Titles and Abstracts

Invited 45’+5’

*1- Lorenzo Piroli (26-30)- Many-body entropies and entanglement from polynomially-many local measurements

Randomized measurements (RMs) provide a practical scheme to probe complex many-body quantum systems. While they are a very powerful tool to extract local information, global properties such as entropy or bipartite entanglement remain hard to probe, requiring a number of measurements or classical post-processing resources growing exponentially in the system size. In this work, we address the problem of estimating global entropies and mixed-state entanglement via partial-transposed (PT) moments, and show that efficient estimation strategies exist under the assumption that all the spatial correlation lengths are finite. Focusing on one-dimensional systems, we identify a set of approximate factorization conditions (AFCs) on the system density matrix which allow us to reconstruct entropies and PT moments from information on local subsystems. Combined with the RM toolbox, this yields a simple strategy for entropy and entanglement estimation which is provably accurate assuming that the state to be measured satisfies the AFCs, and which only requires polynomially-many measurements and post-processing operations. We prove that the AFCs hold for finite-depth quantum-circuit states and translation-invariant matrix-product density operators, and provide numerical evidence that they are satisfied in more general, physically-interesting cases, including thermal states of local Hamiltonians. We argue that our method could be practically useful to detect bipartite mixed-state entanglement for large numbers of qubits available in today's quantum platforms.

*2- Marin Bukov (26—2) Control phases and phase transitions in few-particle quantum systems: an analytical approach

I will present a mapping of quantum control problems to classical spin models that allows us to interpret correlations in the landscape minima as a proxy for phase transitions. Recent ongoing results allow us to obtain analytical expressions for the landscape which reproduce the control phase diagram in few-qubit control problems.

*3- Xhek Turkeshi (26-1)- Error-resilience Phase Transitions in Encoding-Decoding Quantum Circuits

Understanding how errors deteriorate the information encoded in a many-body quantum system is a fundamental problem with practical implications for quantum technologies. Here, we investigate a class of encoding-decoding random circuits subject to local coherent and incoherent errors. The existence of a phase transition separating an error-protecting phase at weak error strength from an error-vulnerable phase is analytically demonstrated. We derive exact expressions showing that this transition is accompanied by entanglement, localization and non-stabilizerness transitions. The emergence of multifractal features in the considered system is highlighted. 

*4- Hannes Pichler (26—30)  Quantum Computing with Globally driven Rydberg Atom Arrays

We discuss a new model for quantum computation with Rydberg atom arrays, which only relies on programmable positioning of atoms, global driving and the Rydberg blockade mechanism. Importantly this model eliminates the requirement of local addressing of individual atoms. Instead, in this model a quantum circuit is imprinted in the (static) trap positions of the atoms in a dual-species setup, and the algorithm is executed by an alternating sequence of global laser pulses driving the two species. We discuss all the ingredients for universal quantum computation in this setup, including initialization, execution of single and two-qubit gates, and readout, as well as the overhead in atom numbers with respect to standard quantum processor designs.  

5- Natalia Chepiga (29-1)- Resilient infinite randomness criticality for a disordered chain of interacting Majorana fermions

The quantum critical properties of interacting fermions in the presence of disorder are still not fully understood. While it is well known that for Dirac fermions, interactions are irrelevant to the non-interacting infinite randomness fixed point, the problem remains largely open in the case of Majorana fermions which further display a much richer disorder-free phase diagram. I will show how pushing the limits of DMRG simulations we carefully examine the ground-state of a Majorana chain with both disorder and interactions. Building on appropriate boundary conditions and key observables such as entanglement, energy gap, and correlations, we strikingly find that the non-interacting Majorana infinite randomness fixed point is very stable against finite interactions, in contrast with previous claims.

*6- Alessio Lerose (26-1)- Theory of robust quantum many-body scars in long-range interacting systems

Quantum many-body scars (QMBS) are exceptional energy eigenstates of quantum many-body systems associated with violations of thermalization for special non-equilibrium initial states. Their various systematic constructions require fine-tuning of local Hamiltonian parameters. In this work we demonstrate that the setting of \emph{long-range} interacting quantum spin systems generically hosts \emph{robust} QMBS. We analyze spectral properties upon raising the power-law decay exponent $\alpha$ of spin-spin interactions from the solvable permutationally-symmetric limit $\alpha=0$. First, we numerically establish that despite spectral signatures of chaos appear for infinitesimal $\alpha$, the towers of $\alpha=0$ energy eigenstates with large collective spin are smoothly deformed as $\alpha$ is increased, and exhibit characteristic QMBS features. To elucidate the nature and fate of these states in larger systems, we introduce an analytical approach based on mapping the spin Hamiltonian onto a relativistic quantum rotor non-linearly coupled to an extensive set of bosonic modes. We exactly solve for the eigenstates of this interacting impurity model, and show their self-consistent localization in large-spin sectors of the original Hamiltonian for $0<\alpha<d$. Our theory unveils the stability mechanism of such QMBS for arbitrary system size, and predicts instances of its breakdown e.g. near dynamical critical points or in presence of semiclassical chaos, which we verify numerically in long-range quantum Ising chains. As a byproduct, we find a predictive criterion for absence of heating under periodic driving for $0<\alpha<d$, beyond existing Floquet-prethermalization theorems. 

*7- Pieter Claeys (26-2) - Krylov complexity and Trotter transitions in unitary circuit dynamics 

We investigate many-body dynamics where the evolution is governed by unitary circuits through the lens of `Krylov complexity', a recently proposed measure of complexity and quantum chaos. We extend the formalism of Krylov complexity to unitary circuit dynamics and focus on Floquet circuits arising as the Trotter decomposition of Hamiltonian dynamics. For short Trotter steps the results from Hamiltonian dynamics are recovered, whereas a large Trotter step results in different universal behavior characterized by the existence of local maximally ergodic operators: operators with vanishing autocorrelation functions, as exemplified in dual-unitary circuits. These operators exhibit maximal complexity growth, act as a memoryless bath for the dynamics, and can be directly probed in current quantum computing setups. These two regimes are separated by a crossover in chaotic systems. Conversely, we find that free integrable systems exhibit a nonanalytic transition between these different regimes, where maximally ergodic operators appear at a critical Trotter step.

*8- Silvia Pappalardi (26-1)- From Designs to ETH via Free Probability

Unitary Designs have become a vital tool for investigating pseudorandomness since they approximate the statistics of the uniform Haar ensemble. Despite their central role in quantum information, their relation to quantum chaotic evolution and in particular to the Eigenstate Thermalization Hypothesis (ETH) are still largely debated issues. This work provides a bridge between the latter and k-designs through Free Probability theory. First, by introducing the more general notion of k-freeness, we show that it can be used as an alternative probe of designs. In turn, free probability theory comes with several tools, useful for instance for the calculation of mixed moments or for quantum channels. Our second result is the connection to quantum dynamics. Quantum ergodicity, and correspondingly ETH, apply to a restricted class of physical observables, as already discussed in the literature. In this spirit, we show that unitary evolution with generic Hamiltonians always leads to freeness at sufficiently long times, but only when the operators considered are restricted within the ETH class. Our results provide a direct link between unitary designs, quantum chaos and the Eigenstate Thermalization Hypothesis, and shed new light on the universality of late-time quantum dynamics.

9- Vladimir Gritsev (29—1)  Solvable models of driven-dissipative systems

*10- Anatoly Dimarsky (26-2) - Emergence of unitary symmetry in quantum chaotic systems

One of key features of quantum chaotic systems is the emergent universality of the coarse-grained quantities, giving rise to their statistical description. Perhaps the most famous example of such universality is the Random Matrix Theory description of the energy level statistics. It is natural to ask to what extent a similar picture would apply to matrix elements of simple observables, going beyond the framework of ETH. We propose that below certain observable-dependent scale collective statistical properties of matrix elements exhibit emergent unitary symmetry, and can be described by a single trace random matrix model. We introduce readily testable criteria and demonstrate the onset of unitary symmetry numerically (using numerical technique based on quantum typicality). We then proceed to discuss the relation between the scale marking the onset of unitary symmetry with Thouless energy, and the connection between emergent unitary symmetry and  late time thermalization dynamics. 

*11- David Luitz (26-29) -  The statistical properties of eigenstates in chaotic many-body quantum systems 

We consider the statistical properties of eigenstates of the time-evolution operator in chaotic many-body quantum systems. Our focus is on correlations between eigenstates that are specific to spatially extended systems and that characterise entanglement dynamics and operator spreading. In order to isolate these aspects of dynamics from those arising as a result of local conservation laws, we consider Floquet systems in which there are no conserved densities. The correlations associated with scrambling of quantum information lie outside the standard framework established by the eigenstate thermalisation hypothesis (ETH). In particular, ETH provides a statistical description of matrix elements of local operators between pairs of eigenstates, whereas the aspects of dynamics we are concerned with arise from correlations amongst sets of four or more eigenstates. We establish the simplest correlation function that captures these correlations and discuss features of its behaviour that are expected to be universal at long distances and low energies. We also propose a maximum-entropy Ansatz for the joint distribution of a small number n of eigenstates. In the case n=2 this Ansatz reproduces ETH. For n=4 it captures both the growth with time of entanglement between subsystems, as characterised by the purity of the time-evolution operator, and also operator spreading, as characterised by the behaviour of the out-of-time-order correlator. We test these ideas by comparing results from Monte Carlo sampling of our Ansatz with exact diagonalisation studies of Floquet quantum circuits.

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Contributed (25’+5’)

12- Laura Batini - Real-time dynamics of false vacuum decay

False vacuum decay is a well-defined initial value problem in (real) time, in which the system starts from a metastable state that eventually decays and thermalizes due to fluctuations. It can be formulated in non-equilibrium quantum field theory on a closed time path and studied using correlation functions. We simulate the dynamics of a relativistic scalar field by classical-statistical field theory on a lattice in the high-temperature regime. In general, we find that the decay rates depend on time. Furthermore, we show that the decay rates in real time are comparable to those obtained by the conventional Euclidean (bounce) approach in the presence of a time-dependent effective potential. Finally, we show how quantum corrections to the equations of motion of the one- and two-point correlation functions can lead to transitions that are not captured by the statistical-classical approximations.

13- Alessio Paviglianiti - Multipartite entanglement in measurement induced phase transitions of the quantum ising chain.

14- Rishabh Jha- Dynamics in Sachdev-Ye-Kitaev model

Most of the condensed matter is dominated with models with quasiparticles in the form of Fermi liquid theory. However physics becomes quite interesting where there is a lack of quasiparticles in so-called strange metals. We will introduce the physics of non-Fermi liquids in the form of a model without quasiparticles, namely the Sachdev-Ye-Kitaev (SYK) model. We will discuss its various dynamic and thermodynamic properties including charge transport in SYK chains. We will conclude by making a connection between these strange metals and their holographic dual to black holes using gauge-gravity duality that perhaps points towards some deeper yet unknown connections between seemingly different areas of physics. 

15- Saul Polatowski Cameo (MIT) -Complete Hilbert-Space Ergodicity in Quantum Dynamics of Generalized Fibonacci Drives.

Ergodicity of quantum dynamics is often defined through statistical properties of energy eigenstates, as exemplified by Berry’s conjecture in single-particle quantum chaos and the eigenstate thermalization hypothesis in many-body settings. Can quantum systems exhibit a stronger form of ergodicity, wherein any time-evolved state uniformly visits the entire Hilbert space over time? Such a phenomenon, called complete Hilbert-space ergodicity (CHSE) is more akin to the intuitive notion of ergodicity as an inherently dynamical concept. CHSE cannot hold for time-independent or even time-periodic Hamiltonian dynamics, owing to the existence of (quasi)energy eigenstates. However, there exists a family of aperiodic, yet deterministic drives with minimal symbolic complexity — generated by the Fibonacci word and its generalizations — for which CHSE can be proven to occur. These results provide a basis for understanding thermalization in general time-dependent quantum systems [arXiv:2306.11792].

16- Lorenzo Correale 

18- Giovanni Di Fresco