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arXiv:2401.07795 · Machine Learning Science and Technology

Unsupervised learning of quantum many-body scars using intrinsic dimension

Harvey Cao, Dimitris G. Angelakis, Daniel Leykam

Published May 17, 2024• 7 citations
arXivHTMLPDF

Abstract

Abstract Quantum many-body scarred systems contain both thermal and non-thermal scar eigenstates in their spectra. When these systems are quenched from special initial states which share high overlap with scar eigenstates, the system undergoes dynamics with atypically slow relaxation and periodic revival. This scarring phenomenon poses a potential avenue for circumventing decoherence in various quantum engineering applications. Given access to an unknown scar system, current approaches for identification of special states leading to non-thermal dynamics rely on costly measures such as entanglement entropy. In this work, we show how two dimensionality reduction techniques, multidimensional scaling and intrinsic dimension estimation, can be used to learn structural properties of dynamics in the PXP model and distinguish between thermal and scar initial states. The latter method is shown to be robust against limited sample sizes and experimental measurement errors.

DOI
10.1088/2632-2153/ad4d3f

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Abstract Quantum many-body scarred systems contain both thermal and non-thermal scar eigenstates in their spectra. When these systems are quenched from special initial states which share high overlap with scar eigenstates, the system undergoes dynamics with atypically slow relaxation and periodic revival. This scarring phenomenon poses a potential avenue for circumventing decoherence in various quantum engineering applications. Given access to an unknown scar system, current approaches for identification of special states leading to non-thermal dynamics rely on costly measures such as entanglement entropy. In this work, we show how two dimensionality reduction techniques, multidimensional scaling and intrinsic dimension estimation, can be used to learn structural properties of dynamics in the PXP model and distinguish between thermal and scar initial states. The latter method is shown to be robust against limited sample sizes and experimental measurement errors.
Quantum many-body scars are atypical, highly nonthermal eigenstates embedded in a sea of thermal eigenstates that have been observed in, for example, kinetically constrained quantum many-body models. These special eigenstates are characterized by a bipartite entanglement entropy that scales as most logarithmically with the subsystem size. We use numerical optimization techniques to investigate if quantum many-body scars of the experimentally relevant PXP model can be well approximated by Gaussian states. Gaussian states are described by a number of parameters that scales quadratically with system size, thereby having a much lower complexity than generic quantum many-body states, for which this number scales exponentially. We find that while quantum many-body scars can typically be well approximated by (symmetrized) Gaussian states, this is not the case for ergodic (thermal) eigenstates. This observation suggests that the non-ergodic part of the PXP Hamiltonian is related to certain quadratic parent Hamiltonians, thereby hinting on the origin of the quantum many-body scars.
Abstract We investigated the stability of quantum many-body scars under perturbations using a PXP model. Using numerical simulations, we analyzed the fidelity and correlation functions of the system to track its evolution and assess the persistence of revivals. We explored two distinct types of perturbations: imperfections in the initial state, which naturally arise in experimental settings, and disorder in the Hamiltonian, which was introduced as a computational tool to probe the system’s response to external disturbances. We found that while certain initial state modifications can partially stabilize oscillations by restricting the system’s accessible dynamics, others accelerate thermalization by increasing overlap with the full eigenstate spectrum. Similarly, disorder in the Hamiltonian gradually suppresses revivals and enhances thermalization, but scars demonstrate robustness for small perturbations. Our results provide insights into the conditions under which quantum many-body scars persist, offering valuable implications for experimental realizations and controlled quantum dynamics.
Abstract Given that any subsystem of a closed out-of-equilibrium quantum system is an open quantum system, its dynamics (reduced from the full system’s unitary evolution) can be either Markovian (memory-less) or non-Markovian, with the latter necessarily impeding the process of relaxation and thermalization. Seemingly independently, such non-ergodic dynamics occurs when an initial state has spectral weight on the so-called quantum many-body scar states, which are non-thermalizing eigenstates embedded deep in the spectrum of otherwise thermal eigenstates. In this article, we present numerical evidence that, in the class of systems which exhibit scars-induced entanglement oscillations, the presence of quantum scars is a microscopic ingredient that enables and enhances non-Markovianity of the dynamics of subsystems. We exemplify this with the PXP model and its deformations which either enhance or erase the signatures of scarred dynamics when quenched from simple product states with significant overlaps with the scarred states. The effect of thermalizing or scarring initial states is also similarly investigated. By probing information backflows with the dynamical behaviour of the distances between temporally-separated transient states of small subsystems, systematic signatures of subsystem non-Markovianity in these models are presented. It is seen that scarring-enhancing (erasing) deformations also exhibit enhanced (diminished) subsystem non-Markovianity. Likewise, results relating scarring (thermalizing) initial states to stronger (weaker) subsystem non-Markovianity are also presented. The retention of memory and revivals between transient subsystem states is a finer form of memory effect than captured by the revivals of full system’s fidelity with the initial states. This sheds new light on the dynamical memories associated with quantum scarring, and opens interesting new questions at the interface of quantum scarring and an open quantum systems approach to investigating far-from-equilibrium and non-thermalizing isolated quantum many-body systems.
Highly excited eigenstates of quantum many-body systems are typically featureless thermal states. Some systems, however, possess a small number of special, low-entanglement eigenstates known as quantum scars. We introduce a quantum-inspired machine-learning platform based on a quantum variational autoencoder (QVAE) that detects families of scar states in spectra of many-body systems. Unlike a classical autoencoder, QVAE performs a parametrized unitary operation, allowing us to compress a single eigenstate into a smaller number of qubits. We demonstrate that the autoencoder trained on a scar state is able to detect the whole family of scar states sharing common features with the input state. We identify families of quantum many-body scars in the PXP model beyond the Z2{\mathbb{Z}}_{2}Z2​ and Z3{\mathbb{Z}}_{3}Z3​ families and find dynamically decoupled subspaces in the Hilbert space of disordered, interacting spin-ladder model. The possibility of an automatic detection of subspaces of scar states opens new pathways in studies of models with a weak breakdown of ergodicity and fragmented Hilbert spaces.
Quantum many-body scars (QMBS)---rare eigenstates that evade thermalization---are typically characterized by their low entanglement entropies compared to surrounding thermal eigenstates. However, due to finite-size effects in systems accessible via exact diagonalization, this measure can be ambiguous. To address this limitation, we propose using the correlation matrix spectrum as an alternative probe to identify QMBS. In cases of exact QMBS that either have known analytic expressions or are captured by various frameworks of QMBS, we find that the dimensionality of the null space of the correlation matrix---an integer value, and thus immune to finite-size effects---can qualitatively identify QMBS. Beyond serving as a diagnostic tool, the correlation matrix method enables the manipulation of the QMBS subspace. For approximate QMBS, such as those in the PXP model, we observe that the correlation matrix spectrum features numerous approximate zero eigenvalues, thereby distinguishing these states. We demonstrate the effectiveness and utility of this method with several paradigmatic QMBS examples.
Quantum many-body scarred systems exhibit atypical dynamical behavior, evading thermalization and featuring periodic state revivals. In this Letter, we investigate the impact of projective measurements on the dynamics in the scar subspace for the paradigmatic PXP model, revealing that they can either disrupt or enhance the revivals. Local measurements performed at random times rapidly erase the system's memory of its initial conditions, leading to fast steady state relaxation. In contrast, a periodic monitoring amplifies recurrences and preserves the coherent dynamics over extended timescales. We identify a measurement-induced phase resynchronization, countering the natural dephasing of quantum scars, as the key mechanism underlying this phenomenon.