Machine learning has had great success in classifying and recognising patterns in a variety of inputs. This includes classifying phases of matter based on data from experiments or simulations. However, there exist exotic phases known as topological phases, which are indistinguishable from trivial noninteracting states by straightforward local measurements, even though they carry intricate patterns of quantum correlations and entanglement.

Part 1

In this part of the project, you will explore whether machine-learning techniques can distinguish symmetry-protected topological (SPT) phases from conventionally ordered and disordered ones through the example of a spin-chain Hamiltonian. You will learn about principal component analysis (PCA) and variational autoencoders (VAEs), tools designed to extract similarities and differences from data, as well the DMRG algorithm for efficiently computing ground states of interacting quantum Hamiltonians. You will study whether these tools can distinguish the phases through conventional measurements (e.g., correlation functions).

Part 2

In this part, you will explore how direct quantum measurements (i.e., samples from the Born probability distribution) may be used as input data. This part also involves learning about SPTs and DMRG as example systems to which to deploy the results. However, the focus is understanding the statistical and information theoretic principles underlying VAEs and designing one that works directly with the Born probability distribution.

How to apply

If you are interested in one or both parts of the project, please email me and tell me about why you are interested in the project. Please also tell me which part of the project you are more interested in (both might be too much for one master’s project), as well as any relevant background you may have in machine learning and/or condensed matter.

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