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* '''Location:''' Université Grenoble Alpes, Bâtiment IMAG, Grenoble, France.
 
* '''Location:''' Université Grenoble Alpes, Bâtiment IMAG, Grenoble, France.
  
* '''Lecturers: ''' [https://www.icgm.fr/bruno-senjean/ Bruno Senjean] (Montpellier), [https://atos.net/en/expert/thomas-ayral Thomas Ayral] (Paris), [https://scienceimpulse.cea.fr/fr/projects-in-progress/building-quantum-computer-bit-by-bit/ Zachary Blunden-Codd (replacing David Herrera-Martı́)] (Grenoble), [https://www.saad-yalouz.com/ Saad Yalouz] (Strasbourg)
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* '''Confirmed speakers (up to now): ''' [https://www.icgm.fr/bruno-senjean/ Bruno Senjean], [https://atos.net/en/expert/thomas-ayral Thomas Ayral]
  
 
* '''Organizers:''' [https://www.robertapoloni.com/ Roberta Poloni], [http://cermics.enpc.fr/~cances/ Eric Cancès], [http://quantique.u-strasbg.fr/doku.php?id=en:pageperso:ef:welcome Emmanuel Fromager], [https://etsf.polytechnique.fr/People/Francesco Francesco Sottile], [http://www.lct.jussieu.fr/pagesperso/toulouse/ Julien Toulouse].
 
* '''Organizers:''' [https://www.robertapoloni.com/ Roberta Poloni], [http://cermics.enpc.fr/~cances/ Eric Cancès], [http://quantique.u-strasbg.fr/doku.php?id=en:pageperso:ef:welcome Emmanuel Fromager], [https://etsf.polytechnique.fr/People/Francesco Francesco Sottile], [http://www.lct.jussieu.fr/pagesperso/toulouse/ Julien Toulouse].
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==Presentation==   
 
==Presentation==   
  
Research on quantum computing is rapidly growing and has the potential to reshape simulations in physics and chemistry.
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* The lectures delivered are intended to be of interest to any person working in the field of theoretical chemistry and physics and willing to discover or deepen some mathematical aspects of the field. Master and PhD students, post-docs and any academic are welcome!
These two days aim at providing a pedagogical introduction to this field for the communities of the GDR REST and NBODY, i.e. theoretical physicists, chemists, and applied mathematicians working on the quantum many-body problem. These days are not targeted to experts in quantum computing but rather to people who want to discover this new field.
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* To provide a detailed presentation of subjects, we have chosen to give a good amount of time to each lecturer. The mini-school will thus involve only two lecturers over a three-day period.
  
 
==Program==
 
==Program==
  
We will have four lectures:
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To be announced.
 
 
*'''Bruno Senjean''', ICGM, CNRS and Université de Montpellier, Montpellier
 
  
'''''Introduction to quantum computing for chemistry, variational quantum eigensolver and quantum phase estimation algorithms (2*1h30)'''''
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Two courses will be proposed:
  
<font color="red">
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* 1) '''Finite group theory''' (9 hours) by '''[https://www.lct.jussieu.fr/?page_id=368 Emmanuel Giner]''', Laboratoire de Chimie Théorique, CNRS and Sorbonne Université, Paris.
'''[https://www.youtube.com/watch?v=4b8Z6-_zugQ&list=PLD59gCifE4d_b87M1h-r6me9fgzGZkPrp&index=1 VIDEO1]'''
 
'''[https://www.youtube.com/watch?v=rf5WRG1_91s&list=PLD59gCifE4d_b87M1h-r6me9fgzGZkPrp&index=5 VIDEO2]'''
 
'''[[Media:Senjean introduction QC part1.pdf|[Slides part 1]]]'''
 
'''[[Media:Senjean introduction QC part2.pdf|[Slides part 2]]]'''
 
'''[[Media:Senjean derivations QC.pdf|[Handwritten derivations]]]'''
 
</font>
 
  
 
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''Indicative program (subject to changes and extension):''<br>
*'''Thomas Ayral''', ATOS, Paris
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- Definition of symmetries in quantum mechanics<br>
 
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- Definition of groups and related concepts (group axioms, classes)<br>
'''''Noise in variational algorithms and classical simulation of quantum computing (2*1h30)'''''
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- Basics of linear representation of groups (representation, irreducible representations, characters)<br>
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- Useful theorems of linear representation of groups and their application in quantum mechanics (Schur's lemma and the Hamiltonian, orthogonality theorems, projection operators)<br>
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- Product representations (representation on tensor-product vector spaces, Clebsch-Gordon coefficients, irreducible tensor operators)<br>
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- Examples for electronic-structure theory
  
 
<font color="red">
 
<font color="red">
'''[https://www.youtube.com/watch?v=JxvE3tDWm1I&list=PLD59gCifE4d_b87M1h-r6me9fgzGZkPrp&index=2 VIDEO1]'''
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'''Download [[Media:Lecture notes giner.pdf|lecture notes]]'''
'''[https://www.youtube.com/watch?v=ewQ3eKpSvg0&list=PLD59gCifE4d_b87M1h-r6me9fgzGZkPrp&index=3 VIDEO2]'''
 
 
</font>
 
</font>
  
  
*'''Saad Yalouz''', LCQ, Université de Strasbourg, Strasbourg
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* 2) '''The mathematical description of solids''' (9 hours) by '''[https://www.ceremade.dauphine.fr/~lewin/ Mathieu Lewin]''', CEREMADE, CNRS and Université Paris Dauphine, Paris
 
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'''''Quantum algorithm developments and applications: wave-function theory and density-functional theory (1h30)'''''
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''Indicative program (subject to changes and extension):''<br>
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I. Quick introduction to spectral theory<br>
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- A bit of history about the concept of self-adjoint operators<br>
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- Continuous spectrum and generalized eigenfunctions, example of plane waves<br>
  
<font color="red">
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II. One-electron systems in a periodic background<br>
'''[https://www.youtube.com/watch?v=mTtp_Dul_Rk&list=PLD59gCifE4d_b87M1h-r6me9fgzGZkPrp&index=4 VIDEO]'''
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- Bloch-Floquet theory<br>
'''[[Media:Saad Yalouz Lecture Grenoble WFT and DFT.pdf|[Slides]]]'''
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- Regularity of Bloch surfaces, absolute continuity of the spectrum<br>
'''[[Media:Saad Yalouz ExpPauliString.pdf|[Lecture notes]]]'''
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- Symmetry groups and the universality of Dirac cones in 2D, graphene<br>
</font>
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- Spectral projections, infinite Hartree-Fock states<br>
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- SCF models, Kohn-Sham<br>
  
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III. Interacting systems<br>
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- Thermodynamic limit for Coulomb systems<br>
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- Uniform Electron Gas: the known and the unknown<br>
  
*'''Zachary Blunden-Codd (replacing David Herrera-Martı́)''', CEA, Grenoble.
 
  
'''''Introduction to fault-tolerant quantum computing. Limits of quantum phase estimation on fault-tolerant quantum computing (1h30)'''''
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<center>
 
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[[Image:emmanuel_giner_2022.jpg|300px]] [[Image:mathieu_lewin_2022.jpg|300px]] [[Image:participants_minischool_2022.jpg|300px]]  
<font color="red">
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</center>
'''[https://www.youtube.com/watch?v=rxZ2nXnrL8Q&list=PLD59gCifE4d_b87M1h-r6me9fgzGZkPrp&index=6 VIDEO]'''
 
'''[[Media:Zach_and_David_QCPC23.pdf|[Slides]]]'''
 
</font>
 
  
 
== Schedule ==
 
== Schedule ==
 
  
 
{| border="5" |
 
{| border="5" |
! <center><font color="blue">Thursday 19 January</font>
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! <center><font color="blue">Monday 30 May Morning</font> <br>
</center>
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Tower 15-16, room 309</center>
! <center><font color="blue">Friday 20 January</font>
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! <center><font color="blue">Tuesday 31 May Morning</font> <br>
</center>
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Tower 15-16, room 309</center>
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! <center><font color="blue">Wednesday 1 June Morning</font><br>
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Tower 15-16, room 309</center>
 
|- align="left"
 
|- align="left"
!'''<font color="red">9:00 Start</font>'''
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!'''<font color="red">8:45-9:00 Arrivals/Welcome</font>'''!! !!
 
|- align="left"
 
|- align="left"
!'''9:00-10:30''' Bruno Senjean I
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! '''9:00-10:30''' Giner 1
 
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!'''9:00-10:30''' Lewin 3
!'''9:00-10:30''' Saad Yalouz
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!'''9:00-10:30''' Giner 5
 
|-align="left"
 
|-align="left"
!<font color="green">10:30-11:00 Coffee break</font>  
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!<font color="green">10:30-10:45 Coffee break</font>
!<font color="green">10:30-11:00 Coffee break</font>  
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!<font color="green">10:30-10:45 Coffee break</font>
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!<font color="green">10:30-10:45 Coffee break</font>
 
|-align="left"
 
|-align="left"
!'''11:00-12:30''' Bruno Senjean II
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!'''10:45-12:15''' Giner 2
!'''11:00-12:30''' Zachary Blunden-Codd
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!'''10:45-12:15''' Lewin 4
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!'''10:45-12:15''' Giner 6
 
|-align="left"
 
|-align="left"
!  <font color="green">12:30 Lunch (buffet) </font>
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!  <font color="green">12:15-14:00 Lunch at L'Ardoise (Tower 25)</font>
!  <font color="green">12:30 Lunch (buffet) </font>
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!  <font color="green">12:15-14:00 Lunch at L'Ardoise (Tower 25)</font>
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!  <font color="green">12:15-14:00 Lunch at L'Ardoise (Tower 25)</font>
 
|-align="left"
 
|-align="left"
!'''14:00-15:30''' Thomas Ayral I
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! <center><font color="blue">Monday 30 May Afternoon</font> <br>
!'''<font color="red">14:00 End</font>'''
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Tower 15-16, room 309</center>
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! <center><font color="blue">Tuesday 31 May Afternoon</font> <br>
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Tower 15-16, room 309</center>
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! <center><font color="blue">Wednesday 1 June Afternoon</font><br>
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Tower 15-16, room 309</center>
 
|-align="left"
 
|-align="left"
! <font color="green">15:30-16:00 Coffee break</font>
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!'''14:00-15:30''' Lewin 1
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!'''14:00-15:30''' Giner 3
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!'''14:00-15:30''' Lewin 5
 
|-align="left"
 
|-align="left"
!'''16:00-17:30''' Thomas Ayral II
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! <font color="green">15:30-15:45 Coffee break</font>
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!  <font color="green">15:30-15:45 Coffee break</font>
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!  <font color="green">15:30-15:45 Coffee break</font>
 
|-align="left"
 
|-align="left"
! <font color="green"> 19:30 Dinner at Caffe Forte (Grenoble hypercentre) </font>
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!'''15:45-17:15''' Lewin 2
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!'''15:45-17:15''' Giner 4
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!'''15:45-17:15''' Lewin 6
 
|}
 
|}
  
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=== Registration ===
 
=== Registration ===
  
'''The maximum number of participants is around 50'''.
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'''Registration is closed'''.
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To facilitate the participation of young researchers, no registration fees will be asked.
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However, accommodation will not be provided but must be arranged independently by the participants.
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=== Location of the mini-school ===
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The mini-school will take place on the Pierre et Marie Curie (or Jussieu) campus of [http://www.sorbonne-universite.fr/ Sorbonne Université], 4 place Jussieu, 75005 Paris.
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Subway (Metro) lines 7 or 10: get off at "Jussieu" station.
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From the main entrance of the campus, go to '''Tower 16'''. Take the stairs or the elevator to the '''third level'''. Find '''corridor 15-16''', and then the '''room 309'''. This is the seminar room of Laboratoire Jacques-Louis Lions.<br>
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=== Lunches ===
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Each day, lunch at Restaurant L'Ardoise (Jussieu campus, entrance near Tower 25) will be offered to a maximum 50 registered participants to the mini-school (see the list of registered participants on the page [[MINI-SCHOOL 2022 List of registered participants|List of registered participants]]).
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=== Arriving by Plane ===
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Both Paris-Charles de Gaulle (CDG) and Paris-Orly international airports are connected to the center of Paris by RER (fast regional railway) or coaches. The RER is connected to the subway (Metro) network. It costs about 10 euros to go from either airport to the center of Paris and it takes about one hour.
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For more information, check the [http://www.aeroportsdeparis.fr/Adp/en-GB/Passagers/ Paris airports website].
  
No registration fees will be asked. However, accommodation will not be provided but must be arranged independently by the participants.
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=====From Paris-Charles de Gaulle (CDG) airport=====
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From the airport take RER line B. Stop at "St-Michel-Notre-Dame" station. Take subway line 10 direction "Austerlitz" and stop at "Jussieu" station.
  
To register, please send an email to [mailto:qc-school@theory.polytechnique.fr qc-school@theory.polytechnique.fr] and indicate your name and affiliation.
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=====From Paris-Orly airport=====
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From the airport take the monorail "OrlyVal" to "Antony". Take RER line B. Stop at "St-Michel-Notre-Dame" station. Take subway line 10 direction "Austerlitz" and stop at "Jussieu" station.
  
=== Location  ===  
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===Arriving by Train===
  
Université Grenoble Alpes, Bâtiment IMAG, Grenoble, France.
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All the railway stations are in downtown Paris and are connected to the subway network. For train reservation, check the [http://www.voyages-sncf.com SNCF web site].
  
In order to reach the location from the train station, take tram B direction ''GIERES Plaine des Sports'' and stop at " Bibliothèque Universitaire "
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From any train station follow the sign "M" to the subway.
  
=== Social Dinner  ===  
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===Arriving by Subway or Bus===
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For more information on the RER, Subway and Bus systems, check the [http://www.ratp.fr/ RATP web site], and in particular the [http://www.ratp.fr/plan-interactif/ Subway and RER map].
  
Caffe Forte, 4 Pl. de Lavalette, 38000 Grenoble (tram B, arrêt ''Notre-Dame - Musée'')
 
 
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