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.

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)

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.

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.

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.

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.

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)

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).