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Quantum anneleaing

$${\mathcal{H}}_p=\sum _{i=0}^N{h}_i{\sigma }_i^Z+\sum _{i,j=0}^N{J}_{ij}{\sigma }_i^Z{\sigma }_j^Z$$

Jargon

D Wave

Super conducting quantum annealing

15 ans d'avance sur la creation de ses machines

• Spin up qubit
  $|\uparrow ⟩$
• Spin up qubit
  $|\downarrow ⟩$

Quantum annealing and ising model

$${\mathcal{H}}_p=\sum _{i=0}^N{h}_i{\sigma }_i^Z+\sum _{i<j}^N{J}_{ij}{\sigma }_i^Z{\sigma }_j^Z$$

• ${\mathcal{H}}_p$: system hamiltonian
• $h_i$: energy difference between 2 states of qubits i
• $v_i$: vertices containing qubit i
• $J_{ij}$: coupling between vertices
  $v_i$ et
  $v_j$ with close i and j
• $E$: edge, connecting qubits

Computing process

Starts with converting the probleme into a Ising model or QUBO (Quadratic Unconstrained Binary Optimization)

1. Initialization of qubits states to
   $|\uparrow ⟩$ or
   $|\downarrow ⟩$
2. Setting qubits bias levels
   $h_i$
3. Slowly growing
   $J_{ij}$ coupling
4. System converging to minimal
   ${\mathcal{H}}_p$
5. Readout
   $|\uparrow ⟩$ or
   $|\downarrow ⟩$ states for all qubits, giving the solution to the problem of finding the energy minimum for
   $H_p$

Le chimera est la facon dont les qubits sont relies entre eux physiquement dans le processeur

Algorithms

Pegasus / Advantage 2020 generation

5436 qubits

Each qubits is connected to 15 neighbour qubits through 37440 couplers, from 6 per qubit in previous generations.

Qubits are operating at 15,8 mK

One order of magnitude improvement in time spent solving problems vs D-Wave 2000Q launched in 2017

Pourquoi c'est plus dur de rajouter de nouveaux qubits ?

C'est plus dur a intriquer

Superconducting qubits

Qubits operating temperatures rationale

Pourquoi est-ce qu'on doit les refroidir ces qubits ?

On veut eviter la decoherence des qubits mais pas que
Les micro-ondes qu'on envoie sur les qubits sont conditionnees par le niveau d'energie
On refroidit pour que le bruit ambiant soit inferieur a la puissance des micro-ondes

5 Superconducting qubits lab configuraiton

IBM

Roadmap

Google

Google’s 1 million physical qubits plan

C'est quoi la consommation energetique ? - Theotime

Alice & Bob

French startup created by Théau Peronnin and Raphaël
Lescanne, from ENS

with the help from Benjamin Huard (ENS Lyon), Zaki
Leghtas (ENS Paris), Mazyar Mirrahmi (Inria), Philippe
Campagne-Ibarcq (Inria) and Emmanuel Flurin (CEA)

• use cat-qubits based on two photons coupling in a cavity to increase reliability of superconducting qubits
• qubit information comes from measuring cavity photon number parity without measuring photon number
• expect to build a logical superconducting qubit with only 30 cat-qubits instead of 10 000 classical superconducting qubits
• significantly reduce the burden to create a LSQ FTQC (large scale quantum / fault tolerant quantum computer)
• plan to produce a first processor with logical qubits by 2023

Amazon

Amazon announced in december 2020 it will build its own quantum computers using cat-qubits superconducting, in a 118 pages theoretical paper

it plans to use surface codes QEC

it’s partnering with Caltech (incl John Preskill), Yale (Devoret/Schoelkopf teams)
and other universities

Summary

Electron spins qubits

Different electron spins qubit platforms

How to detect a single charge?

How to manipulate a single spin?

How to realize a two-qubit gate?

State of the art of two qubit gates

planar systems with a huge number of electrodes to:

• define the reservoirs - source and drain
• control the height of the barrier between quantum dots
• define the depth of the quantum well
• manipulate the qubits
• read out the qubits

Toward a scalable platform

C12 Quantum Electronic

french startup created by Matthieu and Pierre Desjardins with the help from Taki Kontos (LPENS) electron spins qubits trapped in carbon nanotubes 5 qubits demonstrator planned for 2021/2022

Summary

NV centers qubits

NV centers implementation and controls

Quantum brillance

Australian startup

• ambiant temperature qubits
• 5 NV centers qubits demonstrated in 2021
• they plan to scale > 50 qubits in 2022
• fits on a desktop computer form factor

qubits NV centers

Topologic qubits

The topological qubit bit

Chez microsoft:

• better stability qubits
• low decoherence noise
• few errors
• long coherence time
• high gate speed

• nothing demonstrated so far
• no prototype
• different algorithms

Majorana fermions summary

Trapped ions qubits

IonQ

La boite la plus calee et ayant recu le plus de fonds: $

$82$M en 2015

Maryland and Duke Universities spin-off launched by Christopher Monroe

$\text{color}green\text{pros}$	$\text{color}red\text{cons}$
laser controlled gates	slow gates
$32$ qubits with a large quantum volume of $2^{22}$ reached in 2020	not easy to scale, planning to network several tiny units (above)
long coherence time and good qubits fidelity
excellent qubit connectivity thanks to phonons
available on Microsoft and Amazon cloud services

IPO planned in 2021

Honeywell

• 2D trapped ions announced in march 2020
• 4 qubits in march 2020
• 6 qubits in june 2020
• 10 qubits in septembre 2020

Better scalability project

Trapped ions qubits summary

Cold atoms qubits

Cold atoms and Rydberg states

Etat de Rydberg: etat tres energisant

Cold atoms qubits summary

Photon qubits

Photons qubits types and tools

Qubits

Instrumentation

Quantum dot photon source

Quantum dot photon source

DV and CV photon qubits

Photons qubits summary