### PROJECT AREAS AND PROJECTS

## Project Area A

Topology and fractionalization

## Project Area B

Entanglement, measurement, and information

## Project Area C

Design and functionality of entangled quantum devices

### Topology and fractionalization

### Project A01: Topology and dynamics

The project investigates how topological states and excitations can be created and manipulated in time-dependent systems focusing on time crystals, anomalous Floquet topological phases, and corresponding quantum devices. We explore how quantum pumps and time crystals can be realized in solid state systems and how Coulomb interactions affect Floquet-Majorana states. Topological defects in space-time crystals will be studied with a focus on properties which do not have any counterpart in equilibrium.

Rudner | Rosch | Berg

### Project A02: Gapless topological phases

Initially, research on topological matter focused on gapped phases, such as topological insulators or superconductors. Project A02 considers the more recent extensions of the topology paradigm to the strongly spin-orbit entangled gapless phases such as Weyl or nodal-line semimetals. It combines abstract theoretical questions concerning the classification of topological gapless phases with the theoretical and experimental study of boundary signatures and their stability to disorder or phonon scattering.

Brouwer | Egger | Beidenkopf

### Project A03: Disordered topological matter

Project A03 addresses the physics of topology and entanglement in systems lacking translational invariance. The project includes two principal lines of activity. The first explores the stability of topological phases in the presence of disorder, and the generation of novel boundary phenomena by conspiracies of impurity scattering and topological structures. The second focuses on statistical distributions of systems with strong entanglement such as SYK matter, systems with Fock space or many body localization, and random tensor networks.

Brouwer | Eisert | Altland

### Project A04 (B03): Theory of fractionalized topological phases of matter

Project A04 focuses on topological phases that exhibit fractionalization — the emergence of quasiparticles with microscopically forbidden quantum numbers, such as charge-neutral spin-1/2 `spinons‘ in quantum magnets. It combines a variety of analytical and numerical techniques to study gapless quantum spin liquids and correlated insulators in graphene flat bands. The goals are to classify the possible ground states for given microscopic symmetries and to develop a coherent understanding of the conditions under which such exotic quantum phases may arise.

Reuther | Trebst | Mross | Stern

### Entanglement, measurement, and information

### Project B01: Entanglement and machine learning

Project B01 will further the conceptual understanding of entanglement in the context of describing topological phases of matter and will serve as a methods development laboratory. Tensor networks feature strongly as a tool to capture the intricate correlations in states of quantum many-body systems and to grasp properties of natural and realistic quantum many-body systems. Intertwined with this effort, (quantum) machine learning enters as a new method to describe and learn properties of complex quantum systems and to identify novel applications of synthetic quantum devices – again with notions of entanglement in the center.

Eisert | Rizzi | Trebst

### Project B02: Measurement and control of open quantum matter

Recently, there has been a strong rise of interest in open quantum matter – many-body quantum systems where Hamiltonian and dissipative dynamical resources interplay, bringing together the disciplines of quantum optics and condensed physics. In this project, we will characterize these systems, study the effect of quantum measurements, and design protocols for controlling and manipulating quantum states, with particular emphasis on topological aspects. To this end, we will combine field theoretical analytical techniques and numerical approaches in part based on optimal control theory.

Koch | Diehl | Gefen

### Project B04 (C04): Entangled and synthetic quantum devices

This project proposes synthetic quantum systems with long-range entanglement that are composed of elementary mesoscopic units, and studies their properties and applications. We will explore the potential for building computationally universal quantum matter, using advanced tensor network approaches and coupled-chain networks. For finite-length spin chains as elementary unit, we will study analytically accessible constructions for chiral spin liquid phases. We also investigate how such platforms may be used for quantum error correction, decoding, and fault-tolerant quantum computation.

Eisert | Altland | Egger | Oreg

### Design and functionality of entangled quantum devices

### Project C01: Measurement and manipulation of topological excitations

This project proposes and studies experimentally feasible protocols aimed at the measurement, manipulation, and measurement-induced manipulation of topological excitations in quantum devices. Common to these protocols is a prescribed time sequence of operations. In particular, we will explore many-body interferometric approaches in the time-energy domain which apply for localized topological quasi-particles. We will also develop a comprehensive theory of quantum measurements for Majorana qubits and study transport spectroscopy protocols for parafermionic systems.

Eisert | Altland | Egger | Oreg

### Project C02: Engineering topological states of matter

Project C02 will pursue novel concepts to design entangled topological states of matter. In one part of the project, we will explore the potential of twisted bilayer graphene for realizing topological states of matter. This line of research will also include efforts to unravel the underlying interaction physics of this system in collaboration with experiment. In addition, we will search for and explore topological phases in single- and multi-wall carbon nanotubes. Finally, we will consider heterostructures of transition metal dichalcogenides as a possible building block for two-dimensional topological superconductivity.

v. Oppen | Berg | Ilani | Oreg

### Project C03: Majorana platforms

Project C03 will study three platforms for realizing topological superconductivity and corresponding signatures of Majorana bound states. We will explore novel wire concepts for semiconductor quantum wires proximity coupled to conventional superconductors, with the goal of reducing the requirements on or obviating the need for an applied magnetic field. We will pursue strategies to optimize a very recent platform for Majoranas based on long Josephson junctions in a two-dimensional electron system. Finally, we will attempt to realize and understand topological superconductivity in chains of magnetic adatoms on superconductors, which can be built by manipulation with a scanning tunneling microscope tip.

Flensberg | Marcus | Franke | v. Oppen | Stern

### Project C05 (N): Transmon qubits

Coupled superconducting transmon circuits are one of the leading platforms in quantum information science. Their hallmark, the nonlinearity of Josephson junctions, is Janus-faced, enabling the definition of the qubit subspace in the first place but giving rise to correlated errors and possibly many-body quantum chaos. In this project, we will study entanglement in transmon circuits and transmon-resonator networks through the lens of the transmon as a nonlinear quantum element. We will seek novel ways of mitigating the undesirable effects of nonlinearities but also explore nonlinearities as a resource for quantum networks and quantum simulation.

Altland | Koch | Metelmann | Rudner