Welcome to our Quantum Computing group website!

We are part of Informatics 5 at TUM. Our research focuses on quantum computing applications, strongly correlated quantum systems and transport properties of physical systems.

We are always looking for talented students - if you are interested in a student project, Bachelor, Master or PhD thesis, drop by or contact us.

# Research

## Quantum computing applications

We are planning to explore and substantiate how a (future) quantum computer can be employed for scientific simulations and technical applications, e.g., solving high-dimensional partial differential equations, boosting performance of machine learning problems, or simulating high-temperature superconductors on a laboratory system of ultracold atoms in an optical lattice.

Related publications:

- Christian B. Mendl, Michael M. Wolf.
*Unital quantum channels - Convex structure and revivals of Birkhoff’s theorem*

**Commun. Math. Phys. 289**, 1057-1086 (2009)

## Numerical algorithms for simulating quantum systems

Our expertise is in DMRG/tensor network and quantum Monte Carlo methods. Currently we are also exploring neural network quantum states, i.e., employing neural networks as Ansatz for quantum wavefunctions.

Specifically, we have implemented matrix-product-operator techniques to study out-of-time ordered correlation (OTOC) functions and elucidate scrambling of quantum information. Complementary to tensor network methods, quantum Monte Carlo is suited for 2D systems at high temperatures; we have applied the determinant quantum Monte Carlo (DQMC) algorithm to a three-band Hubbard model of high-Tc cuprate superconductors.

Selected publications:

- Edwin W. Huang, Christian B. Mendl, Shenxiu Liu, Steven Johnston, Hong-Chen Jiang, Brian Moritz, Thomas P. Devereaux.
*Numerical evidence of fluctuating stripes in the normal state of high-Tc cuprate superconductors*

**Science 358**, 1161-1164 (2017)

Code on GitHub: hubbard-dqmc - Annabelle Bohrdt, Christian B. Mendl, Manuel Endres, Michael Knap.
*Scrambling and thermalization in a diffusive quantum many-body system*

**New J. Phys. 19**, 063001 (2017)

Code on GitHub: tensor_networks - Christian B. Mendl.
*PyTeNet: A concise Python implementation of quantum tensor network algorithms*

**JOSS 3**, 948 (2018)

Code on GitHub: pytenet

## Statistical physics and nonlinear fluctuating hydrodynamics

One-dimensional physical systems can exhibit interesting anomalous transport properties. A characteristic signature is the time-dependent response of the local energy to a small, localized perturbation of the equilibrated system, expressed by the energy-energy time-correlation. One approach to understand such behavior is a nonlinear extension of fluctuating hydrodynamics, which has attracted particular interest in recent years due to surprising connections to the KPZ universality class. Specifically, nonlinear fluctuating hydrodynamics predicts that the energy correlation function contains a left- und right-moving “sound peak” with asymptotic scaling form

where is a model-dependent coefficient, denotes the left or right peak and is the KPZ function. Together with Herbert Spohn, we have worked out the detailed connection between statistical physics models and KPZ theory and performed numerical molecular dynamics simulations.

Selected publications:

- Christian B. Mendl, Herbert Spohn.
*Shocks, rarefaction waves, and current fluctuations for anharmonic chains*

**J. Stat. Phys. 166**, 841-875 (2017) - Christian B. Mendl, Herbert Spohn.
*Low temperature dynamics of the one-dimensional discrete nonlinear Schrödinger equation*

**J. Stat. Mech.**(2015) P08028 - Christian B. Mendl, Herbert Spohn.
*Dynamic correlators of Fermi-Pasta-Ulam chains and nonlinear fluctuating hydrodynamics*

**Phys. Rev. Lett. 111**, 230601 (2013)

Accompanying Mathematica code: fluct-hydro-chains