### The Quantum Talents Symposium in Munich

The symposium is designed to bring together outstanding PhD students and early-career postdocs from all over the world to present their groundbreaking research work in the field of quantum science and technology.

**Our mission: to provide a platform for emerging young researchers, facilitate knowledge sharing, inspire collaboration, and promote career opportunities in quantum science. **

Special attention will be given to increasing diversity in the field of quantum science, fostering a more inclusive and equitable environment that values the contributions of researchers from all backgrounds.

### Finalists 2024

##### Quantum Fluctuations and Collective Modes in Disordered 2D Superconductors

Abstract

Together with my collaborators, we explore how electron-electron interactions and weak (anti)localization phenomena in two-dimensional systems can enhance the superconducting transition temperature in the so-called multifractal regime. By developing a comprehensive theoretical framework, we highlight the impact of quantum fluctuations and uncover the critical role of collective modes in disordered superconductors. This work establishes a direct connection between the self-consistent gap equation at the superconducting transition temperature and the renormalization group equations for interaction parameters in the normal state.

Building on this foundation, we investigate the dynamics of the collective amplitude Schmid-Higgs (SH) mode in Bardeen–Cooper–Schrieffer (BCS) superconductors and fermionic superfluids with non-magnetic disorder. By examining the SH susceptibility, we determine the zero-temperature dispersion relation and damping rate of the SH mode across the transition from diffusive to ballistic scales. Our findings reveal that the imaginary part of the SH susceptibility peaks along the real frequency axis above twice the superconducting gap. In the diffusive limit, the SH susceptibility pole is below the continuum edge but re-emerges in the ballistic regime, showing non-monotonic dispersion. Furthermore, the SH mode’s dispersion exhibits a logarithmic non-analyticity in the diffusive range of momenta, causing an anomalous spatial decay at distances longer than the coherence length.

##### Proximity-induced gapless superconductivity in two-dimensional Rashba semiconductor in magnetic field

Abstract

Two-dimensional semiconductor-superconductor heterostructures form the foundation ofnumerous nanoscale physical systems. However, measuring the properties of suchheterostructures, and characterizing the semiconductor in-situ is challenging. A recentexperimental study by [Phys. Rev. Lett. 128, 107701 (2022)] was able to probe thesemiconductor within the heterostructure using microwave measurements of the superfluiddensity. This work revealed a rapid depletion of superfluid density in semiconductor,caused by the in-plane magnetic field which in presence of spin-orbit coupling creates socalledBogoliubov Fermi surfaces. The experimental work used a simplified theoreticalmodel that neglected the presence of non-magnetic disorder in the semiconductor, hencedescribing the data only qualitatively. Motivated by experiments, we introduce atheoretical model describing a disordered semiconductor with strong spin-orbit couplingthat is proximitized by a superconductor. Our model provides specific predictions for thedensity of states and superfluid density. Presence of disorder leads to the emergence of agapless superconducting phase, that may be viewed as a manifestation of BogoliubovFermi surface. When applied to real experimental data, our model showcases excellentquantitative agreement, enabling the extraction of material parameters such as mean freepath and mobility, and estimating g-tensor after taking into account the orbital contributionof magnetic field. Our model can be used to probe in-situ parameters of othersuperconductor-semiconductor heterostructures and can be further extended to give accessto transport properties.

##### Real-time Quantum Control of Qubits

Abstract

Quantum computing relies on developing quantum devices that are robust against small and uncontrolled parameter variations in the Hamiltonian. One can apply feedback by estimating such uncontrolled variations in real time to stabilize quantum devices and improve their coherence. This task is important for many quantum platforms such as spins, superconducting circuits, trapped atoms, and others towards error suppression or correction.

In the first part of the talk, we focus on real-time closed-loop feedback protocols to estimate uncontrolled fluctuations of the qubit Hamiltonian parameters, followed by enhancing the quality of qubit rotations [1]. First, we coherently control two entangled electron spins with a low-latency quantum controller. The protocol uses a singlet-triplet spin qubit implemented in a gallium arsenide double quantum dot. We establish real-time feedback on both control axes and enhance the resulting quality factor of coherent spin rotations. Even with some components of the Hamiltonian purely governed by noise, we demonstrate noise-driven coherent control. As an application, we implement Hadamard rotations in the presence of two fluctuating control axes.

*(a) Entangled electron spins (qubit) schedule, alternating between periods Top of quantum information processing (dashed box), and short periods Test for efficiently learning the fluctuating environment (gray box). (b) Overhauser field fluctuations, tracked in real-time by the relative rotation of the two electron spins, on a scanning electron micrograph of a gallium arsenide spin qubit array.*

Next, we present a protocol for a physics-informed real-time Hamiltonian estimation [2]. We estimate the fluctuating nuclear field gradient within the double dot on-the-fly by updating its probability distribution according to the Fokker-Planck equation. We further improve the physics-informed protocol by adaptively choosing the free evolution time of the entangled electrons singlet pair, based on the previous measurement outcomes. The protocol results in a ten-fold improvement of the estimation speed compared to former schemes.

Our approaches introduce closed-loop feedback schemes aimed at mitigating the effects of decoherence and extending the lifetime of quantum systems. In this view, our schemes provide valuable insights into the synergy between quantum control, quantum computation, and computer science.

**References**

[1] F. Berritta et al., Nat. Commun. **15**, 1676 (2024)

[2] F. Berritta et al., arXiv:2404.09212 (2024)

**Single quantum coherent spins in hexagonal boron nitride at ambient conditions**

Abstract

**A journey through quantum networks and quantum simulations with atoms and ions**

The creation of entanglement between particles is one of the essential ingredients of quantum technologies and doubtlessly a major challenge for experimentalists working on quantum hardware. I this talk, I will review our efforts in creating entanglement from very different perspectives. In the first half, I will describe how to achieve entanglement between only two particles, but over large spatial distances with the goal of demonstrating building blocks of a quantum network. In such a network, entanglement between remote parties acts as a resource of many applications such as secure communication or distributed quantum computing. Specifically, I will show why nonlinear-optics based frequency conversion techniques of single photons are important and finalize this part with an experiment to entangle two trapped neutral atoms, which are located at spatially separated laboratories in the city center of Munich, over a fiber distance of 33 km with a fidelity of 62.2(2) %. In the second part, I switch gears to creating entangled states between a large number of particles over short, micrometer-scale distances, which is the focus of my postdoctoral work. Our workhorse is a novel analog quantum simulator based on trapped ions. Here, the ions are confined in a single 3D electric potential and form a two-dimensional Coulomb crystal with up to 105 particles. I will show recent results where we generate spin-squeezed states as well as GHZ states in these crystals with exciting applications for quantum metrology.

##### Topologically ordered phases of 2+1d fusion surface models

Abstract

Fusion surface models [1] are 2+1d quantum lattice models constructed from fusion 2-categories, extending the concept of 1+1d anyon chains to higher dimensions. With their inherent 1-form symmetries derived from the input category, fusion surface models are prime candidates for exhibiting various kinds of topological order.

In my talk, I will show how Kitaev’s honeycomb model [2] can be generalized within the fusion surface model framework to models with more exotic symmetries. This includes a ZN symmetric generalization [3] based on the Tambara-Yamagami category and a novel Fibonacci honeycomb model. Their phase diagrams reveal two particularly interesting regimes. In the anisotropic limit, they reduce to Levin-Wen string-nets, displaying non-chiral topological order. In the opposite limit, they are characterized by weakly coupled anyon chains and are capable of realizing chiral topological order when time-reversal symmetry is broken.

**References:**

[1] Kansei Inamura and Kantaro Ohmori, SciPost Phys. 16, 143 (2024)

[2] Alexei Kitaev, Annals of Physics 321 (2006)

[3] Maissam Barkeshli et al., Phys. Rev. Lett. 114, 026401 (2015)

##### Heavy-fermion physics and superconductivity in twisted bilayer graphene

Abstract

Twisted bilayer graphene (TBG) has shown two seemingly contradictory characters: (1) quantum-dot-like behavior in STM indicates localized electrons; (2) the transport experiments suggest the itinerant electrons. Two features can both be captured by a topological heavy-fermion model, in which the topological conduction electron bands couple to the local moments [1]. We study the local-moment physics and the Kondo effect in this model. We demonstrate that, at the integer fillings, the Kondo effect is irrelevant and the RKKY interactions stabilize long-range ordered states [2, 3]. However, at non-integer fillings, the Kondo effect is relevant [3, 4], and Kondo resonance appears in the single-particle spectrum. Based on the heavy-fermion model, we explore the transport properties of the TBG [5]. In addition, we demonstrate the critical role of f-electron spin, valley, and orbital fluctuations in inducing superconducting instability within the Kondo phase

**References:**

[1] Z. Song, and B. A. Bernevig, Phy. Rev. Lett. 129, 047601 (2022).

[2] H. Hu, B. A. Bernevig, and A. M. Tsvelik, Phys. Rev. Lett. 131, 026502 (2023).

[3] G. Rai, et al., arXiv: 2309.08529 (2023).

[4] H. Hu, et al., Phys. Rev. Lett. 131, 166501 (2023).

[5] D. Călugăru, H. Hu, et al., arXiv:2402.14057 (2024).

**Combining transformer neural networks and quantum simulators: A hybrid approach to simulating quantum many-body systems**

Abstract

Owing to their great expressivity and versatility, neural networks have gained attention for simulating large two-dimensional quantum many-body systems. However, their expressivity comes with the cost of a challenging optimization due to the in general rugged and complicated loss landscape. In this talk, I will present a hybrid optimization schemes for neural quantum states that involves a data-driven pre-training with external (numerical or experimental) data and a second, energy-driven optimization stage. In contrast to previous works, we do not not employ data from the computational basis but also from other measurement configurations by training local expectation values such as spin-spin correlations evaluated in the rotated basis, giving access to the sign structure of the state. I will show results obtained with this method for the ground state search of the 2D transverse field Ising model and the 2D dipolar XY model on 6x6 and10x10 square lattices, with experimental data from a programmable Rydberg quantum simulator [Chen et al., Nature 616 (2023)], using a transformer wave function. In all cases, we find a great optimization speedup and significantly improved convergence when applying the hybrid training. I will discuss how this method can be applied to other quantum states, e.g. ground and excited states of fermionic systems such as the t-J model, pointing the way for a reliable and efficient optimization of neural quantum states competitive with state-of-the art methods.

##### Quantum control of interlayer excitons in atomically thin semiconductor heterostructures

Abstract

Two-dimensional materials and their heterostructures provide a highly tunable platform for many-body interactions and strongly correlated phenomena, including Mott insulators, generalized Wigner crystals and excitonic insulators. Of particular interest are atomically thin transition metal dichalcogenides (TMDs), such as MoS2, MoSe2 and WSe2. They strongly interact with light to form excitons – electrons and holes bound by Coulomb attraction – which remain stable up to room temperature. The reduced dimensionality together with the relatively large effective mass and low kinetic energy of the charge carriers yield strong interactions between the individual electrons and excitons in the system. In addition, new excitonic species can be formed when combining two or more TMD monolayers, where the electrons and holes are separated between the individual layers – so-called interlayer excitons (IXs). The ability to engineer and control the properties of the thin semiconductors by external means makes these systems a versatile platform for rich exciton and electron physics and unique opto-electronic applications.

Here, we investigate strongly correlated phenomena in two varieties of TMD bilayers – homobilayer MoS21-3 and heterobilayer MoSe2/WSe24. These host IXs with large out-of-plane electric dipoles. We study the quantum-confined Stark effect of the IXs in these systems, as well as their interaction with additional charges.In homobilayer MoS2, we observe an unusual IX interaction, suggesting the electronic many-body state develops an order parameter in the form of interlayer electron coherence. Under conditions when electron tunneling between the layers is negligible, we electron dope the sample and observe that the two excitons with opposing dipoles – which normally should not interact – hybridize in a way distinct from both conventional level crossing and anti-crossing. We show that these observations can be explained by stochastic coupling between the excitons, which increases with electron density and decreases with temperature.

*Illustration of*

**a**, bilayer MoS2 with transparent top and bottom graphene gates, and**b,**an ultrathin quantum-light emitting device consisting of a n-doped MoSe2 layer and a p-doped WSe2 layer, separated by a thin sheet of hexagonal boron nitride (h-BN). Both systems host interlayer excitons (IXs).In homobilayer MoS2, we observe an unusual IX interaction, suggesting the electronic many-body state develops an order parameter in the form of interlayer electron coherence. Under conditions when electron tunneling between the layers is negligible, we electron dope the sample and observe that the two excitons with opposing dipoles – which normally should not interact – hybridize in a way distinct from both conventional level crossing and anti-crossing. We show that these observations can be explained by stochastic coupling between the excitons, which increases with electron density and decreases with temperature.

In heterobilayer MoSe2/WSe2, we combine electro- and photo-luminescence experiments to study the nature of strongly driven non-equilibrium states. Applying a forward bias, we electrically inject electrons and holes that recombine as IXs (Figure b). We tune the relative electron-hole imbalance with electrostatic gates to study the formation of IXs interacting with an underlying Fermi sea. Further, modulating the out-of-plane dipole by adjusting the distance of the electron and holes and by an applied electric field, we demonstrate control of the IXs at the quantum level.

N. Leisgang acknowledges support from the Swiss National Science Foundation (SNSF) (Grant No. P500PT_206917).

**References**

[1] __N. Leisgang__ *et al*., Nat. Nanotechnol. 15, 901-907 (2020).

[2] L. Sponfeldner, __N. Leisgang__ *et al*., Phys. Rev. Lett. 129, 107401 (2022).

[3] X. Liu*, __N. Leisgang__*, P. E. Dolgirev* *et al.*, manuscript in preparation.

[4] A. M. Mier Valdivia, …, __N. Leisgang__ *et al.*, manuscript in preparation.

##### Single quantum coherent spins in hexagonal boron nitride at ambient conditions

Abstract

Colour centres in wide bandgap materials can provide spin-photon interfaces that act as the building blocks in quantum networks and quantum sensing applications. Despite rapid progress reported across several candidate systems, those possessing quantum coherent single spins at room temperature remain extremely rare [1]. Here, we show that hexagonal boron nitride hosts single emitters that combine room-temperature spin coherence and single-photon emission with scalable and compact hardware. Via optical and microwave spectroscopy at room temperature, we investigate the ground-state spin Hamiltonian of these individual emitters. We identify a spin-triplet electronic ground state with zero-field coherences that survive up to microseconds at ambient conditions, and unravel how the symmetry of the spin-Hamiltonian protects the electronic spin from decoherence in the near-zero-field regime [2]. Our results demonstrate the rich spin dynamics underpinning this novel solid-state qubit platform and further reveal the potential of van der Waals materials for quantum information and sensing, where their reduced dimensionality opens exciting routes to new nanoscale quantum devices and sensors.

**References**

[1] G. Wolfowicz, “Quantum guidelines for solid-state spin defects,” Nat. Rev. Mater. 6 (2021).

[2] H. L. Stern*, C. M. Gilardoni*, *et al*. “A quantum coherent spin in hexagonal boron nitride at ambient conditions,” Nat. Mater. (2024).

##### Alice, Bob and the quantum ice-cream

Abstract

In this talk, I will focus on two topics of quantum physics, whose salient aspects can be analyzed through the lens of entanglement. The first one concerns how to enable the teleportation of quantum states between distant parties and to what extent the entanglement of a many-body wave function transfers under imperfect quantum teleportation protocols. The second subject concerns the study of the symmetry breaking in a subsystem, which can be quantified once again by exploiting the theory of entanglement in many-body quantum systems. This leads to the definition of the entanglement asymmetry, which neatly detects some physical remarkable features out-of equilibrium, and it reveals an unexpected quantum Mpemba effect.

##### Non-Abelian topological order from wavefunction collapse on a trapped-ion quantum processor

Abstract

Non-Abelian topological order (TO) is a coveted state of matter that despite extensive efforts has remained elusive. I will show that adaptive quantum circuits – the combination of measurements with unitary gates whose choice can depend on previous measurement outcomes – can be leveraged to prepare long-range entangled quantum states such as non-Abelian topological phases with a circuit depth that is independent of system size. Using this, I will present the first unambiguous realization of non-Abelian TO and demonstrate control of its anyons. We create the ground state wave function of D4 TO of 27 qubits on Quantinuum’s H2 trapped-ion quantum processor and obtain fidelity per site exceeding98.4%. In particular, we are able to detect a non-trivial braiding where three non-Abelian anyons trace out the Borromean rings in spacetime, a signature unique to non-Abelian topological order.

This work is based on Nature 626 505-511 (2024)

##### Electrically defined quantum dots for neutral excitons

Abstract

Quantum dots (QDs) are semiconductor nanostructures that confine particle motion in all three spatial dimensions, yielding discrete energy levels reminiscent of artificial atoms. Since their advent, QDs confining excitons – bound electron–hole pairs – have been pivotal, serving as emitters of light in commercial displays to sources of single photons for quantum information processing. Due to the limitations of current fabrication techniques, a key requirement in these applications that has remained unmet, is the realization of bright emitters that are identical to each other and can be fabricated using scalable methods.

Here, I will describe how we overcome this hurdle and realize fully tunable gate-defined QDs for excitons in a monolayer transition metal dichalcogenide semiconductor. Through precise design of gate electrodes, we dynamically modulate the in-plane electric fields in our device, enabling the tuning of QD resonance frequencies via the dc Stark effect [1, 2]. Simultaneously, the exciton confinement length is modified, allowing a direct control over the oscillator strength and linewidth of the excitonic transition. Our structure is distinct from previous implementations, as it realizes quantum-confined bosonic modes with a nonlinear response arising solely from exciton–exciton interactions.

The ability to place an exciton in a gate-defined quantum box offers the prospect for realizing an array of bright and identical single photon sources, which are essential for applications in quantum communication and photonic quantum information processing. Another exciting future direction would be to interface these excitonic/photonic dots with their electronic counterparts in bilayer graphene [3], allowing for the realization of a quantum spin–photon interface in van der Waals materials. Lastly, such quantum emitters hold promise as a foundational element of a strongly interacting many-body photonic system [4].

**References**

[1] D. Thureja, et al. Electrically tunable quantum confinement of neutral excitons. *Nature* 606 (7913), 298-304 (2022).

[2] D. Thureja, et al. Electrically defined quantum dots for bosonic excitons. *arXiv preprint* arXiv:2402.19278 (2024).

[3] A. O. Denisov, et al. Ultra-long relaxation of a Kramers qubit formed in a bilayer graphene quantum dot. *arXiv preprint* arXiv:2403.08143 (2024).

[4] I. Carusotto & C. Ciuti. Quantum fluids of light. *Reviews of Modern Physics* 85 (1), 299, (2013).

##### Spin-Photon Entanglement

Abstract

Spin qubits represent a promising candidate for the development of quantum computers. Despite their potential, the implementation of scalable quantum systems is hindered by the short-range nature of spin-entangling gates, necessitating a coupler for long-range entanglement. Therefore, achieving coherent coupling between a spin qubit and a photon becomes highly desirable [1].

We realize an architecture that accomplishes this coupling using high-quality, magnetic-field resilient, high-impedance superconducting resonators combined with semiconducting nanowires [2,3]. By leveraging the intrinsic spin-orbit interaction present in these nanowires, we attain the strong coupling regime between a spin singlet-triplet qubit and a single photon [4]. This finding is supported by the spectroscopy of maximally entangled spin-photon states. The spin-photon interface allows us to pinpoint an optimal operating point that maximizes both spin coherence and dipole moment without compromise [5]. Our results are a crucial step toward scaling-up spin-based quantum processors through long-range quantum entanglement.

**References**

[1] Vandersypen, L.M.K., et al. npj Quantum Information 3.1 (2017).

[2] Ungerer, Jann H., et al. EPJ Quantum Technology 10.1 (2023).

[3] Ungerer, Jann. H., et al. Materials for Quantum Technology 3.3 (2023).

[4] Ungerer, Jann H., et al. Nature Communications 15.1 (2024).

[5] Ungerer, Jann H., et al. arXiv 2405.10796 (2024).

### Symposium Jury

**Prof. Dr. Michael Hartmann** | Friedrich-Alexander-Universität

**Prof. Dr. Robert König** | Technische Universität München

**Dr. Nadezhda Kukharchyk** | Walter-Meißner-Institut

**Dr. Farsane Tabataba-Vakili **| Ludwig-Maximilians-Universität München

**Dr. Johannes Zeiher** | Max Planck Institute of Quantum Optics

#### Schedule

16 September

Day 1

13:00–13:30 | **Welcome talk**

13:30–14:00 | **Elizaveta Andriyakhina, "Quantum Fluctuations and Collective Modes in Disordered 2D Superconductors"**

14:00–14:30 | **Serafim Babkin, "Proximity-induced gapless superconductivity in two-dimensional Rashba semiconductor in magnetic field" **

14:30–15:00 | **Haoyu Hu, "Heavy-fermion physics and superconductivity in twisted bilayer graphene" **

15:30–16:00 **Coffee Break**

16:00–16:30 | **Fabrizio Berritta, "Real-time Quantum Control of Qubits" **

16:30–17:00 | **Matthias Bock, "Single quantum coherent spins in hexagonal boron nitride at ambient conditions"**

17:00–17:30 | **Nadine Leisgang, "Quantum control of interlayer excitons in atomically thin semiconductor heterostructures" **

17:30–18:00 | **Carmem Maia Gilardoni, "Single quantum coherent spins in hexagonal boron nitride at ambient conditions"**

17 September

Day 2

09:00–09:30 | **Hannah Lange, "Combining transformer neural networks and quantum simulators: A hybrid approach to simulating quantum many-body systems" **

09:30–10:00 |** Sara Murciano, "Alice, Bob and the quantum ice-cream" **

10:00–10:30 | **Luisa Eck, "Topologically ordered phases of 2+1d fusion surface models"**

10:30–11:00 | **Coffee Break**

11:00–11:30 | **Deepankur Thureja, "Electrically defined quantum dots for neutral excitons"**

11:30–12:00 | **Nathanan Tantivasadakarn, "Non-Abelian topological order from wavefunction collapse on a trapped-ion quantum processor"**

12:00–12:30 |** Jann Hinnerk Ungerer, "Spin-Photon Entanglement"**

12:30–13:30 | **Lunch at MPQ**

13:30–15:30 | **Poster Session, Networking**

19:00–21:00 | **Closing Dinner for Finalists, Announcement of Prizes**

### Date & Venue

16-17 September 2024

Max Planck Institute of Quantum Optics, Garching, Munich

### Symposium Partners

Munich Center for Quantum Science and Technology (MCQST), International Max Planck Research School for Quantum Science and Technology (IMPRS-QST), Munich Quantum Valley (MQV), Women in Quantum Optics Postdoctoral Program (WiQO) of the Max Plank Institute of Quantum Optics, LMU Munich, TU Munich

### Contact

For further inquiries or additional information, contact us at quantum-talents-munich[at]mcqst.de