**Research Synopsis.** My current research mainly focusses on three different avenues within the realms of Quantum Technologies: (i) Quantum Technologies with Rydberg atoms, (ii) Quantum materials in cavities for new quantum technologies and (iii) Solving real-world problems on a quantum computer.

A detailed description of these research activities can be found below.

**Quantum technologies with Rydberg atoms**

Rydberg atoms are atoms in highly excited electronic states and exhibit extremely exaggerated properties compared to their ground state counterparts. For example, they exhibit a quasi-continuum of very strong dipole transitions in the terahertz and microwave range, and the lifetime of Rydberg states increases dramatically with their principal quantum number. This project explores how these properties can be harnessed for the efficient interconversion of millimeter-wave and optical fields [1,2], which has numerous applications in classical and quantum technologies.

[1] M. Kiffner, A. Feizpour, K. T. Kaczmarek, D. Jaksch and J. Nunn, *Two-way interconversion of millimeter-wave and optical fields in Rydberg gases*, New J. Phys. 18, 093030 (2016).

[2] J. Han, T. Vogt, C. Gross, D. Jaksch, M. Kiffner, and W. Li, *Free-space microwave-to-optical conversion via six-wave mixing in Rydberg atoms*, Phys. Rev. Lett. 120, 093201 (2018).

[3] T. Vogt, C. Gross, J. Han, S. B. Pal, M. Lam, M. Kiffner, and W. Li, Efficient microwave-to-optical conversion using Rydberg atoms, Phys. Rev. A 99, 023832 (2019).

We explore how Rydberg ensembles can be used for the generation and sensitive detection of electromagnetic radiation in frequency bands where standard generation and detection methods are inefficient. Our most recent work employs an ensemble of thermal Rydberg atoms for the simultaneous generation of UV light [311 nm] and THz radiation [3.28 THz].

[4] M. Lam, S. B. Pal, T. Vogt, C. Gross, M. Kiffner, and W. Li, *Collimated UV light generation by two-photon excitation to a Rydberg state in Rb vapor, *Optics Letters **44**, 2931 (2019).

**Quantum materials in cavities for new quantum technologies **

This project considers quantum hybrid systems comprised of solid state materials that are strongly coupled to quantised modes of microwave (MW), terahertz (THz) or optical radiation. Quantum hybrid systems with a solid state component have the great advantage of being scalable since they inherit most of the production expertise developed for semiconductor devices. The overarching goal of this project is to advance the physics of solid state materials coupled to quantised radiation fields and to foster the development of novel quantum technologies emerging from these insights.

Of particular interest are quantum materials where small microscopic changes can result

in large macroscopic responses due to strong electron-electron interactions. Coupling these systems to cavities opens up the fascinating possibility of investigating the ultimate quantum limit where macroscopic properties of quantum materials are determined by quantum

light fields and vice versa.

As a paradigmatic example of these systems we consider the Fermi-Hubbard model and find that the electron-cavity coupling reduces the magnetic interaction between the electron spins in the ground-state manifold. At half filling this effect can be observed by a change in the magnetic susceptibility. At less than half filling, the cavity re-normalises the hopping amplitude, introduces a next-nearest-neighbor hopping and mediates a long-range electron-electron interaction between distant sites. We study the ground-state properties with tensor network methods and find that the cavity coupling can induce a phase characterized by a momentum-space pairing effect for electrons.

[1] M. Kiffner, J. Coulthard, F. Schlawin, A. Ardavan, and D. Jaksch, *Manipulating Quantum Materials with Quantum Light*, Phys. Rev. B 99, 085116 (2019). See also Erratum at Phys. Rev. B 99, 099907 (2019).

In the manifold of states with one photon or one doublon excitation the cavity results in the formation of Mott polaritons. The vacuum Rabi splitting of the two outermost branches is collectively enhanced and can exceed the width of the first excited Hubbard band. This effect can be experimentally observed via measurements of the optical conductivity.

[2] M. Kiffner, J. Coulthard, F. Schlawin, A. Ardavan, and D. Jaksch, *Mott polaritons in cavity-coupled quantum materials, *New J. Phys. **21**, 073066 (2019).

**Solving real-world problems on a quantum computer**

This project is done in collaboration with IBM-Q, which provides several devices with up to twenty qubits. We currently pursue two different avenues:

**(i) Electronic structure calculations.** Dynamical Mean Field Theory (DMFT) is an advanced and powerful tool for electronic structure calculations of solid state systems. Recently, hybrid quantum-classical schemes have been suggested [1,2] where the so-called DMFT impurity problem is solved on a quantum computer.

We numerically emulate noisy intermediate-scale quantum (NISQ) devices using Qiskit and determine the minimal hardware requirements for two-site hybrid quantum-classical dynamical mean-field theory (DMFT) [3]. We develop a circuit recompilation algorithm which significantly reduces the number of quantum gates of the DMFT algorithm and find that the quantum-classical algorithm converges if the two-qubit gate fidelities are larger than 99%. The converged results agree with the exact solution within 10%, and perfect agreement within noise-induced error margins can be obtained for two-qubit gate fidelities exceeding 99.9%. By comparison, the quantum-classical algorithm without circuit recompilation requires a two-qubit gate fidelity of at least 99.999% to achieve perfect agreement with the exact solution. We thus find quantum-classical DMFT calculations can be run on the next generation of NISQ devices if combined with the recompilation techniques developed in this work.

[1] J. M. Kreula et al., Scientific reports 6, 32940 (2016).

[2] J. M. Kreula et al., EPJ Quantum Technology 3, 11 (2016).

[3] B. Jaderberg, A. Agarwal, K. Leonhardt, M. Kiffner, and D. Jaksch, Minimum Hardware Requirements for Hybrid Quantum-Classical DMFT, arXiv:2002.04612.

**(ii) Variational Quantum Algorithms for Nonlinear Problems.** We show that nonlinear problems including nonlinear partial differential equations can be efficiently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat nonlinearities efficiently and by introducing tensor networks as a programming paradigm. The key concepts of the algorithm are demonstrated for the nonlinear Schrödinger equation as a canonical example. We numerically show that the variational quantum ansatz can be exponentially more efficient than matrix product states and present experimental proof-of-principle results obtained on an IBM Q device.

[4] M. Lubasch, J. Joo, P. Moinier, M. Kiffner, and D. Jaksch, *Variational Quantum Algorithms for Nonlinear Problems, *Phys. Rev. A 101, 010301(R) (2020).