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Tutorial

T8 Process Tensor Matrix-product States

Efficiently modeling the dynamics of a quantum system coupled to a complex environment is key to many fields.

Efficiently modeling the dynamics of a quantum system coupled to a complex environment is key to many fields. Most directly it is relevant for modelling open quantum systems with strong coupling to their environment, but more broadly, this problem is also at the core of impurity models needed for dynamical mean field-theory (DMFT). A new paradigm has recently emerged to formulating and solving these problems: the process tensor, and particularly matrix-product operator representations of the process tensor. The process tensor is a multilinear map from a sequence of operations on a quantum system to its final density matrix, and the recent breakthrough has been the realization that it is possible to efficiently construct a matrix product state representation of this object. This has led to a wide range of applications in open quantum systems and, more recently, as an improved impurity-solver for DMFT. For open quantum systems, it can go beyond simulating the time-evolution of the system, to allow also multi-time correlations, back-propagation for optimal control, and integration into solving many-body open quantum systems problems. As well as the direct relevance of these methods to solving specific problems, they provide a key illustration of how the matrix-product operator methods can find applications away from their traditional setting of one-dimensional quantum dynamics.

Topics

  • Introduction to the process tensor: What it is, and its significance. The concept of higher-order maps.
  • Practical calculations with the process tensor. Introduction to the OQuPy library; applications of process tensors
  • Fermionic process tensors and use of the process tensor as an impurity solver for DMFT.
  • Many-body physics with the process tensor.

Who should attend?

Theorists in several fields: open quantum systems, quantum control, modelling of organic materials, quantum impurity solvers. Experimentalists who are interested in ways to model open quantum systems.

Organizer

  • Jonathan Keeling, University of St Andrews

Presenters

  • Kavan Modi, Monash, University/Quantum for New South Wales
  • Gerald Fux, ICTP Trieste
  • Gunhee Park, California Institute of Technology
  • Jonathan Keeling, University of St Andrews