Understanding and coherently controlling the properties of interacting quantum many-body systems is a central challenge in non-equilibrium quantum physics. While in the past decades, a wide range of many-body Hamiltonians have been introduced to study quantum chaos, atypical eigenstates, and quantum resources, systematically engineering and continuously tuning these properties within a single microscopic model remains largely unexplored. Here, we employ a pulse engineering scheme to construct an effective Hamiltonian that continuously interpolates between a chaotic Heisenberg (XXX) chain with a local impurity and the ZX Hamiltonian. Along this interpolation, we identify several families of analytically tractable atypical eigenstates embedded in the excited-state spectrum with distinct entanglement and nonstabilizerness properties. In the XXX limit, these states exhibit exact plateaus in both entanglement and stabilizer R\'enyi entropy and correspond to coherent superpositions of long-range valence-bond solid (VBS) states. As the pulse strength increases, the effective Hamiltonians exhibit a hierarchy of new set of approximate entanglement plateaus in the low-energy spectrum. Interestingly, in the fully pulse-engineered ZX limit, we uncover a distinct pair of long-range entangled stabilizer eigenstates, corresponding to rainbow scar states. We further show that pulse engineering preserves the distinct chaotic and non-chaotic regimes of the original model, while that is largely absent in the dynamical generation of entanglement and nonstabilizerness. The pulse-engineered models generate nearly identical quantum resources in both regimes, revealing a partial decoupling between quantum chaos and quantum-resource generation. Our results establish pulse engineering as a versatile framework for generating many-body Hamiltonians with structured eigenstates and tunable quantum resources.
Quantum Monte Carlo (QMC) methods are among the central numerical tools for studying strongly correlated quantum many-body systems, particularly in higher dimensions. As quantum information has introduced new information-theoretic perspectives and diagnostics into many-body physics, QMC methods have accordingly been extended beyond the measurement of conventional linear observables. This review summarizes recent progress in adapting QMC to many-body quantum-information, focusing on qubit or spin-$1/2$ systems as a concrete setting while keeping the discussion broadly applicable to qudit and bosonic systems. We present a unified perspective on the extraction of nonlinear diagnostics, including entanglement entropies and entanglement spectra, R\'enyi negativities for mixed-state entanglement, stabilizer entropies for quantum magic, and decoherence-driven phenomena such as the interplay between imaginary-time evolution and decoherence and strong-to-weak spontaneous symmetry breaking.
The study of quantum systems far from equilibrium has become a cornerstone in the development of emerging quantum technologies. Real-world quantum devices, such as quantum computers, simulators, and sensors, inevitably operate under conditions of driving, dissipation, and decoherence. Consequently, non-equilibrium dynamics are not an exception but a defining feature of these systems. A fundamental understanding of how quantum systems relax, thermalize, or avoid thermalization is essential for stabilizing coherence, extending memory lifetimes, and protecting entanglement. Experimental observations of turbulent Bose–Einstein condensates (BECs) have demonstrated the existence of distinct relaxation pathways. Depending on system conditions, a turbulent BEC may evolve toward a recondensed coherent state or decay into a thermal, non-degenerate quantum fluid. This evolution proceeds through well-defined dynamical stages, characterized by complex vortex interactions, energy cascades, and the redistribution of coherence across scales. Understanding these pathways provides critical insight into the mechanisms governing quantum turbulence and the emergence of order from strongly non-equilibrium states, offering new opportunities to control and harness quantum coherence in realistic environments.
S. Sab, Michelle Moreno-Amijos, A. D. Garc'ia-Orozco et al.· Photonics for Quantum· 0 citations
Quantum computers promise advantages for simulating strongly correlated quantum many-body systems, like atomic nuclei, that are beyond the reach of classical computers. Realizing this potential requires understanding the quantum complexity structure of the target problem. We investigate the time-evolution of two key indicators of quantum complexity, bipartite entanglement entropy and non-local magic (non-stabilizerness), in nuclear reaction dynamics. We analyze two representative dynamical processes: scattering in a one-dimensional model of strongly interacting fermions governed by the Negele potential, and a realistic simulation of $^{240}$Pu fission within time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory. In the former case, we find that interactions dynamically generate both entanglement and non-local magic, leaving persistent signatures of quantum complexity in the outgoing states. In the latter, we observe that substantial quantum complexity survives in the spatial bipartition of daughter fragments well beyond scission. The presence of significant non-local magic and entanglement in both cases strongly indicate that quantum computers would provide substantial advantages for accurately simulating nuclear reaction dynamics.
Saurabh V. Kadam, Antonio Bjelčić, Nicolas Schunck et al.· 0 citations
Quantum resource theories characterize distinct forms of nonclassicality in many-body quantum states, raising the question of whether these resources evolve independently under generic ergodic dynamics. Considering diagnostics quadratic in the state, we show that the dynamics of different resource measures become mutually interdependent and are governed by a few common degrees of freedom. For Haar-random circuits, the purity together with a single resource witness suffices to reconstruct the remaining resource measures, as we demonstrate for coherence, various asymmetries, and number entropies. The same relations hold, to a good approximation, under chaotic Floquet and continuous-time Hamiltonian dynamics, establishing that this dynamical resource equivalence extends beyond random circuits. We further derive an exact coherence--imaginarity relation, remarkably accurate also beyond Haar-random circuits. Our results reveal an emergent simplification of many-body dynamics, in which sufficiently strong scrambling reduces seemingly distinct quantum resources to a few common dynamical degrees of freedom.
Sreemayee Aditya, X. Turkeshi, P. Sierant· 1 citation
Krylov state complexity, or spread complexity, has emerged as a sharp and versatile diagnostic of quantum chaos, information spreading, and many-body dynamics. Built from the Lanczos algorithm and grounded in the optimal-basis theorem, Krylov complexity thereby provides a robust spectroscopic window into quantum dynamics. A central theme is the characteristic overshoot observed in chaotic systems: a complexity peak in which chaotic evolution drives the state deeper into the Krylov chain than in integrable systems before relaxing to equilibrium. This behavior, tied to random-matrix universality classes of spectral statistics, is illustrated across a broad range of models, including quantum billiards, quantum spin chains, and variants of the SYK model. We also discuss proposed holographic descriptions of Krylov complexity in Einstein gravity, and conclude by outlining future directions and open problems, including time-dependent systems and quantum-field-theoretic formulations. A Mathematica notebook is provided for numerical exploration of Krylov complexity and spectral statistics across models.
The interplay between coherent unitary evolution and environment-induced dissipation can give rise to a wide range of non-equilibrium dynamics in open quantum systems, ranging from interesting transport phenomena to dynamical phase transitions. However, accessing such long-time dynamics remains challenging for the existing methods developed for the simulation of many-body open quantum systems. We address this problem by developing a quantum generating function (QGF) formalism for open many-body systems for both ensemble-averaged dynamics governed by a Markovian quantum master equation and trajectory-resolved dynamics described by the quantum trajectory formalism, including quantum jumps, and quantum state diffusion. Our approach computes the dynamics of higher-order moments and fluctuation statistics without explicitly evolving the quantum state, thereby providing an efficient and scalable approach for investigating many-body open quantum systems. We demonstrate the versatility of the formalism by applying it to both the integrable open XXZ chain and the nonintegrable open next-nearest-neighbor XXZ spin chain, where it uncovers distinct initial state dependent long-time transport regimes. Our work establishes quantum generating functions as an efficient and scalable framework for investigating long-time dynamics in open quantum many-body systems.
Katha Ganguly, Dario Poletti, B. Agarwalla· 0 citations
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