Tensor Network States and Algebraic Geometry 2012 at ISI Torino

Joint Sponsors: ISI Foundation and Department of Mathematics, Penn State University

Aims and scope

Tensor Network States represents a rapidly growing area of theoretical physics, which seeks, in part, to understand quantum many-body systems, by a merger of computer science techniques (based in part on novel methods of lossy compression) paired with physical insight. These techniques have recently started to defy long held intuitions on the classes of quantum systems which can be simulated efficiently using classical computer algorithms. The initial success of these ideas have consequently attracted significant interest, with several subtopics emerging. This culminates in the use of more sophisticated mathematics to understand and reason about quantum systems in general and touches upon notions of complex systems and modern network theory. This workshop aims to explore this overlap and to seed a cross pollination of ideas from tensor network states and algebraic geometry as well as the modern theory of complex systems.

Topics of interest include:

The workshop will have tutorial lectures on Tuesday November 6 and Wednesday November 7 with talks on November 8.

Tuesday November 6

Joint Sponsors: ISI Foundation and Department of Mathematics, Penn State University

Aims and scope

Tensor Network States represents a rapidly growing area of theoretical physics, which seeks, in part, to understand quantum many-body systems, by a merger of computer science techniques (based in part on novel methods of lossy compression) paired with physical insight. These techniques have recently started to defy long held intuitions on the classes of quantum systems which can be simulated efficiently using classical computer algorithms. The initial success of these ideas have consequently attracted significant interest, with several subtopics emerging. This culminates in the use of more sophisticated mathematics to understand and reason about quantum systems in general and touches upon notions of complex systems and modern network theory. This workshop aims to explore this overlap and to seed a cross pollination of ideas from tensor network states and algebraic geometry as well as the modern theory of complex systems.

Topics of interest include:

- Applications of Penrose's graphical notation as a formal system of equational reasoning for tensor network states, algebraic geometry and complex systems
- Applications of the paradigm of modern network theory in algebraic statistics and tensor network states (and conversely)
- Chirality and time-symmetry breaking in quantum and classical network transport, quantum walks and Markovian process such as the spread of infectious disease
- Applications of tensor contraction algorithms appearing in algebraic geometry to problems faced in quantum physics, and machine learning (and conversely)
- Invariant theory for tensor network states

The workshop will have tutorial lectures on Tuesday November 6 and Wednesday November 7 with talks on November 8.

Tuesday November 6

- Coffee from 10-10:30
- 10:30 - 11:30: Introduction to network theory and network measures, Giovanni Petri (confirmed)
- 11:35 - 12:35: Introduction to tensor network states, Ville Bergholm (confirmed)
- Lunch
- 2 - 3: Introduction to algebraic geometry for physicists and computer scientists, Jason Morton (confirmed)
- 3:05 - 4:05: Introduction to classical circuit complexity, Jacob Turner (confirmed)
- 4:10: Introduction to Category Theory as a language to model complex systems, Francesco Vaccarino (confirmed)

- Coffee from 10-10:30
- 10:30 - 11:30: A primer on phase transitions, Zsolt Bertalan (confirmed)
- 11:35 - 12:35: Introduction to network visualization tools, Andre Panisson
- Lunch
- 2-3: Introduction to tensor network states II, Ville Bergholm (confirmed)
- 3:05-4:05: Introduction to algebraic geometry II, Jason Morton (confirmed)
- 4:10-5:10: Introduction to quantum vs classical correlations and decay, Michele Allegra (confirmed)

- 10-10:30: Coffee
- 10:30-10:40: Welcome, Jason Morton
- 10:40-11:05: Tensor networks for open systems, Chris Wood
- 11:05-11:30: 0/1 Constraint satisfaction problems and tensor networks, Susan Margulies
- 11:30-11:55: Determinantal circuits, Jacob Turner
- 11:55-12:20: Groud state spin logic, Mauro Faccin
- 12:20-12:45pm: Graph infection, control and algebraic geometry, Daniel Burgarth
- 12:45-2:00pm: Lunch
- 2:00-3:00pm: Tutorial: Introduction to quantum complexity theory, Daniel Nagaj
- 3:00-3:25pm: When does a mixture of products contain a product of mixtures?, Guido Montufar
- 3:25-3:50pm: Wick's theorem for matrix product states, Robert Huebener
- 3:50-4:15pm: Time-symmetry breaking in quantum processes, Zoltan Zimboras
- 7:30pm-: Workshop Aperitivo, Lobelix, Piazza Vittorio Veneto, 23, 10124