
THEMATIC PROGRAMS 

December 4, 2021  
Thematic Program on Mathematics
in Quantum Information

July 2731, 2009
Organizing Committee: 

Matthias Christandl (LMU Munich) Robert Erdahl (Queen's University) 
Patrick Hayden (McGill University)
Mary Beth Ruskai (Tufts University) 
Workshop Program  Confirmed Participants 
Abstracts  Invited Talks  Abstracts  Contributed Talks/ Posters 
Visitor Information  Hotels and Housing 
Mailing List : To receive updates on the program please subscribe to our mailing list at www.fields.utoronto.ca/maillist
In order to have a workshop format with ample time for discussions,
all talks will be invited, but suggestions for speakers are welcome.
It is neither necessary nor desirable that all participants give
a formal talk. All participants can submit a poster and every presenter
of a poster will have an opportunity to give a 5 minute presentation
to let people know who they are and what they are working on. These
will take place early in the workshop before the reception or breaks.A
few poster submissions may be selected, at the option of the organizers
for 20 minute talks on recent developments.
Abstract Submission for Contributed Talk/Poster (closed
deadline to submit was June 28)
In the last decade, new methods have been developed which use the twoelectron RDM to study Nelectron systems while circumventing the Nrepresentability problem. More recently, two striking results were obtained on this longstanding question, the solution of the pure state problem for the oneparticle RDM and a proof of the existence of computationally intractable model Hamiltonians (even with a quantum computer) for the twoparticle RDM.
Quantum information theory has led to developments in different directions. There are some surprising connections with representations of the symmetric group and with spin coherent states. A different type of approximation for symmetric density matrices is treated by the socalled quantum di Finetti theorems. Recent developments involving density matrix renormalization methods for treating strongly correlated systems in spin chains will be treated, with emphasis on the practical implications.
Because Schubert calculus plays a key role some recent developments,
Allen Knutson will give a "crash course" on this topic
during the first two days. By bringing together quantum chemists,
mathematicians and quantum information scientists, we hope to identify
the new mathematical challenges in this area and the practical uses
of recent theoretical developments.
Monday July 27  
8:45  9:00 a.m.  Welcome and Introduction Fields Director Ed Bierstone and Workshop Organizers 
9:0010:00 a.m.  Allen Knutson (University of California, San
Diego) Schubert Calculus short course 
10:0010:30 a.m.  Coffee Break 
10:3011:15 a.m.  Robert Erdahl (Queen's University) Reduced density matrices, the lower bound method and the contracted Schroedinger equation 
11:1512:00 a.m.  Paul W. Ayers (McMaster University) Variational Reduced Density Matrix Theory: Successes and Failures 
12:002:00 p.m.  Lunch Break 
2:003:00 p.m.  Allen Knutson (University of California,
San Diego) Schubert Calc. short course 
3:003:30 p.m.  Tea Break 
3:304:15 p.m.  Stefano Pironio (University of
Geneva) Noncommutative polynomial optimization and the varianional RDM method 
4:155:00 p.m.  very short talks 
5:00  6:00 p.m.  Reception Fields Institute 
Tuesday July 28  
9:0010:00 a.m.  Allen Knutson (University of California, San
Diego) Schubert Calc. short course 
10:0010:30 a.m.  Coffee Break 
10:3011:15 a.m.  Garnet KinLic Chan (Cornell
University) The DMRG and Correlator Product States 
11:1512:00 noon  Frank Verstraete (University of Vienna) Density matrices in realspace renormalization group methods 
12:002:00 p.m.  Lunch Break 
2:003:00 p.m.  Allen Knutson (University of California, San
Diego) Schubert Calc. short course 
3:003:30 p.m.  Tea Break 
3:304:30 p.m.  Robert Koenig (Caltech) and Graeme
Mitchison (University of Cambridge) de Finetti theorems for quantum states 
4:305:00 p.m.  First Wrap Up 
Wednesday July 29  
9:009:40 a.m.  Mary Beth Ruskai (Tufts University) transition remarks 
9:4010:30 a.m.  Renato Renner
(ETH Zurich) De Finetti and entropies 
10:3011:00 a.m.  Coffee Break 
11:0012:00 noon  Alexander Klyachko (Bilkent University) Quantum marginal problem 
Free Afternoon  
Thursday July 30  
9:009:45 a.m.  Matthias Christandl (LudwigMaximiliansUniversität
München) Estimating the spectrum of an operator  a technique for the analysis of spectral relations via representation theory 
9:4510:30 a.m.  Michael M. Wolf (Niels Bohr Institute) Bell inequalities and joint measurability  relating classical and quantum marginal problems 
10:3011:00 a.m.  Coffee Break 
11:0012:00 p.m.  Alexander Klyachko (Bilkent University) The Pauli exclusion principle and beyond 
12:002:00 p.m.  Lunch Break 
2:002:45 p.m.  Bastiaan Braams (Emory University) The reduced density matrix method and some complexity issues 
2:45  3:30 pm  YiKai Liu (California Institute
of Technology) Nrepresentability is QMAcomplete 
3:30  4:00 p.m.  Tea Break 
4:00  4:25  TzuChieh Wei (University of Waterloo) Bosonic Nrepresentability problem is also QMAcomplete 
4:254:50 p.m.  Peter Love (Haverford College) QMAcomplete problems for stoquastic Hamiltonians and Markov matrices 
4:50  5:15 p.m.  discussion 
Friday July 31  
9:30  10:15 a.m.  AspuruGuzik (Harvard University) Quantum computer simulation for chemical dynamics and molecular electronic structure 
10:15  11:00 a.m.  Coffee Break 
11:00  11: 45 a.m.  Andreas Winter (University of Bristol) A new inequality for the von Neumann entropy 
11:45  12:15  wrapup discussion 
Coleman dinner in Kingston 
Full Name  University/Affiliation 
Acin, Antonio  ICFO 
Anderson, James  McMaster University 
Andrews, Rob  (no affiliation) 
AspuruGuzik, Alán  Harvard University 
Ayers, Paul  McMaster University 
Belinschi, Serban  University of Saskatchewan 
Beny, Cedric  National University of Singapore 
Berta, Mario  LudwigMaximiliansUniversität München 
Boche, Holger  Technical University Berlin 
Braams, Bastiaan J.  Emory University 
Brooke, James  University of Saskatchewan 
Chan, Garnet  Cornell University 
Changlani, Hitesh  Cornell University 
Choi, ManDuen  University of Toronto 
Christandl, Matthias  LudwigMaximiliansUniversität München 
Collins, Benoît  University of Ottawa 
Cubitt, Toby  University of Bristol 
CuevasSaavedra, Rogelio  McMaster University 
Cui, Wei  University of Toronto 
Curty, Marcos  University of Vigo 
De Baerdemacker, Stijn  University of Toronto 
Dupuis, Frédéric  University of Montreal 
Erdahl, Robert  Queen's University 
Fan, Guangzhe  University of Waterloo 
GarciaSaez, Artur  ICFO  The Institute of Photonic Sciences 
Gottlieb, Alexander  Wolfgang Pauli Institute 
Guenda, Kenza  University of Algiers 
Halevy, Itamar  
Hayden, Patrick  McGill University 
Helwig, Wolfram  University of Toronto 
Janssen, Gisbert  Technische Universitaet Berlin 
Ji, Zhengfeng  Perimeter Institute 
Johnson, Paul  McMaster University 
Klyachko, Alexander  Bilkent University 
Knutson, Allen  University of California, San Diego 
Koenig, Robert  California Institute of Technology 
Kulikov, Pavel  McMaster University 
Lim, Jacques Bunrith  IRMAR 
Liu, YiKai  California Institute of Technology 
Love, Peter J.  Haverford College 
Lyons, David  Lebanon Valley College 
Matthews, William  University of Waterloo 
Menicucci, Nicolas  Perimeter Institute for Theoretical Physics 
Mitchison, Graeme  Centre for Mathematical Sciences 
Mosonyi, Milan  Centre for Quantum Technologies, NUS 
Movassagh, Ramis  Massachusetts Institute of Technology 
Myhr, Geir Ove  University of Waterloo 
Nakata, Maho  RIKEN 
Nechita, Ion  Institut Camille Jordan, Université Claude Bernard Lyon 1 
Noetzel, Janis  Technische Universität Berlin 
Orser, Brenda  B.I.O. Letha Information Systems, Inc. 
Piani, Marco  University of Waterloo 
Pironio, Stefano  University of Geneva 
Ralph, Claire  Cornell University 
Renner, Renato  ETH Zürich 
Rosgen, Bill  University of Waterloo 
Ruskai, Mary Beth  Tufts University 
Schuch, Norbert  MaxPlanckInstitute for Quantum Optics 
van Aggelen, Helen  Ghent University 
Van Neck, Dimitri  Ghent University 
Verstraete, Frank  University of Vienna 
Walck, Scott  Lebanon Valley College 
Walgate, Jonathan  Perimeter Institute 
Wei, TzuChieh  University of Waterloo 
Winter, Andreas  University of Bristol 
Wolf, Michael  Copenhagen University 
Zeier, Robert  Technische Universitaet Muenchen 