Shi-Xin Zhang

Monitored quantum circuits host a rich variety of exotic non-equilibrium phases. Among the most representative examples are measurement-induced phase transitions between distinct area-law entangled states. However, because these transitions are characterized by specific entanglement quantities such as mutual information or topological entanglement entropy that are nonlinear functionals of the density matrix, their experimental observation requires multiple identical quantum trajectories via post-selection, which becomes exponentially infeasible for large systems. Here, we leverage modern machine learning tools to address this challenge. We devise a neural network (NN) architecture combining a convolutional NN with an attention mechanism, and use raw measurement outcomes directly as input to classify trivial, long-range entangled, and symmetry-protected topological phases. Rather than estimating trajectory-resolved entanglement measures, the network acts as a classifier of the unconditional distribution of measurement records, trained at the pure-phase points and calibrated against phase boundaries independently established from entanglement diagnostics. We show that the system’s relaxation to a steady-state phase manifests as a sharp convergence in the classifier’s accuracy, without any quantum state reconstruction. We systematically study the performance of our network as a function of sample size, input data, spatial and temporal constraints, and system size scalability. Our results demonstrate that this approach is robust and post-selection-free, offering a practical pathway for experimentally probing measurement-induced phases.

We introduce a qudit-native framework for engineering rich and robust discrete time crystals (DTCs) by leveraging their internal multilevel structure. Unlike in qubit systems, qudit-based DTCs exhibit distinct dynamical mechanisms that arise only in multilevel systems, as supported by a dressed normal-form analysis in the heating-suppression regime. These mechanisms are manifested in representative systems: we show that subspace-selective embedded kicks stabilize higher-order subharmonic responses and suppress thermalization, as demonstrated in spin-1 chains; in spin-3/2 systems, extending embedded kicks to more levels enables different level partitions and reveals that DTC robustness is dictated by the symmetry of the partition; and in spin-2 platforms, we realize concurrent period-doubled and period-tripled DTCs under a unified drive. These findings establish a systematic, hardware-efficient methodology for designing stable and multifunctional Floquet phases of matter on modern qudit-based quantum processors.

Studies of entanglement dynamics in quantum many-body systems have focused largely on initial product states. Here, we investigate the far richer dynamics from initial entangled states, uncovering universal patterns across diverse systems ranging from many-body localization (MBL) to random quantum circuits. Our central finding is that the growth of entanglement entropy can exhibit a counterintuitive nonmonotonic dependence on the initial entanglement in many nonergodic systems, peaking for moderately entangled initial states. To understand this phenomenon, we introduce a conceptual framework that decomposes entanglement growth into two mechanisms: "build" and "move." The "build" mechanism creates new entanglement, while the "move" mechanism redistributes preexisting entanglement throughout the system. Specifically, we demonstrate that MBL dynamics are "move-dominated," exhibiting a quantitative agreement with a random SWAP circuit that serves as a model of pure "move" dynamics by uniformly distributing preexisting entanglement. This implies that MBL acts as a redistributor of a hidden entanglement reservoir quantified by the bipartition-averaged entropy. This "build-move" framework offers a unified perspective for classifying diverse physical dynamics, deepening our understanding of entanglement propagation and information processing in quantum many-body systems.

Artificial intelligence in dynamic, real-world environments requires the capacity for continual learning. However, standard deep learning suffers from a fundamental issue: loss of plasticity, in which networks gradually lose their ability to learn from new data. Here we show that quantum learning models naturally overcome this limitation, preserving plasticity over long timescales. We demonstrate this advantage systematically across a broad spectrum of tasks from multiple learning paradigms, including supervised learning and reinforcement learning, and diverse data modalities, from classical high-dimensional images to quantum-native datasets. Although classical models exhibit performance degradation correlated with unbounded weight and gradient growth, quantum neural networks maintain consistent learning capabilities regardless of the data or task. We identify the origin of the advantage as the intrinsic physical constraints of quantum models. Unlike classical networks where unbounded weight growth leads to landscape ruggedness or saturation, the unitary constraints confine the optimization to a compact manifold. Our results suggest that the utility of quantum computing in machine learning extends beyond potential speedups, offering a robust pathway for building adaptive artificial intelligence and lifelong learners.

The search for non-ergodic mechanisms in quantum many-body systems has become a frontier area of research in non-equilibrium physics. In this work, we introduce Hilbert subspace imprint (HSI)—a new mechanism that enables evasion of thermalization, standing as an independent non-ergodic mechanism alongside quantum many-body scars (QMBS) and Hilbert space fragmentation (HSF). HSI manifests when initial states overlap exclusively with a polynomial scaling (with system size) set of eigenstates. We demonstrate this phenomenon through two distinct approaches: weak symmetry breaking and initial state engineering. In the former case, we observe that ferromagnetic states including those with a single spin-flip display non-thermal behavior under weak U (1) breaking, while antiferromagnetic states thermalize. In contrast, the Z ₂ -symmetric model shows thermalization for both ferromagnetic and antiferromagnetic states. In the latter case, we engineer the initial state prepared by shallow quantum circuits that enhance the overlap with the small target subspace.

Noisy monitored quantum circuits have emerged as a versatile and unifying framework connecting quantum many-body physics, quantum information, and quantum computation. In this review, we provide a comprehensive overview of recent advances in understanding the dynamics of such circuits, with an emphasis on their entanglement structure, information-protection capabilities, and noise-induced phase transitions. A central theme is the mapping to classical statistical models, which reveals how quantum noise reshapes dominant spin configurations. This framework elucidates universal scaling behaviors, including the characteristic q − 1 / 3 entanglement scaling with noise probability q and distinct timescales for information protection. We further highlight a broad range of constructions and applications inspired by noisy monitored circuits, spanning variational quantum algorithms, classical simulation methods, mixed-state phases of matter, and emerging approaches to quantum error mitigation and quantum error correction. These developments collectively establish noisy monitored circuits as a powerful platform for probing and controlling quantum dynamics in realistic, decohering environments.

The reliability of artificial intelligence hinges on the integrity of its training data, a foundation often compromised by noise and corruption. Here, through a comparative study of classical and quantum neural networks on both classical and quantum data, we reveal a fundamental difference in their response to data corruption. We find that classical models exhibit brittle memorization, leading to a failure in generalization. In contrast, quantum models demonstrate superior resilience, underscored by a phase transition-like response to increasing noise, revealing a critical point beyond which the model’s performance changes qualitatively. We further introduce a framework of quantum machine unlearning, the process of efficiently forcing a trained model to forget bad influences. We show that classical models form rigid, stubborn memories of erroneous data, while the quantum model is significantly more amenable to efficient forgetting with approximate unlearning methods. Our findings establish that quantum machine learning possesses the dual advantage of intrinsic resilience and efficient adaptability, providing a promising paradigm for the trustworthy and reliable artificial intelligence of the future.