independently copied

$$\sum _{i=1}^{2^N}{\alpha }_i^2=1$$

handles

$2^{N+1}-1$ real numbers

• measurement
  • Ends superposition and entanglement
• outputs
  • $N$ probabilistic classical bits
• computing
  • has to be run many times and results average

Adressing the noise challenge

• decoherence
  • progressively ends superposition and entanglement
  • coherence times between
    $100\mu s$ and a couple seconds
• errors
  • significant during computing
  • $0.1\mathrm{\%}$ to
    $8\mathrm{\%}$ error rates per gate and for qubits readouts
• erros correction
  • requires a very large number of additional qubits
  • $1-100$ to
    $1-10000$ ratio between logical and physical qubits
• scalability challenges
  • aulity qubits, cabling, control electronics, cryogenics abd energetics engineering

Distributed quantum computing ?

Complex numbers and phase

• $r$: amplitude, modulus, norm
• $\theta$: phase angle

Euler formula:

$$e^{i\theta }=\cos \theta +\sin \theta$$

Phase angles add up

qubit Bloch sphere representation

Opposite vectors in sphere are mathematically orthogonal

$\alpha$ and

$\beta$ are complex numbers altitudes:

$$|\mathrm{\Psi }⟩=\alpha |0⟩+\beta |1⟩$$

Probabilities and Born normalization constraint:

$$\alpha +\beta =1$$

Using polar coordinates

$\theta$ and

$\varphi$ and no global phase:

$$|\mathrm{\Psi }⟩=\cos \frac{\theta }{2}|0⟩+\sin \frac{\theta }{2}{e}^{i\varphi }|1⟩$$

Euler formula:

$$e^{i\varphi }=\cos \varphi +i\sin \varphi$$

Alternate "symetric" version with a global phase of

$e^{-\frac{i\varphi }{2}}$

$$|\mathrm{\Psi }⟩=\cos \frac{\theta }{2}{e}^{\frac{-i\varphi }{2}}|0⟩+\sin \frac{\theta }{2}{e}^{\frac{i\varphi }{2}}|1⟩$$

The global phase doen't change the probabilities

$|\alpha {|}^2$ and

$|\beta {|}^2$ for measurement

Other representations

Poincare's sphere:

Linear algebra 101

$$f(\lambda )$$

Vectors Dirac notation:

$$\begin{gathered} |\mathrm{\Psi }⟩=\left[\begin{array}{c}\alpha \\ \beta \end{array}\right]\mathrm{\Psi }\text{ ket} \\ \overline{\alpha }=\alpha \ast ⟨\mathrm{\Psi }|=[\overline{\alpha },\overline{\beta }]\psi \text{ bra} \end{gathered}$$

Bra-ket:

$$⟨{\mathrm{\Psi }}_1|{\mathrm{\Psi }}_2⟩=[{\overline{\alpha }}_1,{\beta }_1]\times \left[\begin{array}{c}{\alpha }_2\\ {\beta }_2\end{array}\right]$$

How to read that ?

$$⟨\mathrm{\Psi }|A|\varphi ⟩$$
Average valye in

$\mathrm{\Psi }$ of the value

$$A^{✞}=(A^T)\ast \underset{\text{matrix conjugate}}{\underbrace{A^{\ast }}}+\stackrel{\text{matrix transpose}}{\overbrace{A^T}}\Rightarrow {\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]}^{✞}$$

$$|\mathrm{\Psi }⟩=\underset{n=1}{\overset{N}{⨂}}|i⟩$$