Thermalization of a many-body quantum system is an intriguing property, with deep connections to other important concepts in quantum information science, such as entanglement spread, quantum information scrambling, and operator growth, among others. This makes it relevant across multiple disciplines, including quantum statistical physics, quantum information, condensed matter physics, and quantum gravity.

In the first part of this talk, we will discuss a recently introduced concept of deep thermalization, which leverages quantum chaos as a resource to construct approximate higher-order quantum state designs through measurements, a framework a.k.a emergence of quantum state t-designs. Although ubiquitous, the effects of symmetries on this phenomenon remain outstanding. Our study unveils the intricate relationship between the symmetries and measurements in constructing the approximate quantum state designs. Relying on the translational symmetry, we derive a generic sufficient condition for the measurement basis needed to obtain the designs and illustrate the deep thermalization in quantum chaotic quantum systems with symmetries.

In the latter part of the talk, we shall discuss the generalization of the celebrated Eigenstate Thermalization Hypothesis (ETH) for non-hermitian quantum systems. We demonstrate the importance of the right choice of basis to formulate this hypothesis to obtain consistent thermalization aspects found in the evolution of generic chaotic non-Hermitian systems. Finally, we shall briefly discuss a generic theoretical framework, explaining disordered averaged chaotic closed evolution through an effective Lindblad equation.

[1] Quantum 7, 1022 (2023)
[2] Quantum 8, 1456 (2024)
[3] arXiv:2309.00049 (2023)

Hole spin qubits in silicon and germanium quantum dots are rising as leading candidates for large-scale quantum computers because of their pronounced spin-orbit inter- actions (SOIs) and remarkable tunability, which permits efficient and ultrafast all-electric qubit control without additional components.

In this talk, I will discuss various strategies for harnessing this tunability to enhance the performance of current hole spin qubits, with a focus on both silicon and germanium qubits.

One avenue of exploration involves exploiting the tunable nature of hole spin qubits to mitigate the impact of charge and hyperfine noise, which directly influences the qubit decoherence time. By identifying optimal operating conditions, referred to as sweet spots, where such noise is effectively eliminated, the performance of the qubits can be significantly improved.

Moreover, charge noise presents a significant obstacle for shuttling spins, a critical require- ment to establish long-range connectivity between distant qubits. Here, I will explore how SOIs can induce intricate spin dynamics that effectively filter out low-frequency noise, thereby improving the efficiency of spin shuttling processes.

Furthermore, the influence of SOIs extends to two-qubit gates, where exchange anisotropies, induced by these interactions, offer avenues for accelerating the execution of two-qubit gates without compromising fidelity. This implies that by leveraging the unique properties of SOIs, novel methods can be devised to expedite gate operations, paving the way towards large-scale spin-based quantum information processing.

Understanding the fundamental nature of gravity at the interface with quantum theory is a major open question in theoretical physics. Recently, the study of gravitating quantum systems, for instance a massive quantum system prepared in a quantum superposition of positions and sourcing a gravitational field, has attracted a lot of attention: experiments are working towards realising such a scenario in the laboratory, and measuring the gravitational field associated to a quantum source is expected to give some information about quantum aspects of gravity. However, there are still open questions concerning the precise conclusions that these experiments could draw on the nature of gravity, such as whether experiments in this regime will be able to test more than the Newtonian part of the gravitational field.

In my talk, I will present a new result, where a delocalised quantum source gives rise to effects that cannot be reproduced using the Newton potential nor as a limit of classical General Relativity. These effects can in principle be measured by performing an interference experiment, and are independent of graviton emission.

Identifying stronger quantum aspects of gravity than those reproducible with the Newton potential is crucial to prove the nonclassicality of the gravitational field and to plan a new generation of experiments testing quantum aspects of gravity in a broader sense than what proposed so far.

Quantum computers hold great promise for efficiently simulating Fermionic systems, benefiting fields like quantum chemistry and materials science. To achieve this, algorithms typically begin by choosing a Fermion-to-qubit mapping to encode the Fermionic problem in the qubits of a quantum computer. The mapping transforms a local problem in Fermionic space into a non-local one in the qubit space, resulting in deep circuits, particularly on current quantum computers with limited qubit connectivity.

In the recent works by Algorithmiq, we propose an algorithm for designing flexible fermion-to-qubit mappings using ternary trees. We explore the relationship between the structure of these trees and key properties of the resulting mapping, such as Pauli weight and mode occupation delocalization. We demonstrate how well-known mappings like Jordan-Wigner, Parity, Bravyi-Kitaev, and ternary-tree mappings fall into this formalism and introduce the Bonsai algorithm for generating mappings tailored to the limited hardware connectivity. When applied to Heavy-Hexagon layouts, the algorithm achieves favourable Pauli weight scaling of square root of the number of qubits. Building upon this, we present treespilation, which is a method for optimizing the mapping based on the Fermionic representation of the state we want to implement on the quantum computer and the desired transpilation scheme. We demonstrate its effectiveness by reducing the CNOT gate counts needed for simulating chemical ground states found with ADAPT-VQE, achieving significant reductions, up to 74%, on fully connected systems. We observe similar reductions on devices with limited qubit connectivity like IBM Eagle chips, with CNOT counts in certain instances surpassing those initially achieved on fully connected devices. Broadly speaking, these results show that the formulation of the problem -in this case a Fermionic problem- with the transpilation scheme in mind benefits the overall transpilation procedure.

We demonstrate how to incorporate a catalyst to enhance the performance of a heat engine. Specifically, we analyze efficiency in one of the simplest engines models, which operates in only two strokes and comprises of a pair of two-level systems, potentially assisted by a d-dimensional catalyst. When no catalysis is present, the efficiency of the machine is given by the Otto efficiency. Introducing the catalyst allows for constructing a protocol which overcomes this bound, while new efficiency can be expressed in a simple form as a generalization of Otto's formula. The catalyst also provides a bigger operational range of parameters in which the machine works as an engine.

Although an increase in engine efficiency is mostly accompanied by a decrease in work production (approaching zero as the system approaches Carnot efficiency), it can lead to a more favorable trade-off between work and efficiency. The provided example introduces new possibilities for enhancing performance of thermal machines through finite-dimensional ancillary systems.

[1] Phys. Rev. Lett. 132, 260403 (2024)
[2] arXiv:2402.10384 (2024)

Current quantum computers and simulators are almost exclusively built for binary information processing, yet the underlying hardware almost always natively supports multi-valued logic. I will discuss the opportunities and challenges such an approach opens up in a trapped ion platform and the extent to which it can help improve quantum information processing. This will be exemplified with recent experimental result for qudit-enhanced QIP, as well as native qudit quantum simulations.

We study bidirectional teleportation while explicitly taking into account an environment [1]. This environment initially causes pure dephasing decoherence of the Bell state which assists teleportation. We find that when teleportation is performed in one direction it is accompanied by a transfer of correlations into the post-teleportation state of qubit C, which results in decoherence of the state. In the other direction, if no new decoherence process occurs, we find that not only the state of the qubit but also its correlations with an environment are being teleported with unit Fidelity. These processes do not depend on the measurement outcome during teleportation and do not differentiate between classical and quantum correlations. If, on the other hand, the second teleportation step is preceded by decoherence of the Bell state then the situation is much more complicated. Teleportation and transfer of correlations occur simultaneously, yielding different teleported qubit-environment states for different measurement outcomes. These states can differ in the degree of coherence of the teleported qubit, but only for an entangling Bell-state-environment interaction in the first step of teleportation, can they have different amounts of qubit-environment entanglement. In the extreme case, one of the teleported qubit states can be entangled with the environment while the other is separable.

We find that the decoherence effects from the first step can be suppressed during the second quantum teleportation. This effect is probabilistic and works only for certain measurement outcomes in the teleportation procedures. The effect is purely quantum and most pronounced for qubit systems, where in 25% of instances the decoherence can be reversed completely [2].

[1] Phys. Rev. A 105, 012407 (2022)
[2] Quantum 7, 923 (2023)

In this talk we will discuss the phenomenon of Einstein, Podolsky, and Rosen (EPR) steering, and its relation to Bell nonclassicality. We will focus on the so-called non-signalling resources (those that could in principle be achieved in non-signalling theories) in both Bell and EPR experiments, in particular those which cannot be realised with a quantum setup (called post-quantum). Previous work shows how EPR scenarios allow for postquantum resources which, from the viewpoint of the associated Bell scenario, generate only correlations compatible with quantum theory.

In this talk we will see how one can activate the post-quantumness of such EPR resources by placing them in a larger Bell-like network, so that the observed correlations may violate a Bell inequality beyond what's possible in a quantum experiment. That is, we will show how to activate post-quantum steering so that it can now be witnessed as post-quantum correlations in a Bell scenario.

We discuss recent progress on entanglement catalysis, including the equivalence between catalytic and asymptotic transformations of quantum states and the impossibility to distill entanglement from states having positive partial transpose, even in the presence of a catalyst. A more general notion of catalysis is the concept of entanglement battery. In this framework, we show that a reversible manipulation of entangled states is possible. This establishes a second law of entanglement manipulation without relying on the generalized quantum Stein's lemma.

Many phenomena and fundamental predictions, ranging from Hawking radiation to the early evolution of the Universe rely on the interplay between quantum mechanics and gravity or more generally, quantum mechanics in curved spacetimes. However, our understanding is hindered by the lack of experiments that actually allow us to probe quantum mechanics in curved spacetime in a repeatable and accessible way.

In this talk we review recent results of quantum optics on rotating platforms that are forming the link between theoretical ideas about the quantum gravity interface and the current experimental realities. Such experiments can no longer be explained in a Newtonian picture of the world, but rather require the introduction of Einsteinian notions or relativity. We will discuss how ostensibly quantum phenomena can be controlled with low-frequency mechanical rotations using a coupling arising from the underlying spacetime metric. The experimental data conclusively shows that low-frequency mechanical rotations affect the bunching behaviour of photon pairs [1], and can transform photons from perfectly indistinguishable (bosonic behaviour), to perfectly distinguishable (fermionic behavior) [2,3]. Furthermore, we predict the generation of intraparticle entanglement with low frequency mechanical rotations [4], and of rotationally-induced quantum non-local entanglement, which can maximally violate the Bell-Clauser-Horne-Shimony-Holt inequality in an experimentally accessible regime [5].

[1] Phys. Rev. Lett. 123, 110401 (2019)
[2] Phys. Rev. A 101, 043837 (2020)
[3] Phys. Rev. Research 5, L022005 (2023)
[4] Phys. Rev. Lett. 129, 260401 (2022)
[5] arXiv:2407.14276 (2024)

In this presentation, I will explore the challenges and methodologies associated with proving the presence of spectral gaps in quantum many-body systems, with a focus on the 1D AKLT model. Spectral gaps are central in our understanding of physical properties, such as ground state structure and correlation laws. In addition, spectral gaps are of direct importance in quantum computing, as they indicate how efficient an adiabatic quantum computation can be with provable guarantees of success.

We introduce two innovative constructions based on semidefinite programming (SDP) aimed at local, frustration-free, and translation-invariant Hamiltonians. The first employs positive operator decompositions to obtain translation invariant operators, enhancing the accuracy of the gap's lower bound with increased operator support size. The second utilizes the moment matrix method for a tighter lower bound through sum-of-squares decompositions involving non-commuting variables represented as Pauli operators.

Furthermore, I will discuss the role of SU(2) symmetries in simplifying the problem via Schur-Weyl duality, leading to significant computational efficiency improvements. This approach not only advances our understanding of quantum systems but also serves as a precursor for practical applications, such as the adiabatic preparation of tensor network states, by providing a reliable method to certify spectral gaps.

I will review the results on "quantum learning", i.e., the art of storing quantum dynamics in states of quantum systems and the later retrieval of their action. I will describe the optimal solutions for approximate and probabilistic versions of this tasks, focused on the case of unitary gates. Further we will discuss the consequences for quantum programmability and noise robustness of the "retrieving machines".