ON-LINE QLunch: Daniel Stilck França

Speaker: Daniel Stilck França from QMATH

Title: Simulating quantum matter: to the boundary and beyond

Quantum entanglement, a form of correlation with no clear classical analog, makes the simulation of quantum systems a daunting challenge, as describing arbitrary entangled states requires exponentially many parameters. Luckily, physically relevant states have a much more tame, local entanglement structure. Tensor network states form a variational ansatz class that efficiently captures the entanglement structure found in physical systems and can still represent exotic phases of matter, such as states exhibiting topological order. This property makes tensor network states one of the most successful techniques to simulate quantum matter. However, their intricate geometry makes it challenging to find such efficient representations. Indeed, some states of interest lie on the classes' boundary, which is unreachable with standard methods. In this work, we take inspiration from the geometry of quantum states and algebraic geometry and address this issue. We define a new ansatz class that includes states on the boundary and show how to optimize over them efficiently.

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