*Dr Ian McCulloch, UQ*

* This colloquium will be held 12 noon, 3rd March, in Prentice 42-216*

Simulating quantum many-body systems with a classical computer is a difficult problem, principally because the number of degrees of freedom required to represent a wave function (measured by the dimension of the associated Hilbert space) is exponentially large. However that doesn’t mean that the information content of a physical state can be arbitrarily big. A striking example is the holographic principle, inspired by black hole thermodynamics: the information content of a black hole is proportional to the surface area of the event horizon, rather than the volume. Similarly, certain types of quantum systems have a very specific spatial dependence of the entanglement, implying that the relevant degrees of freedom are confined to a relatively tiny corner of the Hilbert space.

Tensor Networks provide a framework for representing many-body states that captures these entanglement properties, resulting in an extremely compact representation. This has led to many widely used computational algorithms for simulating ground-state and dynamics of many-body quantum systems. A tensor network can be seen as a form of information compression, and more recently this has led to potential applications in machine learning.