# Methods Development

## Machine Learning Quantum Matter

**Project Leader: ** Titus Neupert

**Main Contributors: **Mark H. Fischer, Michael Denner, Nikita Astrakhantsev

Machine learning rapidly changes the way we access and process data in our daily life as well as in the sciences. We employ machine learning algorithms to better understand and simulate quantum matter for a range of purposes.

Most immediate applications are in data analysis. For instance, we have developed an algorithm that detects the symmetry class of a crystal directly from powder diffraction data, bypassing an involved crystallographic analysis. In another project, we were able to discern phases of matter from numerical data, namely the entanglement patterns in the quantum state of a system.

A central problem numerical calculations face is how to store the many-body quantum state of a systems: due to an exponential growth of the size of the Hilbert space with the system size it quickly exceeds any available memory. We use neural networks to represent quantum many-body states in a compressed form, taking up much less memory. Based on these neural network quantum states (NQS), we develop algorithms that give quantitatively accurate descriptions of complex interacting quantum phases of matter with exotic properties.

## Quantum Computers for Quantum Many-body Problems

**Project Leader: **Titus Neupert

**Main Contributors: **Mark H. Fischer, Nikita Astrakhantsev

Computation is undergoing a paradigm shift with the arrival of quantum simulation devices. In the immediate future, these machines, which are currently being developed and explored by all major tech companies, do not work with ‘digital’ precision but rather deliver probabilistic results. While quantum algorithms are currently envisioned for many applications from finance via image recognition to novel search algorithms, the devices may be particularly useful for intrinsically quantum mechanical calculations as they appear in condensed matter physics or quantum chemistry.

In collaboration with researchers at IBM Rüschlikon, we use the IBM quantum computers to explore their potential for generic quantum many-body calculations. Foundational to this endeavor is the ability to represent and manipulate entangled quantum states on these device. Beyond this first steps, we develop algorithms that simulate the time evolution or find ground states.