Preparing highly entangled quantum states on quantum platforms remains a central challenge in quantum information science and condensed matter physics. While previous studies have primarily focused on measurement-based preparation using local observables, we introduce a novel approach that leverages global observables to efficiently generate entanglement across an entire quantum system. Specifically, our log-depth protocol employs quantum phase estimation to measure global observables such as total magnetization and momentum through local measurements, enabling the preparation of structured excited states from area-law entangled states. This method facilitates the preparation of quantum many-body scar states in diverse models, including the Affleck-Kennedy-Lieb-Tasaki model, constrained domain-wall models, and spin-1/2 and spin-1 XX chains, and it is also applicable for generating high-weight Dicke states. Moreover, our nondestructive momentum measurement enables the preparation of states such as the Arovas A state. By integrating theoretical insights with experimental feasibility-where all operations involve only few-bit gates and limited postselection-we propose measurement-based approaches as powerful tools for accessing highly excited states, with applications in quantum metrology, error correction, and the study of nonequilibrium quantum dynamics.

Understanding universal aspects of many-body systems is one of the central themes in modern physics. Recently, the stabilizer Rényi entropy (SRE) has emerged as a computationally tractable measure of nonstabilizerness, a crucial resource for fault-tolerant universal quantum computation. While numerical results suggested that the SRE in critical states can exhibit universal behavior, its comprehensive theoretical understanding has remained elusive. In this work, we develop a field-theoretical framework for the SRE in a (1+1)-dimensional many-body system and elucidate its universal aspects using boundary conformal field theory. We demonstrate that the SRE is equivalent to a participation entropy in the Bell basis of a doubled Hilbert space, which can be calculated from the partition function of a replicated field theory with the interlayer line defect created by the Bell-state measurements. This identification allows us to characterize the universal contributions to the SRE on the basis of the data of conformal boundary conditions imposed on the replicated theory. We find that the SRE of the entire system contains a universal size-independent term determined by the noninteger ground-state degeneracy known as the g-factor. In contrast, we show that the mutual SRE exhibits the logarithmic scaling with a universal coefficient given by the scaling dimension of a boundary condition changing operator, which elucidates the origin of universality previously observed in numerical results. As a concrete demonstration, we present a detailed analysis of the Ising criticality, where we analytically derive the universal quantities at arbitrary Rényi indices and numerically validate them with high accuracy by employing tensor network methods. These results establish a field-theoretical approach to understanding the universal features of nonstabilizerness in quantum many-body systems.

We demonstrate that the stabilizer Rényi entropy (SRE), a computable measure of quantum magic, can serve as an information-theoretic probe for universal properties associated with conformal defects in one-dimensional quantum critical systems. Using boundary conformal field theory, we show that open boundaries manifest as a universal logarithmic correction to the SRE, whereas topological defects yield a universal size-independent term. When multiple defects are present, we find that the universal terms in the SRE faithfully reflect the defect-fusion rules that define noninvertible symmetry algebra. These analytical predictions are corroborated by numerical calculations of the Ising model, where boundaries and topological defects are described by Cardy states and Verlinde lines, respectively.

Self-propulsion is a quintessential aspect of biological systems, which can induce nonequilibrium phenomena that have no counterparts in passive systems. Motivated by biophysical interest together with recent advances in experimental techniques, active matter has been a rapidly developing field in physics. Meanwhile, over the past few decades, topology has played a crucial role to understand certain robust properties appearing in condensed matter systems. For instance, the nontrivial topology of band structures leads to the notion of topological insulators, where one can find robust gapless edge modes protected by the bulk band topology. We here review recent progress in an interdisciplinary area of research at the intersection of these two fields. Specifically, we give brief introductions to active matter and band topology in Hermitian systems, and then explain how the notion of band topology can be extended to nonequilibrium (and thus non-Hermitian) systems including active matter. We review recent studies that have demonstrated the intimate connections between active matter and topological materials, where exotic topological phenomena that are unfeasible in passive systems have been found. A possible extension of the band topology to nonlinear systems is also briefly discussed. Active matter can thus provide an ideal playground to explore topological phenomena in qualitatively new realms beyond conservative linear systems.

Cavity quantum electrodynamics offers a route to control quantum phases by using vacuum fluctuations of confined electromagnetic fields. In particular, planar cavities based on polar van der Waals materials can generate strongly confined modes and are promising for controlling two-dimensional correlated materials. Recently, moiré materials have become central platforms for studying two-dimensional heavy-fermion systems and their quantum phase transitions. Kondo lattices provide a prototypical model for studying quantum phase boundaries, driven by competition between Kondo screening and the ordering of local magnetic moments. We show that a cavity-induced interaction can shift the quantum phase transitions between a heavy-fermion phase and an antiferromagnetic phase in a two-dimensional Kondo lattice through a momentum-dependent self-energy of the conduction bands. For the longitudinal projected field motivated by h-BN hyperbolic phonon polaritons, the self-energy favors Kondo hybridization and expands the heavy-fermion region. Transverse and circular in-plane model structures give distinct effects, with the transverse case relatively favoring the magnetically ordered phase and the circular case lying between the longitudinal and transverse cases. These results indicate that electromagnetic vacuum fluctuations can effectively modify the control parameters of strongly correlated two-dimensional Kondo materials.

Continuous quantum metrology holds promise for realizing high-precision sensing by harnessing information progressively carried away by the radiation quanta emitted into the environment. Despite recent progress, a comprehensive understanding of the precision limits of continuous metrology with bosonic systems is currently lacking. We develop a general theoretical framework for quantum metrology with multimode free bosons under continuous Gaussian measurements. We derive analytical expressions for the asymptotic growth rates of the global quantum Fisher information (QFI) and the environmental QFI, which quantify the total information encoded in the joint system-environment state and the information accessible from the emitted radiation, respectively. We show that the asymptotic growth rates of the global and environmental QFIs coincide in a class of continuous sensing protocols with dissipative system-environment couplings, while they are in general qualitatively distinct when a system-environment coupling exhibits no damping. We further derive bounds on these quantities, showing that while a quadratic scaling with the number of modes is attainable, the precision scales at most linearly with time and a meaningful energy resource. To illustrate our findings, we analyze several concrete setups, including coupled cavity arrays and trapped particle arrays. While a local setup yields a linear scaling with resources, a globally coupled setup can achieve a quadratic scaling in terms of the mode number. Furthermore, we demonstrate that a nonreciprocal setup can leverage the non-Hermitian skin effect to realize an exponentially enhanced global QFI. Notably, however, this enhancement cannot be reflected in the environmental QFI, highlighting a fundamental distinction between the information stored within the joint state and the information radiated into the environment. ...

Topological defects govern much of the flow behavior and orientational order in active nematics, making their control relevant for active matter physics, smart materials, and microfluidics. Applied activity patterns can induce self-propulsion of active nematic defects, but general-purpose methods for exploiting this effect to control defects remain largely unexplored. Here we use deep reinforcement learning (RL) to perform minimum-time position control of +1/2 defects in hybrid lattice Boltzmann simulations of active nematodynamics. Spatiotemporally patterned activity, implemented as a control field in the active stress, steers defects through microchannel geometries and reveals finite-time reachable regions of defect position space. Reachability is shaped by director anisotropy, homeotropic wall anchoring, and the allowed activity patterns: local patterns steer defects in free domains but fail in junctions, whereas global patterns open otherwise inaccessible channels. In constrained geometries, the original defect may be unable to reach some goals intact, but controlled pair creation enlarges the effective reachable set by transferring control to a newly created +1/2 defect. The trained RL controllers outperform static and rule-based baselines, and controllers trained only on simple junctions can be combined without fine-tuning into a meta-controller that successfully steers defects through a larger test maze. Free energy visualizations show that guided defects write persistent, history-dependent distortions into the director field that can later be partially erased by -1/2 defects. Thus, RL-based control uncovers how confinement, anchoring, actuation geometry, and defect creation determine reachable motion in active nematics, providing a framework for other control tasks in soft and active matter.

Despite their remarkable success in modeling complex data, generative models face a fundamental tradeoff. Global approaches can capture full structural coherence but suffer from high computational costs, while local models are efficient but often fail to reproduce long-range correlations and global coherence. The renormalization group (RG) bridges this gap by seamlessly connecting spatial structures across different length scales, retaining quasi-local descriptions at each step while preserving long-range correlations. We introduce renormalization group flow matching (RGFM), a generative framework that systematically structures data generation across different spatial scales. By using an exact RG flow as the probability path, RGFM progressively generates data from long- to short-wavelength structures. To reconcile scalability with global structure, we exploit two key properties of the RG: quasi-locality and scale separation. We rigorously show that the RGFM probability flow can be accurately approximated by local velocity fields acting over a spatial range O(Λ^-1[ln L+ln(1/ε)]) for RG wavenumber scale Λ, linear system size L, and prescribed error tolerance ε. This property enables local generative modeling with patches of size O(ln L) and a computational cost that scales nearly linearly with the system volume. We numerically demonstrate that local RGFM reproduces long-range correlations far beyond its receptive field in representative one-dimensional distributions, while conventional local flow matching exhibits substantial errors at long distances. On FFHQ images, RGFM yields far more coherent and higher-quality samples than local flow matching at 64x64 and 256x256. Our results establish RG-guided probability flows as a promising route toward scalable generative modeling that captures long-range structure using only local computation.

Characterizing a quantum state through the lens of quantum resources provides an information-theoretic perspective on many-body systems. While quantum entanglement serves as the paradigmatic example of a quantum resource, recent studies have shown that quantum magic, a resource for universal quantum computation, can capture aspects of many-body states complementary to those described by entanglement. For instance, in spin systems, conformal field theory (CFT) analysis of the stabilizer Rényi entropy has revealed universal features of nonstabilizerness that are qualitatively distinct from entanglement. In bosonic and fermionic systems, however, a comparable formulation for their computational resource, non-Gaussianity, has yet to be established. In this work, we introduce a unified measure, the magic Rényi entropy (MRE), to quantify computational resources in spins, bosons, and fermions on an equal footing. This allows us to reveal common universal aspects of nonstabilizerness and non-Gaussianity in critical many-body states. In particular, our CFT analysis shows that the universal contribution to the MRE appears as the size-independent term determined by the Affleck-Ludwig boundary entropy. We find that non-Gaussianity can continuously renormalize this universal contribution or drive a boundary phase transition through bulk-induced boundary renormalization-group flows. As a concrete demonstration, we present a detailed CFT analysis of non-Gaussianity in interacting spinless fermions described by the Tomonaga-Luttinger liquid, showing boundary transitions at the Luttinger parameters K=1/3 and K=3. We perform numerical calculations that confirm our field-theoretical predictions. These results provide a unified field-theoretical understanding of many-body magic across spins, bosons, and fermions.

We investigate two-dimensional Dirac fermions embedded in a deep-subwavelength cavity formed by high-impedance metasurfaces. We point out that, unlike conventional metallic boundaries, these metasurfaces support quasielectrostatic transverse-magnetic modes that mediate a long-range interaction between two-dimensional electrons. Combining static electronic screening with a Dyson-Schwinger analysis, we show that this engineered interaction can qualitatively alter the ground-state properties of Dirac materials. For a fermion flavor number N_f below a critical value N_c=16/π, the interaction drives an excitonic insulating phase through an infinite-order quantum phase transition and spontaneously generates a mass gap. At N_f>N_c, the system remains gapless but enters a non-Fermi-liquid critical regime where the quasiparticle residue is singularly suppressed to zero, and the Dirac cone exhibits a nonanalytic dispersion relation. Furthermore, under a perpendicular magnetic field, the cavity fluctuations dynamically lift the zeroth Landau level degeneracy across all N_f. These results identify high-impedance metasurface cavities as promising platforms for engineering correlated Dirac matter.

The transfer of quantum information between many-qubit states is a subject of fundamental importance in quantum science and technology. We consider entanglement swapping in critical quantum spin chains, where the entanglement between the two chains is induced solely by the Bell-state measurements. We employ a boundary conformal field theory (CFT) approach and describe the measurements as conformal boundary conditions in the replicated field theory. We show that the swapped entanglement exhibits a logarithmic scaling, whose coefficient takes a universal value determined by the scaling dimension of the boundary condition changing operator. We apply our framework to the critical spin-1/2 XXZ chain and determine the universal coefficient by the boundary CFT analysis. We also numerically verify these results by the tensor-network calculations. Possible experimental relevance to Rydberg atom arrays is briefly discussed.

Understanding coupled electron-phonon systems is one of the fundamental issues in strongly correlated systems. In this work, we aim to extend the notion of mixed-state phases to the realm of coupled electron/spinphonon systems. Specifically, we consider a two-dimensional cluster Hamiltonian locally coupled to a set of single bosonic modes with arbitrary coupling strength. First, we adopt a pure-state framework and examine whether a ground state phase transition out of the symmetry-protected topological phase can be captured using the standard polaron unitary transformation. This approach involves restricting the analysis to the low-energy manifold of the phonon degrees of freedom. We find that the pure-state approach fails to detect the anticipated transition to a topologically trivial phase at strong spin-phonon coupling. Next, we turn to a mixed-state picture. Here, we analyze mixed states of the model obtained by tracing out the phonons degrees of freedom. We employ two distinct diagnostics for mixed-state phase transitions: (i) the von Neumann conditional mutual information (CMI) and (ii) the Rényi-2 CMI. We argue that both measures detect signatures of mixed-state phase transitions, albeit at different critical spin-phonon coupling strengths, corresponding to subtly distinct notions of the mixed-state phases.

Diffusion models represent a class of generative models that produce data by denoising a sample corrupted by white noise. Despite the success of diffusion models in computer vision, audio synthesis, and point cloud generation, so far they overlook inherent multiscale structures in data and have a slow generation process due to many iteration steps. In physics, the renormalization group offers a fundamental framework for linking different scales and giving an accurate coarse-grained model. Here we introduce a renormalization group-based diffusion model that leverages multiscale nature of data distributions for realizing a high-quality data generation. In the spirit of renormalization group procedures, we define a flow equation that progressively erases data information from fine-scale details to coarse-grained structures. Through reversing the renormalization group flows, our model is able to generate high-quality samples in a coarse-to-fine manner. We validate the versatility of the model through applications to protein structure prediction and image generation. Our model consistently outperforms conventional diffusion models across standard evaluation metrics, enhancing sample quality and/or accelerating sampling speed by an order of magnitude. The proposed method alleviates the need for data-dependent tuning of hyperparameters in the generative diffusion models, showing promise for systematically increasing sample efficiency based on the concept of the renormalization group.

Nanodiamonds (NDs) are quantum sensors that enable local temperature measurements, taking advantage of their small size. Though model-based analysis methods have been used for ND quantum thermometry, their accuracy has yet to be thoroughly investigated. Here, we apply model-free machine learning with the Gaussian process regression (GPR) to ND quantum thermometry and compare its capabilities with the existing methods. We prove that GPR provides more robust results than them, even for a small number of data points and regardless of the data acquisition methods. This study extends the range of applications of ND quantum thermometry with machine learning.

The competition between quantum many-particle dynamics and continuous monitoring can lead to measurement-induced phase transitions (MIPTs). So far, MIPTs have been extensively explored in fermionic or spin systems. To examine the possibility of an MIPT in bosonic systems, we study the entanglement structure in continuously monitored free bosons with long-range couplings. When the measurement is local, we find that no MIPTs occur because the substantial entanglement generated by the long-range coupling overcomes the entanglement destruction due to the measurement. In contrast, we show that the nonlocal measurement can efficiently suppress the entanglement generation, leading to an MIPT where the bipartite entanglement entropy exhibits the subvolume-to-area law phase transition as the measurement strength is increased. Our numerical results indicate that the critical point should be described by a certain conformal field theory, while the transition does not belong to a conventional universality class such as Berezinskii-Kosterlitz-Thouless class.

In metals containing magnetic impurities, conduction electrons screen the magnetic impurities and induce the Kondo effect, i.e., the enhancement of the electrical resistance at low temperatures. Motivated by recent advances in manipulating quantum materials by cavity confinement, we study how the ultrastrong light-matter coupling can affect the Kondo effect. We show that the ultrastrong coupling can enhance the Kondo temperature and give rise to several notable phenomena, including universal scalings of the cavity-modified Kondo effect, the photon occupation number, and the entanglement entropy between the cavity and electrons. The origin of the cavity enhancement can be understood from the mass renormalization due to the cavity-mediated nonlocal electron-electron interaction, which is akin to the polaronic mass enhancement. We combine the unitary transformations and the Gaussian variational states to analyze the quantum impurity system confined in the cavity. Our nonperturbative framework can be applied to a variety of quantum impurity problems influenced by structured quantum electromagnetic environment.

We investigate the influence of local decoherence on a symmetry-protected topological (SPT) phase of the two-dimensional (2D) cluster state. Mapping the 2D cluster state under decoherence to a classical spin model, we show a topological phase transition of a $\mathbb{Z}_2^{(0)}\times\mathbb{Z}_{2}^{(1)}$ SPT phase into the trivial phase occurring at a finite decoherence strength. To characterize the phase transition, we employ three distinct diagnostic methods, namely, the relative entropy between two decohered SPT states with different topological edge states, the strange correlation function of $\mathbb{Z}_2^{(1)}$ charge, and the multipartite negativity of the mixed state on a disk. All the diagnostics can be obtained as certain thermodynamic quantities in the corresponding classical model, and the results of three diagnostic tests are consistent with each other. Given that the 2D cluster state possesses universal computational capabilities in the context of measurement-based quantum computation, the topological phase transition found here can also be interpreted as a transition in the computational power.

Cavity quantum electrodynamics (QED) studies the interaction between light and matter at the single quantum level and has played a central role in quantum science and technology. Combining the idea of cavity QED with moir\'e materials, we theoretically show that strong quantum light-matter interaction provides a way to control frustrated magnetism. Specifically, we develop a theory of moir\'e materials confined in a cavity consisting of thin polar van der Waals crystals. We show that nontrivial quantum geometry of moir\'e flat bands leads to electromagnetic vacuum dressing of electrons, which produces appreciable changes in single-electron energies and manifests itself as long-range electron hoppings. We apply our general formulation to a twisted transition metal dichalcogenide heterobilayer encapsulated by ultrathin hexagonal boron nitride layers and predict its phase diagram at different twist angles and light-matter coupling strengths. Our results indicate that the cavity confinement enables one to control magnetic frustration of moir\'e materials and might allow for realizing various exotic phases such as a quantum spin liquid.

As first demonstrated by the characterization of the quantum Hall effect by the Chern number, topology provides a guiding principle to realize robust properties of condensed matter systems immune to the existence of disorder. The bulk-boundary correspondence guarantees the emergence of gapless boundary modes in a topological system whose bulk exhibits nonzero topological invariants. Although some recent studies have suggested a possible extension of the notion of topology to nonlinear systems such as photonics and electrical circuits, the nonlinear counterpart of topological invariant has not yet been understood. Here, we propose the nonlinear extension of the Chern number based on the nonlinear eigenvalue problems in two-dimensional systems and reveal the bulk-boundary correspondence beyond the weakly nonlinear regime. Specifically, we find the nonlinearity-induced topological phase transitions, where the existence of topological edge modes depends on the amplitude of oscillatory modes. We propose and analyze a minimal model of a nonlinear Chern insulator whose exact bulk solutions are analytically obtained and indicate the amplitude dependence of the nonlinear Chern number, for which we confirm the nonlinear counterpart of the bulk-boundary correspondence in the continuum limit. Thus, our result reveals the existence of genuinely nonlinear topological phases that are adiabatically disconnected from the linear regime, showing the promise for expanding the scope of topological classification of matter towards the nonlinear regime.

We prove that any quantum many-spin state under genetic local dissipation will be fully separable after a finite time independent of the system size. Such a sudden death of many-body entanglement occurs universally provided that there is a finite damping gap and the unique steady-state density matrix is of full rank. This result is rigorously derived by combining a state-reconstruction identity based on random measurements and the convergence bound for quantum channels. Related works and possible generalizations are also discussed.