New frontiers in out-of-equilibrium quantum many-body dynamics

We analyze the coherence dynamics of a central spin coupled to a spin chain with a time-dependent noisy magnetic field, focusing on how noise influences the system's decoherence. Our results show that decoherency due to the nonequilibrium critical dynamics of the environment is amplified in the presence of uncorrelated and correlated Gaussian noise. We demonstrate that decoherence factor consistently signals the critical points, and exhibits exponential scaling with the system size, the square of noise intensity, and the noise correlation time at the critical points. We find that strong coupling between the qubit and the environment allows partial revivals of coherence, which diminish with increasing noise intensity or decreasing noise correlation time. In contrast, weak coupling leads to monotonic enhanced decoherence. The numerical results illustrate that, the revivals decay and scale exponentially with noise intensity. Moreover, the revivals increase and indicate linear or power law scaling with noise correlation time depends on how the correlated noise is fast or slow.

We investigate multiple carrier generation via impact ionization in a photodriven Mott insulator[1,2]. Our study focuses on a model for photovoltaic energy conversion, consisting of one or several correlated layers connected to metallic leads under a finite bias, driven by a periodic electromagnetic field [1,2,3]. A kink in the photocurrent as a function of the driving frequency suggests the onset of impact ionisation. We present the characteristics of the photocurrent and power conversion, discussing impact ionisation, multilayer effects and phonon dissipation. Results are obtained using a Floquet Dynamical Mean Field Theory with an enhanced impurity solver that combines nonequilibrium Green's functions and Lindblad quantum master equations for open quantum systems [4,5]. [1] E. Manosuakis, Phys. Rev. B 82, 125109 (2010); P. Werner et al., Phys. Rev. B 90, 235102 (2014) [2] M. Sorantin et al., Phys. Rev. B 97, 115113 (2018); P. Gazzaneo et al. Phys. Rev. B 106, 195140 (2022); Phys. Rev. B 109, 235134 (2024) [3] F. Petocchi et al., Phys. Rev. B 100, 075147 (2019) [4] E. Arrigoni et al., Phys. Rev. Lett. 110, 086403 (2013); A. Dorda et al., Phys. Rev. B 89 165105 (2014); [5] D. Werner et al., Phys. Rev. B 107, 075119 (2023)

Rydberg simulators, superconducting qubit arrays and other quantum simulation platforms are increasingly able to simulate isolated quantum many-body dynamics, and explore uncharted territory for theory. For example, recent experiments study order parameter dynamics in quenches involving phase transitions, thereby placing the physics of quantum coarsening in the experimental realm. Here, we present a theory for this non-equilibrium dynamics.

For generic many-body Hamiltonians, eigenstates in the middle of the spectrum are typically highly entangled, featureless, and obey the eigenstate thermalization hypothesis, making the emergence of long-range order at finite energy density particularly striking. In this work, we leverage variational quantum circuits to generate states that exhibit long-range order while maintaining tight spectral support around the middle of the spectrum. Using an adaptive circuit-based approach, we stabilize both Z2 long-range order and Z2 × Z2 topological order, finding that circuit optimization naturally favors structures close to Clifford gates. Beyond their ordered nature, the generated states exhibit signatures of multipartite entanglement and other potentially useful properties for quantum metrology. Our results demonstrate how adaptive quantum circuits can be a powerful tool for engineering ordered phases in highly excited states, opening new perspectives on the interplay between long-range order, adaptive dynamics, and out-of-equilibrium states.

We explore many-body localization (MBL) and the many-body skin effect in non-Hermitian Floquet systems, an emerging direction in condensed matter physics. Our work reveals frequency-tuned quantum phase transitions that are unique to non-Hermitian settings, with no analog in Hermitian systems. These transitions arise from the interplay between quasiperiodic disorder, nonreciprocal hopping, and periodic driving, leading to rich localization and spectral phenomena. Our findings advance the understanding of nonequilibrium phases in interacting, driven quantum matter and offer a new platform to probe MBL beyond conventional Hermitian frameworks.

We study the postselection problem in a solvable model of bosons hopping on a lattice subjected to continuous local measurements of quadrature observables. We find that the postselection overhead for local observables can be reduced by postprocessing the entire measurement record into a few numbers per trajectory and then postselecting based only on these numbers. We then provide a step-by-step protocol designed to recover conditional connected two-point functions, which display an exponentially decaying profile that is not observable in the unconditional, trajectory averaged, state. We test the protocol numerically in a way that mimics real experiments, showing that various conditional observables can be recovered using a single ensemble of quantum trajectories. We then illustrate how to design this post-processing stage using only information present in the unconditional dynamics. These models can be implemented in cavity-QED and circuit-QED

We study the ensemble of states generated by performing projective measurements on the output of a random matchgate (or free-fermionic) quantum circuit. We rigorously show that this `projected ensemble' exhibits deep thermalization: For large system sizes, it converges towards a universal ensemble that is uniform over the manifold of Gaussian fermionic states. As well as proving moment-wise convergence of these ensembles, we demonstrate that the full distribution of any physical observable in the projected ensemble is close to its universal form in Wasserstein-1 distance, which we argue is an appropriate and efficiently computable measure of convergence when studying deep thermalization. Using this metric, we also numerically find that local matchgate circuits deeply thermalize after a timescale $t\sim L^2$ set by the diffusive spreading of quantum information. Our work opens up new avenues to experimentally accessible protocols to probe the emergence of quantum statistical mechanics and benchmark quantum simulators.

We devise tractable models of unitary quantum many-body dynamics on tree graphs, as a first step towards a deeper understanding of dynamics in non-Euclidean spaces. To this end, we first demonstrate how to construct strictly local quantum circuits that preserve the symmetries of trees, such that their dynamical light cones grow isotropically. We show that, for trees with coordination number z, such circuits can be built from z-site gates. We then introduce a family of gates for which the dynamics is exactly solvable; these satisfy a set of constraints that we term 'tree-unitarity'. Notably, tree-unitarity reduces to the previously-established notion of dual-unitarity for z=2, when the tree reduces to a line. Among the unexpected features of tree-unitarity is a trade-off between 'maximum velocity' dynamics of out-of-time-order correlators and the existence of non-vanishing correlation functions in multiple directions, a tension absent in one-dimensional dual-unitary models and their Euclidean generalizations. We give various examples of tree-unitary gates, discuss dynamical correlations, out-of-time-order correlators, and entanglement growth, and show that the kicked Ising model on a tree is a physically-motivated example of maximum-velocity tree-unitary dynamics.

Non-Hermitian many-body localization (NH MBL) has emerged as a possible scenario for stable localization in open systems, as suggested by spectral indicators identifying a putative transition for finite system sizes. In this presentation, I will present a shift of the focus to dynamical probes, specifically the steady-state spin current, to investigate transport properties in a disordered, non-Hermitian XXZ spin chain. Through exact diagonalization for small systems and tensor-network methods for larger chains, we demonstrate that the steady-state current remains finite and decays exponentially with disorder strength, showing no evidence of a transition up to disorder values far beyond the previously claimed critical point. Our results reveal a stark discrepancy between spectral indicators, which suggest localization, and transport behavior, which indicates delocalization. This highlights the importance of dynamical observables in characterizing NH MBL and suggests that traditional spectral measures may not fully capture the physics of non-Hermitian systems. Additionally, we observe a non-commutativity of limits in system size and time, further complicating the interpretation of finite-size studies. These findings challenge the existence of NH MBL in the studied model and underscore the need for alternative approaches to understand localization in non-Hermitian settings.

Qudit-based quantum computing platforms offer unique advantages over conventional qubit-based systems. In particular, the extended on-site Hilbert space in a qudit circuit can protect quantum information even in the presence of frequent disentangling local measurements or errors. In this talk, we present results from the non-unitary dynamics of a novel monitored bosonic quantum circuit. We demonstrate observation of the measurement-induced entanglement phase transition (MIPT) with bosons under various choices of unitary dynamics and local measurement protocols, in the presence of global number conservation. To realize such hybrid dynamics experimentally, we propose a platform based on multimode circuit QED systems. These systems combine ultra-low-loss multimode microwave cavities with superconducting circuits, enabling the realization of bosonic quantum circuits with interspersed local measurements (e.g., parity or photon-number measurements). This platform provides a promising route for both quantum information processing and quantum simulation with bosonic degrees of freedom.

Spontaneous symmetry breaking (SSB) is the cornerstone of our understanding of quantum phases of matter. Recent works have generalized this concept to the domain of mixed states in open quantum systems, where symmetries can be realized in two distinct ways dubbed strong and weak. Novel intrinsically mixed phases of quantum matter can then be defined by the spontaneous breaking of strong symmetry down to weak symmetry. However, proposed order parameters for strong-to-weak SSB (based on mixed-state fidelities or purities) seem to require exponentially many copies of the state, raising the question: is it possible to efficiently detect strong-to-weak SSB in general? Here we answer this question negatively in the paradigmatic cases of $\mathbb{Z}_2$ and $U(1)$ symmetries. We construct ensembles of pseudorandom mixed states that do not break the strong symmetry, yet are computationally indistinguishable from states that do. This rules out the existence of efficient state-agnostic protocols to detect strong-to-weak SSB.

Thermalization is deeply connected to the notion of ergodicity in Hilbert space, implying the equipartition of the wave function over the available many-body Fock states. Under unitary time evolution, an initially structured state spreads in Fock space, approaching a Haar-random state, thereby revealing a deep connection between many-body quantum systems and random matrix theory. In the first part of this talk, I will discuss the dynamics of the self-dual kicked Ising model, a minimal model of many-body quantum chaos that is unitary in both time and space. I will focus on its evolution in Fock space, showing how the probability distribution of the initial state approaches that of a random state, characterized by the Porter-Thomas distribution. In the second part, I will explore general relationships between entanglement and the spread of the wave function in Fock space. I will demonstrate that entanglement entropies can still exhibit fully ergodic behavior, even when the wave function occupies only a vanishing fraction of the full Hilbert space in the thermodynamic limit.

Kinetic constraints imposed by the Rydberg blockade are known to lead to quantum many-body scarring (QMBS), meaning that persistent oscillations can be witnessed after quenches from a few specific states while all other initial conditions thermalize rapidly. In this work, we show that non-ergodic phenomena in these systems are not limited to periodic trajectory, but also take the form of soliton-like excitations travelling through the entire system in a chiral manner. Crucially, we find that these stable local excitations are not built on top of the ground state, but on top of scarred initial states at infinite temperature. We characterise these novel solitonic scars and show that they can also carry energy.

Reference: https://arxiv.org/abs/2411.14359 The notion of ergodicity is one of the fundamental concepts underpinning our understanding of thermalisation in isolated systems since the first developments in classical statistical mechanics. Recently, a similar notion has been introduced for quantum systems, termed complete Hilbert space ergodicity (CHSE), in which the evolving quantum state explores all of the available Hilbert space. This contrasts with the eigenstate thermalisation hypothesis (ETH), in which thermalisation is formulated via the properties of matrix elements of local operators in the energy eigenbasis. In this work we explore how ETH-violation mechanisms, including quantum many-body scars and Hilbert space fragmentation can modify CHSE. We find that the presence of these mechanisms leads to CHSE in decoupled subspaces, a phenomenon we call Hilbert Subspace Ergodicity, and which represents a protocol for constructing t-designs in subspaces.

We study prethermal time-crystalline order in periodically driven quantum Ising models on disorder-free decorated lattices. Using a tensor network ansatz for the state which reflects the geometry of a unit cell of the lattice, we show through finite entanglement scaling that the system has an exponentially long-lived subharmonic response in the thermodynamic limit, which decays nonperturbatively in deviations from a perfect periodic drive. The resulting prethermal discrete time crystal is not only stable to imperfections in the transverse field, but also exhibits a bipartite rigidity to generic perturbations in the longitudinal field. We call this state a bipartite discrete time crystal and reveal a rich prethermal phase diagram, including multiple regions of bipartite time-crystalline order, uniform time-crystalline order, and thermalization, with boundaries depending delicately on the topology of the decorated lattice. Our results thus uncover a variety of time crystals which may be realized on current digital quantum processors and analog quantum simulators. [Phys. Rev. B 111, L100304 (2025)]

Abstract: Fluctuation dynamics of an observable measured in experiments offer an essential signal to understand nonequilibrium systems, along with dynamics of the mean. While universal speed limits for the mean value have intensively been studied recently [1, 2, 3], constraints for the speed of the fluctuation have been elusive. In this talk, we show a theory concerning rigorous bounds to the rate of fluctuation growth [4]. We discover a principle that the speed of the fluctuation of an observable is upper bounded by the fluctuation of an appropriate observable describing velocity; this also indicates a tradeoff relation between the changes for the mean and fluctuation. We demonstrate the advantages of our inequalities for, e.g., processes with non-negligible dispersion of observables, quantum work extraction, and the entanglement growth in noninteracting fermionic systems. Our results open an avenue toward a quantitative theory of fluctuation dynamics in various non-equilibrium systems, including quantum many-body systems and nonlinear population dynamics. [1] L. P. García-Pintos, S. B. Nicholson, J. R. Green, A. del Campo, and A. V. Gorshkov, Phys. Rev. X 12, 011038 (2022). [2] R. Hamazaki, PRX Quantum 3, 020319 (2022). [3] B. Mohan and A. K. Pati, Phys. Rev. A 106, 042436 (2022). [4] R. Hamazaki, Communications Physics 7, 361 (2024).

We investigate critical transport and the dynamical exponent through the spreading of an initially localized particle in quadratic Hamiltonians with short-range hopping in lattice dimension $d_l$. We consider critical dynamics that emerges when the Thouless time, i.e., the saturation time of the mean-squared displacement, approaches the typical Heisenberg time. We establish a relation, $z=d_l/d_s$, linking the critical dynamical exponent $z$ to $d_l$ and to the spectral fractal dimension $d_s$. This result has notable implications: it says that superdiffusive transport in $d_l\geq 2$ and diffusive transport in $d_l\geq 3$ cannot be critical in the sense defined above. Our findings clarify previous results on disordered and quasiperiodic models and, through Fibonacci potential models in two and three dimensions, provide non-trivial examples of critical dynamics in systems with $d_l\neq1$ and $d_s\neq1$.

We present a general framework to implement massive Nambu–Goldstone quasi-particles in driven many-body systems. The underlying mechanism leverages an explicit Lie group structure imprinted into an effective Hamiltonian that governs the dynamics of slow degrees of freedom; the result- ing emergent continuous symmetry is weakly explicitly broken, giving rise to a massive Nambu- Goldstone mode, with a spectral mass gap scaling linearly with the drive period. We discuss explicit and experimentally implementable realizations, such as Heisenberg-like spin models that support gapped spin-wave excitations. We provide a protocol to certify the existence of the massive Nambu- Goldstone mode from the dynamics of specific observables, and analyse the dispersion spectrum and their lifetime in the presence of weak explicit symmetry breaking.

We study the ensemble of Kraus operators on a small subsystem in quantum many-body chaotic dynamics, generated by projective measurements on its bath. These Kraus operators effectively unravel the quantum channel acting on the subsystem. We show that, in the strong chaotic regime, the Kraus operators are distributed according to the complex Ginibre ensemble, while when locality is relevant, an additional log-normal broadening is present in the Kraus operator distribution. These findings provide a dynamical mechanism for “deep thermalization,” a form of equilibration that goes beyond the thermalization of local observables. We further explore quantum-information-theoretic consequences: the subsystem’s reduced dynamics reveal asymptotically minimal information to the bath and form approximate unitary designs, suggesting recoverability of information. Our results bridge emergent universality in many-body dynamics with perspectives on quantum error correction.

Cavity-quantum-materials have emerged as a platform to study non-thermal many-body physics with applications to the control of collective electron behavior. In an electronic system coupled to cavity photons, the superconducting (SC) gap has been predicted previously to be enhanced, due to a ‘Eliashberg effect’ taking place due to electromagnetic fluctuations as instead of a coherent laser source [1,2]. We extend this idea for the case of charge-density-wave (CDW) order and systematically derive a generalized gap equation for the non-thermal situation using field theoretical methods. This allows us to compare the modified gap equations for superconductors and charge-density-waves: we find that while the two equations are exactly equivalent only in thermal equilibrium, they assume different forms in non-thermal settings. We found that the CDW gap is relatively less enhanced than the SC gap. We also observe a ‘re-entrance’ behavior of the gap that makes the transition first order instead of a continuous one. Refs. 1. G. M. Eliashberg, JETP Lett. 11, 114 (1970). 2. J. B. Curtis et. al., PRL 122, 167002 (2019.

Generic non-equilibrium many-body systems display a linear growth of bipartite entanglement entropy in time followed by a volume law saturation. We present a new class of models that display a linear growth followed by bending down of the entanglement, instead of saturation, all the way down to zero. This entanglement dynamics is already known in the field of black hole physics as the Page curve where the peak value is obtained at what is known as the Page time. The two phases of growth in our non-equlibrium condensed matter system, namely the linear growth and the bending down, is shown to be separated by a non-analyticity in the min-entropy before the Page time, thereby leading to two different quantum phases of matter. This can be shown in the thermodynamic limit for a free spinless fermionic chain where the entanglement Hamiltonian undergoes a quantum phase transition at the point of non-analyticity. We further show the persistence of the behaviors, namely the Page curve as well as the non-analyticity of the min-entropy before the Page time, even when we switch on the interactions in the fermionic chain.

The Loschmidt echo - the probability of a quantum many-body system to return to its initial state following a dynamical evolution - generally contains key information about a quantum system. However, it is typically exponentially small in system size, posing an outstanding challenge for experiments. In this talk, I will present our recent results using a quantum gas microscope to measure the subsystem Loschmidt echo — a quasi-local observable that captures key features of the Loschmidt echo.

Experimentally relevant systems in one dimension can often be described as a slightly perturbed integrable models. For instance, interacting bosonic gases are typically close to the Lieb-Liniger model. In my contribution I would like to focus on dynamics of nearly-integrable systems and argue that it can be understood through generalisations of the basic frameworks of kinetic theory. Such analogy appears due to the quasiparticle picture behind integrable dynamics. This picture becomes enriched due to weak integrability-breaking, which provides a mechanism for non-trivial many-particle scatterings between quasiparticles. Even though the system is strongly correlated, this renders the dynamics similar to evolution of weakly coupled gas, a standard subject of kinetic theory. Firstly, I will shortly discuss the generalisation of Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy for correlation functions, which can be used to derive Boltzmann scattering integral for nearly integrable systems, crucial for understanding the timescales and process of thermalisation. Secondly, I would like to address the question of hydrodynamics of such systems. Employing Chapman-Enskog formalism and nonlinear fluctuating hydrodynamics I will show that one can distinguish three hydrodynamic regimes: generalised hydrodynamics, Navier-Stokes regime and Kardar-Parisi-Zhang superdiffusion known to occur in generic 1d non-integrable fluids with momentum conservation. Joint works with Miłosz Panfil, Leonardo Biagetti and Jacopo de Nardis.

Introducing a class of SU(2) invariant quantum unitary circuits generating chiral transport, we examine the role of broken space-reflection and time-reversal symmetries on spin-transport properties. Upon adjusting parameters of local unitary gates, the dynamics can be either chaotic or integrable. The latter corresponds to a generalization of the space-time discretized (Trotterized) higher-spin quantum Heisenberg chain. We demonstrate that breaking of space-reflection symmetry results in a drift in the dynamical spin susceptibility. Remarkably, we find a universal drift velocity given by a simple formula, which, at zero average magnetization, depends only on the values of SU(2) Casimir invariants associated with local spins. In the integrable case, the drift velocity formula is confirmed analytically based on the exact solution of thermodynamic Bethe ansatz equations.

Preparation of thermal and ground states of many-body systems is a central challenge for quantum processors, needed e.g. as the starting point for many quantum physics experiments. In recent works, we provided a simple and efficient algorithm for many-body state preparation, combining engineered bath resetting with modulated system-bath coupling to drive toward the target distribution. We demonstrate its effectiveness for ground states of 1D spin chain and ladder systems, and thermal states of the 2D quantum Ising model. I will also present experimental results on the Google quantum processor, where a variant of the algorithm was used to prepare low-energy states of quantum Ising models — highlighting a viable route to efficient simulation of quantum-correlated states on near-term hardware.

We investigate how engineered disorder influences the collective dynamics of diamond vacancy centers and semiconductor quantum dots. Focusing on parameter regimes of the central spin model that are accessible in current experiments, we explore the feasibility of controlling and observing transitions associated with localized and time-crystalline phases.

The spectral analysis has played a crucial role in analyzing behaviors of quantum systems described by time-independent generators. Examples of such systems include isolated quantum systems where the spectral gaps of Hamiltonians are related to entanglement scalings of ground states and Markovian open quantum systems where the Liouvillian gaps give asymptotic decay rates towards stationary states. Recently, monitored quantum dynamics with temporal randomness have also attracted huge attention. For example, intriguing phenomena such as measurement-induced entanglement transitions [1] and purification transitions [2] have been explored. Naively, it seems difficult to apply the conventional spectral analysis to such monitored systems since there is no static generator due to quantum measurement. In this study, we apply the Lyapunov spectral analysis, originally developed to analyze nonlinear chaotic dynamics, to quantum dynamics exposed to measurements, where we regard the random nonunitary dynamics as an imaginary-time evolution generated through an effective Hamiltonian. In many-body interacting spin systems, we find that the Lyapunov spectrum typically becomes independent of measurement outcomes and there is a transition from the gapless phase to the gapped phase [3]. Interestingly, the spectral transition leads to the entanglement transition and purification transition. We also apply spectral analysis to non-interacting bosonic systems, where the sampling complexity of bosons is quite important since it is related to quantum supremacy [4]. We find that asymptotic decay of bosonic modes governed by the spectral gap and the spectral transition in parity-time symmetric systems have huge effect on the sampling complexity [5,6]. In my presentation, I talk about one or both of these topics. [1] B. Skinner, J. Ruhman, and A. Nahum, Phys. Rev. X 9, 031009 (2019). [2] M. J. Gullans and D. A. Huse, Phys. Rev. X 10, 041020 (2020). [3] K. Mochizuki and R. Hamazaki, Physical Review Letters 134, 010410 (2025). [4] S. Aaronson and A. Arkhipov, Theory of Computing 9, 143 (2013). [5] K. Mochizuki and R. Hamazaki, Physical Review Research 5, 013177 (2023). [6] K. Mochizuki and R. Hamazaki, Physical Review Research 6, 013004 (2024).

Generating highly entangled states is a central goal of quantum simulation. In ultracold atom platforms based on optical lattices, the starting point is typically to first prepare a Bose-Einstein condensate (BEC) in a harmonic trap and then load it adiabatically in the lattice. This constitutes a significant experimental challenge, as it exposes the BEC to decoherence, particle loss, and heating originating from the ubiquitous presence of environmental channels, impairing the subsequent state preparation steps. In this talk, based on [1], I argue that the difficulties associated with such a two-step procedure can be significantly mitigated by efficiently preparing a BEC directly on a lattice. This can be achieved by immersing the lattice in a superfluid that acts as a cooling medium. Furthermore, I will show that by applying a periodic modulation to the optical lattice potential (known as lattice shaking), which dynamically alters the tunneling rates between sites, one can tune the momentum of the target BEC. The effectiveness of this non-equilibrium approach is demonstrated via analytic calculations based on Bogoliubov theory. These indicate that the dissipation strength (i.e. the coupling between the lattice atoms and the superfluid) effectively decreases the repulsion between the bosons, enabling the preparation of high-fidelity BECs even in regimes of strong interactions and finite temperatures. The fraction of non-condensed atoms, as well as the decay of two-point correlation functions, are quadratically suppressed with the dissipation strength, indicating the onset of off-diagonal long-range order. Finding the simplest and fastest-converging initializations is crucial to making this protocol experimentally viable. This can be achieved via the Mpemba effect, an anomalous equilibration phenomenon that originally referred to hot systems cooling down faster than warm ones. In the context of the dissipative preparation of a BEC, we find that the Mpemba effect manifests in the dynamical restoration of a discrete symmetry. The BEC is invariant under reflections about the center of the lattice. Thus, for states that initially break this inversion symmetry, the symmetry needs to be restored by the dissipative dynamics. It can be analytically shown that the symmetry restoration process is slow, and consequently, initial states that are symmetric under reflections about the center of the lattice equilibrate exponentially faster than random states. Optimized states include simple product states such as, in one dimension, the Mott state 1−1...1 and the wedding cake state 1−2−3···−3−2−1 that can easily be realized. Our theoretical predictions are confirmed by matrix product state (MPS) simulations of the dissipative dynamics, quantitatively assessing the speedups yielded by our protocol, as well as the fidelities of the prepared BEC. This protocol significantly increases the efficiency of BEC preparation by drastically reducing coherence losses. Moreover, the symmetry-based approach helps identify fast-converging states without having to perform the prohibitively costly task of diagonalizing the generator of the dynamics. This allows us to explore the Mpemba effect, for the first time, in a many-body open quantum system and unlocks its potential for boosting the preparation of highly entangled quantum states. [1] P. Westhoff, S. Paeckel, and M. Moroder, (2025), arXiv:2504.05549 [cond-mat.quant-gas].

Kinetically constrained models were originally introduced to capture slow relaxation in glassy systems, where dynamics are hindered by local constraints instead of energy barriers. Their quantum counterparts have recently drawn attention for exhibiting highly degenerate eigenstates at zero energy -- known as zero modes -- stemming from chiral symmetry. Yet, the structure and implications of these zero modes remain poorly understood. In this work, we focus on the properties of the zero mode subspace in quantum kinetically constrained models with a $U(1)$ particle-conservation symmetry. We use the $U(1)$ East, which lacks inversion symmetry, and the inversion-symmetric $U(1)$ East-West models to illustrate our two main results. First, we observe that the simultaneous presence of constraints and chiral symmetry generally leads to a parametric increase in the number of zero modes due to the fragmentation of the many-body Hilbert space into disconnected sectors. Second, we generalize the concept of compact localized states from single particle physics and introduce the notion of collective bound states. We formulate sufficient criteria for their existence, arguing that the degenerate zero mode subspace plays a central role, and demonstrate bound states in both example models. Our results motivate a systematic study of bound states and their relation to ergodicity breaking, transport, and other properties of quantum kinetically constrained models.

We introduce a synthetic Mach-Zehnder interferometer for digitized quantum computing devices to probe fractional exchange statistics of anyonic excitations that appear in quantum spin liquids. Employing an IonQ quantum computer, we apply this scheme to the toric ladder, a quasi-one-dimensional reduction of the toric code. We observe interference patterns resulting from the movement of `electric' excitations in the presence and absence of `magnetic' ones. Using this framework, we propose a method to define a many-body quantum coherence length scale, which effectively mirrors the problem of a quantum particle on a ring, with or without flux through it. We propose using the maximum length of the ring for which the presence or absence of flux can be clearly discerned, as a simple measure of the many-body quantum coherence grade (Q-grade) in a given quantum hardware. We demonstrate how this approach can be implemented on gate-based quantum platforms to estimate and compare the quantum coherence of current devices, such as those from Google, IBM, IonQ, IQM, and Quantinuum that we considered here. This work aims to contribute to the creation of a live Web interface where the latest developments and advancements can be demonstrated, and progress in quantum coherence resources tracked over time. Establishing such a standardized quantum test would enable monitoring the growth of quantum coherence in gate-based quantum platforms, in a spirit similar to Moore's law.

Dual-unitary circuits and their generalizations have recently emerged as exactly solvable models of non-integrable quantum dynamics that enable insight into questions of thermalization, information scrambling, and quantum chaos. We present a general framework for constructing such models using biunitary connections. We show that a network of biunitary connections on the Kagome lattice naturally defines a multi-unitary circuit, where three ‘arrows of time’ directly reflect the lattice symmetry. We also discuss the entanglement dynamics of generalized dual-unitary circuits, showing that they exhibit submaximal entanglement growth and thus display a more generic phenomenology than dual-unitary circuits.

The time evolution of an initially unentangled system under the von Neumann equation generally leads to rapid entanglement growth. This poses challenges for numerical tractability. The Information Lattice framework addresses this by systematically discarding accumulated non-local information (i.e., entanglement) to maintain computational feasibility. Within the local-information time evolution (LITE) approach, we propose Renyi-2 entropy as a measure of information, eliminating the need for matrix decomposition. When combined with additional approximations, this approach significantly enhances the efficiency and scalability of simulations in terms of both system size and duration of time evolution. We demonstrate the accuracy of this method by computing high-quality diffusion coefficients and local observables for a large non-integrable system.

We investigate the robustness of the many-body localized (MBL) phase to the quantum-avalanche instability by studying the dynamics of a localized spin chain coupled to a T = ∞ thermal bath through its leftmost site. By analyzing local magnetizations we estimate the size of the thermalized sector of the chain and find that it increases logarithmically slowly in time. This logarithmically slow propagation of the thermalization front allows us to lower-bound the slowest thermalization time, and find a broad parameter range where it scales fast enough with the system size that MBL is robust against thermalization induced by avalanches. The further finding that the imbalance—a global quantity measuring localization—thermalizes over a timescale that is exponential both in disorder strength and system size is in agreement with these results.

In quantum systems, interactions with the environment usually cause entanglement to decay quickly. We find that the presence of strong non-Abelian conserved quantities can lead to highly entangled stationary states even for unital quantum channels. We derive exact expressions for the bipartite logarithmic negativity, Rényi negativities, and operator space entanglement for stationary states restricted to one symmetric subspace, with focus on the trivial subspace. We prove that these apply to open quantum evolutions whose commutants, characterizing all strongly conserved quantities, correspond to either the universal enveloping algebra of a Lie algebra or to the Read-Saleur commutants. The latter provides an example of quantum fragmentation, whose dimension is exponentially large in system size. We find a general upper bound for all these quantities given by the logarithm of the dimension of the commutant on the smaller bipartition of the chain. As Abelian examples, we show that strong U(1) symmetries and classical fragmentation lead to separable stationary states in any symmetric subspace. In contrast, for non-Abelian SU(N) symmetries, both logarithmic and Rényi negativities scale logarithmically with system size. Finally, we prove that while Rényi negativities with n>2 scale logarithmically with system size, the logarithmic negativity (as well as generalized Rényi negativities with n<2) exhibits a volume law scaling for the Read-Saleur commutants. Our derivations rely on the commutant possessing a Hopf algebra structure in the limit of infinitely large systems, and hence also apply to finite groups and quantum groups. Our results provide an exact calculation of various mixed-state measures, which are usually hard to obtain and rather scarce when dealing with quantum many-body states.

Sharma and Bhosale [\href{https://journals.aps.org/prb/abstract/10.1103/PhysRevB.109.014412}{Phys. Rev. B \textbf{109}, 014412 (2024)}; \href{https://journals.aps.org/prb/abstract/10.1103/PhysRevB.110.064313}{Phys. Rev. B \textbf{110}, 064313,(2024)}] recently introduced an $N$-spin Floquet model with infinite-range Ising interactions. There, we have shown that the model exhibits the signatures of quantum integrability for specific parameter values $J=1,1/2$ and $\tau=\pi/4$. We have found analytically the eigensystem and the time evolution of the unitary operator for finite values of $N$ up to $12$ qubits. We have calculated the reduced density matrix, its eigensystem, time-evolved linear entropy, and the time-evolved concurrence for the initial states $\ket{0,0}$ and $\ket{\pi/2,-\pi/2}$. For the general case $N>12$, we have provided sufficient numerical evidences for the signatures of quantum integrability, such as the degenerate spectrum, the exact periodic nature of entanglement dynamics, and the time-evolved unitary operator. In this paper, we have extended these calculations to arbitrary initial state $\ket{\theta_0,\phi_0}$, such that $\theta_0 \in [0,\pi]$ and $\phi_0 \in [-\pi,\pi]$. Along with that, we have analytically calculated the expression for the average linear entropy for arbitrary initial states. We observed that the average linear entropy exhibits a qualitatively similar structure for $J=1$, which depends on the parity of $N$. We numerically find that the average value of time-evolved concurrence for arbitrary initial states decreases with $N$, implying the multipartite nature of entanglement. We numerically show that the values $\langle S\rangle/S_{Max} \rightarrow 1$ for Ising strength ($J\neq1,1/2$), while for $J=1$ and $1/2$, it deviates from $1$ for arbitrary initial states even though the thermodynamic limit does not exist in our model. This deviation is shown to be a signature of integrability in earlier studies where the thermodynamic limit exist. Our results could be experimentally verified in various setups like NMR, superconducting qubits, and laser-cooled atoms. However for higher number of qubits, one can use ion trap.

Classical low-density parity-check (cLDPC) codes defined on expander graphs are a fundamental ingredient in the construction of good quantum LDPC codes, a recent milestone in quantum error correction. They also define interesting statistical mechanics models in their own right, as realizations of spin glass order without quenched randomness. We demonstrate this phenomenon through a case study of a cLDPC code on a locally tree-like expander graph. Recursive techniques on trees, made possible by the locally tree-like property, probe a menagerie of stable, incongruent valleys induced by imposing different boundary conditions at low temperature. A complementary numerical study of the valleys on closed finite graphs reveals the inequivalence of the microcanonical and canonical ensemble for certain valleys. We then adapt these methods to the quantum setting, exploring the landscape of the balanced product of two cLDPC codes.

Volume law phases, characterized by an extensive amount of entanglement, are frequently observed in monitored quantum circuits and have numerous applications, ranging from deepening our understanding of quantum mechanics to advancements in quantum computing and cryptography. Their capacity to host complex entangled quantum information is complemented by their ability to efficiently obscure it through scrambling, reminiscent of encoding and decoding protocols. However, the issue of decodability has primarily been studied in measurement-only models with area-law phases, which limit the entanglement of the encoded state. In this work, we introduce a circuit that features a decodable volume law phase, allowing for information retrieval in logarithmic circuit depths. We present a Sign Coloring Decoder that tracks stabilizers revealing the initial state, akin to monitoring a dynamically-changing syndrome. We demonstrate this approach in scenarios where error locations are either known or unknown to the decoder, and we provide insights about the critical properties of the decodability transition. We propose that this decodability transition is universal across various settings, including different circuit geometries. Our findings pave the way for using volume law states as encoders with mid-circuit measurements, opening potential applications in quantum error correction and quantum cryptography.

Open systems with all-to-all (permutation symmetric) interactions are not only experimentally relevant across various physical platforms but also provide a very useful setting in which to explore new phenomena in quantum many-body non-equilibrium physics. This is because their permutation symmetry can be exploited to significantly enhance both analytical and numerical tractability. We explore non-equilibrium phenomena in such systems along three main directions. First, we study absorbing state phase transitions—relevant to dissipative state preparation and quantum error correction—by introducing a (local) model where quantum dynamics produces critical behavior distinct from typical, classical universality classes. We further show that more detailed analysis of criticality is possible in an all-to-all generalization of the model. Second, we demonstrate how perfect state transfer of mixed states and purification can be achieved in all-to-all systems, with applications to central spin models. Third, we explore topological states within the space of permutation symmetric mixed states.