Abstract Characterizing quantum many-body phase structure is a major goal for quantum simulation. Here, we employ an unsupervised learning approach based on diffusion maps to learn phase transitions in bosonic lattice systems described by Bose–Hubbard type models, which can be realized in ultracold atoms and related quantum simulation platforms. We demonstrate that this approach identifies phase structure across distinct settings without prior knowledge of order parameters or handcrafted observables, including ground-state transitions involving symmetry-protected topological phases and nonequilibrium regimes distinguishing ergodic and many-body localized behavior. Our results indicate that the approach has the potential for direct application to experimentally accessible measurement data for learning quantum phases in current quantum simulators.
Abstract Characterizing quantum many-body phase structure is a major goal for quantum simulation. Here, we employ an unsupervised learning approach based on diffusion maps to learn phase transitions in bosonic lattice systems described by Bose–Hubbard type models, which can be realized in ultracold atoms and related quantum simulation platforms. We demonstrate that this approach identifies phase structure across distinct settings without prior knowledge of order parameters or handcrafted observables, including ground-state transitions involving symmetry-protected topological phases and nonequilibrium regimes distinguishing ergodic and many-body localized behavior. Our results indicate that the approach has the potential for direct application to experimentally accessible measurement data for learning quantum phases in current quantum simulators.
Characterizing quantum many-body phase structure is a major goal for quantum simulation. Here, we employ an unsupervised learning approach based on diffusion maps to learn phase transitions in bosonic lattice systems described by Bose-Hubbard type models, which can be realized in ultracold atoms and related quantum simulation platforms. We demonstrate that this approach identifies phase structure across distinct settings without prior knowledge of order parameters or handcrafted observables, including ground-state transitions involving symmetry-protected topological phases and nonequilibrium regimes distinguishing ergodic and many-body localized behavior. Our results indicate that the approach has the potential for direct application to experimentally accessible measurement data for learning quantum phases in current quantum simulators.
Quantum many-body (QMB) systems are generally computationally hard: the computing resources necessary to simulate them exactly can often exceed the existing computation resources by orders of magnitude. For this reason, Richard Feynman proposed the concept of a quantum simulator: quantum systems engineered to obey a prescribed evolution equation and repeating the experiment multiple times. Experimentally, however, as we explain below, the vast majority of observables describing the system are inaccessible. Thus, while Feynman's idea addresses the problem of simulating quantum dynamics, it leaves unsolved the equally fundamental problem of inferring the underlying physics from the limited observables accessible in experiments. Indeed, many complex phenomena associated with QMB systems remain elusive. Perhaps, the most important example is identifying phase transitions in QMB systems when no simple order-parameter exists, which poses major challenges to this day. Complicating the problem further is the fact that, in most cases, it is impossible to learn from numerical simulations, as the underlying systems are often too large to be computable, and small QMB can show strong finite size effects, masking the presence of the transition. Here, we present an unsupervised machine learning approach to study QMB experiments, specifically aimed at detecting phase transitions and crossovers directly from raw experimental measurements. We demonstrate our methodology on systems undergoing Many-Body Localization cross-over and Mott-to-Superfluid phase-transition, showing that it reveals collective phenomena from the very partial experimental data and without any model-specific prior knowledge of the system. This approach offers a general and scalable route for data-driven discovery of emergent phenomena in complex quantum many-body systems.
Experimental quantum simulators have become large and complex enough that discovering new physics from the huge amount of measurement data can be quite challenging, especially when little theoretical understanding of the simulated model is available. Unsupervised machine learning methods are particularly promising in overcoming this challenge. For the specific task of learning quantum phase transitions, unsupervised machine learning methods have primarily been developed for phase transitions characterized by simple order parameters, typically linear in the measured observables. However, such methods often fail for more complicated phase transitions, such as those involving incommensurate phases, valence-bond solids, topological order, and many-body localization. We show that the diffusion map method, which performs nonlinear dimensionality reduction and spectral clustering of the measurement data, has significant potential for learning such complex phase transitions unsupervised. This method may work for measurements of local observables in a single basis and is thus readily applicable to many experimental quantum simulators as a versatile tool for learning various quantum phases and phase transitions.
Current quantum simulation experiments are starting to explore nonequilibrium many-body dynamics in previously inaccessible regimes in terms of system sizes and timescales. Therefore, the question emerges as to which observables are best suited to study the dynamics in such quantum many-body systems. Using machine learning techniques, we investigate the dynamics and, in particular, the thermalization behavior of an interacting quantum system that undergoes a nonequilibrium phase transition from an ergodic to a many-body localized phase. We employ supervised and unsupervised training methods to distinguish nonequilibrium from equilibrium data, using the network performance as a probe for the thermalization behavior of the system. We test our methods with experimental snapshots of ultracold atoms taken with a quantum gas microscope. Our results provide a path to analyze highly entangled large-scale quantum states for system sizes where numerical calculations of conventional observables become challenging.
Symmetry-protected topological (SPT) phases are short-range entangled phases of matter with a nonlocal order parameter which are preserved under a local symmetry group. Here, by using an unsupervised learning algorithm, namely, diffusion maps, we demonstrate that we can detect phase transitions between symmetry-broken and topologically ordered phases, and between nontrivial topological phases in different classes. In particular, we show that the phase transitions associated with these phases can be detected in different bosonic and fermionic models in one dimension. This includes the interacting Su-Schrieffer-Heeger model, the Affleck-Kennedy-Lieb-Tasaki model and its variants, and weakly interacting fermionic models. Our approach serves as an inexpensive computational method for detecting topological phase transitions associated with SPT systems which can also be applied to experimental data obtained from quantum simulators.
Abstract Identifying phase transitions is one of the key challenges in quantum many-body physics. Recently, machine learning methods have been shown to be an alternative way of localising phase boundaries from noisy and imperfect data without the knowledge of the order parameter. Here, we apply different unsupervised machine learning techniques, including anomaly detection and influence functions, to experimental data from ultracold atoms. In this way, we obtain the topological phase diagram of the Haldane model in a completely unbiased fashion. We show that these methods can successfully be applied to experimental data at finite temperatures and to the data of Floquet systems when post-processing the data to a single micromotion phase. Our work provides a benchmark for the unsupervised detection of new exotic phases in complex many-body systems.