The quantum states in doubly degenerate Kramers pairs can act as an internal degree of freedom. Here, we uncover a Kramers dichroism in PT-symmetric magnets: interband transitions induced by circularly polarized light irradiation can selectively polarize Kramers partnered states allowing to control the Kramers degree of freedom. In contrast, Kramers pairs optically excited by linearly polarized light remain in a completely mixed state. Strikingly, we find a class of second-order nonlinear responses that directly track the polarization between Kramers partnered states. Such Kramers nonlinearities can be pronounced producing large second-order nonlinear layer polarization responses activated by Kramers degeneracy in layered antiferromagnets. Together with Kramers dichroism, these render optical responses a novel means for accessing the Kramers degree of freedom and diagnosing their quantum state.

We demonstrate the possibility of a genuine quantum advantage in the efficiency of quantum batteries by analyzing a model that enables a consistent comparison between quantum and classical regimes. Our system consists of $N$ harmonic oscillator cells coupled to a common thermal reservoir, evolving through Gaussian states. We define the global efficiency as the ratio of extractable work (ergotropy) to stored energy, and derive analytical bounds that distinguish, in order of increasing efficiency, regimes characterized by classical squeezing, quantum squeezing without entanglement, and genuine entanglement. Moreover, numerical simulations support the emergence of a similar hierarchy for the thermodynamic efficiency, defined as the ratio between ergotropy and the total thermodynamic cost of the charging process.

Self-organized three-dimensional (3D) ion Coulomb crystals in linear Paul traps naturally form concentric shells that provide a curved, atomically resolved interface for studying two-dimensional (2D) nanofriction. Building on prior work that used 2D ion crystals to investigate one-dimensional nanofriction and orientational melting, we leverage this foundation to extend friction studies from linear ion chains and planar rings to 3D shell structures. Using molecular-dynamics simulations, we first map shell formation as a function of ion number $N$ and the trapping aspect ratio, yielding a simple relation that can aid ion-number estimation in experiments. We compute a Peierls-Nabarro-type potential for the rotation of the outer shell against the static inner core, by treating the angle of rotation as a collective coordinate. We find that changing $N$ by just one can alter the effective rotational barrier by up to a factor of $\sim 7$, while in extreme cases changing $N$ by a few can modify the barrier by up to a factor of $\sim 60$. We quantify a geometric commensurability measure and show that the barrier reflects a system-dependent interplay between the intershell interaction, the structural response of the outer shell, and the confining potential of the trap. Using dynamical simulations, we apply rotational torques to the outer shell and identify pinned, stick-slip, and smooth-sliding regimes whose depinning thresholds depend sensitively on ion number, inner-shell geometry, and trap aspect ratio, with some configurations exhibiting hysteresis due to torque-induced metastable states. We find that spatially varying coupling to the inner-core corrugation can create coexisting fast- and slow-moving domains within the rotating outer shell, realizing multidimensional friction where intrashell shear and intershell nanofriction act simultaneously. Our results highlight the utility of self-organized ion Coulomb crystals as model systems for 2D nanofriction and open up possibilities for stabilizing complex systems and developing ultra-low-friction nanomechanical systems, such as ion-based nanorotors and torque sensors.

Variational quantum algorithms (VQAs) have emerged as promising candidates for solving complex optimization and machine learning tasks on near-term quantum hardware. However, executing quantum operations remains challenging for small-scale users because of several hardware constraints, making it desirable to delegate parts of the computation to more powerful quantum devices. In this work, we introduce a framework for delegated variational quantum algorithms, where a client with limited quantum capabilities delegates the execution of a VQA to a more powerful quantum server. In particular, we introduce a protocol that enables a client to delegate a variational quantum algorithm to a server while ensuring that the input, the output, and also the computation itself remain secret. Additionally, if the protocol does not abort, the client can be certain that the computation outcome is indeed correct. This work builds on the general verification protocol introduced by Fitzsimons and Kashefi [Phys. Rev. A 96, 012303 (2017)], tailoring it to VQAs. Our approach first proposes a verifiable protocol for delegating the quantum computation at each optimization step of a VQA and then combines the iterative steps into an error-resilient optimization process that offers end-to-end verifiable algorithm execution. We also simulate the performance of our protocol tackling the transverse field Ising model. Our results demonstrate that secure delegation of variational quantum algorithms is a realistic solution for near-term quantum networks, paving the way for practical quantum cloud computing applications.

In this paper, we propose a quantum physics-informed neural network (QPINN) to solve partial differential equations (PDEs) by using residual-based adaptive refinement (RAR). The method incorporates a residual-driven adaptive sampling mechanism into the training of QPINN, which aims to enhance convergence and accuracy by enforcing physical constraints in regions with high residuals. Then, we conduct numerical experiments on the one-dimensional viscous Burgers’ equation and diffusion equation, which have different solution structures, as well as the three-dimensional heat equation. The results show that QPINN with RAR reduces the number of parameters by about 44%, and achieves reductions of 31.65%–39.64%, 15.77%–20%, and 3.31%–23.40% over physics-informed neural network (PINN), PINN with RAR, and QPINN in mean relative $L_2$ error, respectively. In summary, it improves model convergence and solution accuracy even with limited sampling points and fewer parameters. These advantages further illustrate that QPINN with RAR is an efficient and stable pathway to solve complex and high-dimensional PDEs.

Nonequilibrium states of matter, when driven periodically, can exhibit exotic properties and emergent behaviors that are fundamentally distinct from those in equilibrium systems. To investigate the dynamical behavior of a particle system under time-periodic external forces, we performed numerical simulations of the motion of a particle initially trapped in an inverted Gaussian potential. Under strong driving, the center of motion of the particle shifts away from the origin of the trap potential, either toward the positive or negative direction. This behavior is explained by a time-averaged effective potential of the periodically driven system, which becomes double-well shaped under strong driving and thereby induces bistability with respect to the center of motion. Once the center of motion converges to either of the two local minima of the effective potential, inversion symmetry breaking occurs, giving rise to even-order harmonic generation despite the centrosymmetric nature of the original system. We show that the time-averaged position of the particle can be switched between the bistable points by additional control pulses. Conditions under which subharmonic generation occurs are also discussed. The demonstrated inversion symmetry breaking by periodic driving may lead to a scheme for manipulating localized particles and nonlinear optical responses that are inaccessible in the near-equilibrium regime.

We show that quantum advantage in distributed sensing can be achieved with noisy quantum networks that only distribute noisy entangled states. We derive a closed-form expression of the quantum Fisher information (QFI) for estimating the average of local parameters using Greenberger-Horne-Zeilinger-diagonal probe states, a representative distributed sensing scenario. From the QFI, we obtain the necessary condition to achieve quantum advantage over the optimal local sensing strategy, which can also serve as an optimization-free entanglement detection criterion for multipartite states. We further explore the impacts from imperfect local entanglement generation and local measurement constraint, and our results imply that the quantum advantage is more robust against quantum network imperfections than local operation errors. Notably, these implications still hold when we explicitly consider dephasing during the sensing dynamics. Our results significantly advance the understanding of the achievability of quantum advantage in noisy distributed sensing. They also offer practical guidance for real-world implementation of quantum sensor networks.

Collective motion in active matter can arise from interaction rules that generate group-level order. A seminal example is the Vicsek model, which describes flocking using a simple local alignment rule. Despite three decades of research, the network topology induced by the particles’ alignment remains understudied. Here, we explore clusters—defined as connected subgraphs of the system-wide interaction network—through topological and geometric measures at the critical noise and across various speeds and densities. We find that the average degree increases polylogarithmically with cluster mass while the variations from the average degree remain fixed across scales. The average path length scaling reveals a two-dimensional network structure, and the average clustering coefficient converges to a fixed value. Geometric analyses reveal that cluster area grows linearly with mass, with the perimeter growing more slowly. We discuss the findings using the degree distribution and positional roles of particles within a cluster. Our results indicate that clusters in the Vicsek model have uniform density with a self-similar network topology across scales, despite the lack of an explicit mechanism to form such interaction networks.

We derive the full spectrum of decorated Cayley trees that constitute tree analogs of selected two-dimensional Euclidean lattices, namely, the Lieb, the double-Lieb, the kagome, and the star lattice. The common feature of these Euclidean lattices is that their nearest-neighbor models give rise to flat energy bands interpretable through compact localized states. We find that the tree analogs exhibit similar flat or nearly flat energy bands at the corresponding energies. Interestingly, such flat bands in the decorated Cayley trees acquire an interpretation that is absent in their Euclidean counterparts: as edge states localized to the inner or the outer boundary of the tree branches. In particular, we establish an exact correspondence between the Lieb-Cayley tree and an ensemble of one-dimensional Su-Schrieffer-Heeger chains, which maps topological edge states on one side of the chains to flat-band states localized in the bulk of the tree, furnishing the flat energy band with a topological stability. Similar mapping to topological edge states or to states bound to edge defects in one-dimensional chains is shown for flat-band states in all the considered tree decorations. We finally show that the persistence of exact flat bands on infinite decorated trees (i.e., Bethe lattices) arises naturally from a covering interpretation of tree graphs. Our findings reveal a rich landscape of flat-band and topological phenomena in non-Euclidean systems, where geometry alone can generate and stabilize unconventional quantum states.

Many control and detection applications require real-time analysis of signals from sensors, in order to quickly and accurately act upon events revealed by the sensors. Such signal analysis benefits from statistical models of signal and sensor behavior. This creates a need for data analysis methods that are simultaneously model based, computationally efficient, and causal, in the sense that they employ only sensor data available prior to a specific point in time. In this work, we implement sequential data analysis techniques on a spin-noise-based quantum sensor to perform two key tasks: hypothesis testing and quickest change-point detection. These online protocols allow us to detect weak magnetic fields by adaptively collecting measurement data until a predefined confidence threshold is reached. We demonstrate these methods in a realistic experimental setting and derive performance bounds for the achievable precision and response time. Our approach has potential utility when detecting small perturbations to the magnetic field, in both applied and fundamental contexts including biomagnetism, geophysical surveys, detection of concealed materials, searches for dark matter candidates, and exotic spin interactions. Our results demonstrate that sequential techniques enable faster and more sensitive detection, making them a powerful tool for quantum sensing.

Non-Hermitian systems exhibit spectral and topological phenomena absent in Hermitian physics; however, their geometric characterization remains subtle due to the intrinsic ambiguity of biorthogonal eigenspaces. Since left and right eigenvectors are not related by Hermitian conjugation, the associated Berry connection is generally nonunique, leading to complex geometric phases and ambiguously defined holonomies. Here, we formulate a covariant geometric framework for non-Hermitian quantum systems based on the metric structure of the underlying Hilbert space. We show that, in the quantum regime with continuous state evolution, the conventional Berry connection and the associated Berry holonomy over closed parameter-space loops can be consistently defined only in the pseudo-Hermitian limit, where the spectrum is real. For generic non-Hermitian Hamiltonians with complex spectra, the relevant geometric object is instead the Aharonov-Anandan holonomy associated with cyclic evolution in projective Hilbert space. Within the pseudo-Hermitian regime, we construct a unique Hermitian Berry connection that is covariant under arbitrary $\mathrm{GL}(N,\mathbb{C})$ frame transformations and reduces to the standard Berry connection in the Hermitian limit. The resulting formalism separates the intrinsic geometry of the Hamiltonian eigenspace from contributions arising from the parameter dependence of the Hilbert-space metric, revealing that the conventional biorthogonal formulation generally mixes these distinct geometric effects. Consequently, geometric phases, synthetic gauge fields, and topological characteristics commonly attributed to non-Hermitian eigenspace geometry may, in part, originate from the underlying metric structure. Our framework therefore provides a consistent geometric foundation for Berry phases, non-Abelian holonomies, and topological invariants in non-Hermitian quantum systems.

Quantum batteries (QBs) exploit collective quantum resources to surpass the limits of classical energy storage and power delivery. We analyze $N$-qubit cavity-coupled QBs governed by Dicke and Tavis-Cummings models under Gaussian driving and open-system dynamics. Finite-size scaling laws $\mathcal{O}\left(N\right)\sim N^{\alpha }$ demonstrate an optimal region of relaxation and dephasing where coherent driving stabilizes entanglement entropy growth for thermodynamic observables (maximum energy $E_{\max }$, charging time $\tau$, and maximum power ${\overline{P}}_{\max }$) and for qubit and cavity entanglement entropies. The Dicke model exhibits entropy-suppressed extensive behavior, while the Tavis-Cummings model achieves superextensive scaling with ${\alpha }_{E_{\max }}\in [1.08,1.26], {\alpha }_{\tau }\approx -0.49$, and ${\alpha }_{{\overline{P}}_{\max }}\in [1.57,1.73]$, supported by qubit-cavity entanglement. We demonstrate that dissipation can act as a stabilizer source, yielding scaling benchmarks that are relevant to several experimental platforms. Our findings connect entanglement, dissipation-enhanced scaling laws, and superabsorption, outlining a pathway toward scalable quantum batteries offering practical quantum advantage.

Within a circuit quantum electrodynamics architecture, we theoretically investigate the detection of a single propagating microwave photon traveling through a resonant microwave cavity dispersively interacting with a double quantum dot tunnel coupled to a lead. Under suitable conditions, a single photon in the cavity can induce a measurable change in the electronic occupation of the charge states. We develop a quantum cascade approach that enables a time-resolved description of a single-photon wave packet impinging on the cavity. We make use of a simple model of charge detector to assess the efficiency of our photo-detection configuration as functions of key parameters such as coupling strength, tunneling rate, temperature, and photon resonance linewidth. We finally highlight a measurement-induced backaction effect on the cavity mode associated with the dispersive, nonabsorptive detection process.

Efficient charge separation in van der Waals (vdW) heterostructures is crucial for optimizing light harvesting and detection applications. However, precise control over the microscopic pathways governing ultrafast charge transfer remains an open challenge. These pathways are intrinsically linked to charge transfer states with strongly delocalized wave functions that appear at various momenta in the Brillouin zone. Here, we use time- and angle-resolved photoemission spectroscopy to investigate the possibility of steering carriers through specific charge transfer states in a prototypical ${\mathrm{WS}}_2$-graphene heterostructure. By selectively exciting electron-hole pairs at the K point (A-exciton resonance) and close to the Q point (C-exciton resonance) of ${\mathrm{WS}}_2$ with different pump photon energies, we find that charge separation is faster at higher excitation energies. This behavior is attributed to the fact that absorption at the C-exciton resonance generates electron-hole populations at energies well above the direct band gap. The resulting elevated carrier temperatures open an additional, highly efficient charge-transfer channel for holes in the ${\mathrm{WS}}_2$ valence band, leading to an overall acceleration of interlayer hole transfer for C-exciton excitation. The microscopic insights gained in this work can be leveraged to optimize the performance of vdW heterostructures in optoelectronic devices.

Neural quantum states (NQS) are powerful ansätze in the variational Monte Carlo framework, yet their architectures are often treated as black boxes. We propose a physically transparent framework in which NQS are treated as neural approximations to latent imaginary-time evolution. This viewpoint suggests that standard transformer-based NQS (TQS) architectures correspond to physically unmotivated effective Hamiltonians dependent on imaginary time in a latent space. Building on this interpretation, we introduce physics-inspired transformer quantum states, which enforce a static effective Hamiltonian by sharing weights across layers and improve propagation accuracy via Trotter-Suzuki decompositions without increasing the number of variational parameters. For the frustrated $J_1-J_2$ Heisenberg model, our ansätze achieve accuracies comparable to or exceeding state-of-the-art TQS while using substantially fewer variational parameters. This study demonstrates that reinterpreting the deep network structure as a latent cooling process enables a more physically grounded, systematic, and compact design, thereby bridging the gap between black-box expressivity and physically transparent construction.

We present a quantum-enhanced Markov chain Monte Carlo (QE-MCMC) method to sample turbulent acceleration vectors from a joint target distribution that depends on all three components and height to model the transport and dispersion of massless Lagrangian tracer particles in two different turbulent shear flows. A homogeneous shear flow, which is characterized by a uniform shear rate $S$, is considered as the starting point. Second, a turbulent boundary layer, which forms in both halves of a plane turbulent channel flow (TCF) at a friction Reynolds number of ${\mathrm{Re}}_{\tau }=1000$, is considered. Then, the mean shear rate $S\left(y\right)$ varies with distance from the wall $y$. In this hybrid quantum-classical method, the proposal distribution $Q$ for the first of the two Metropolis-Hastings sampling substeps is constructed by a parametric quantum circuit. The algorithm generates synthetic tracer particle tracks. The resulting scaling laws for the tracer particle pair dispersion, a central quantity to probe the turbulent mixing properties of the shear flow from a Lagrangian perspective, are found to agree with a stochastic transport model consisting of a set of coupled Langevin equations and the classical MCMC counterpart. Differently to the classical sampling method, QE-MCMC takes to this end a tempered target distribution. Due to the height dependence of the tracer dynamics in TCF, an effective height-weighted spectral gap between the first and second eigenvalues of the Markov chain transition matrix is introduced. The latter is found to significantly exceed the one of classical MCMC when the sampling is done from a multivariate distribution with cross-correlations at the highest qubit numbers and thus resolutions. Consequently, our results support the applicability of this one-shot algorithm as a generative Lagrangian quantum computing module, possibly embedded in a complex fluid flow problem. Our module is found to work reliably for a relatively small number of qubits per spatial dimension of $N_q\le 6$.

We investigate how fermionic anticommutation shapes transport in a noninteracting resonant-level model where a single central site is coupled to an environment. To this end, we compare a fermionic reservoir with a bath of spin-$\frac{1}{2}$ modes using exact diagonalization and a perturbative expansion of the master equation to identify the differences. Notably, we find different reduced dynamics for the spin and fermionic baths even though both models restrict each local mode to at most one excitation; unlike the fermionic bath, however, the spin bath consists of commuting two-level modes and therefore lacks the global exchange antisymmetry of true fermions. These differences originate from higher-order terms in the system-bath coupling, where fermionic anticommutation introduces exchange signs in higher-order correlations. In contrast, all second-order contributions, set solely by two-point correlators, coincide. Deviations are largest for small to intermediate bath sizes, fading in the effectively Markovian regime where higher-order corrections are negligible. These results identify when spin baths can be a substitute for fermionic reservoirs and vice versa.

We develop an unsupervised physics-informed neural network (PINN) to solve the saddle-point equations (SPEs) governing direct above-threshold ionization (ATI) within the strong-field approximation. This setting provides a well-understood test bed in which the saddle-point structure is known for tailored driving fields, enabling systematic validation of the proposed solver. In this approach, the network is trained by minimizing the residual of the saddle-point equations and requires only the definition of the driving-field shape and its parameters, such as intensity, carrier-envelope phase, ellipticity, and relative phase. We introduce a window parametrization strategy that maps unconstrained network outputs to prescribed regions of the complex-time plane, guiding the optimization toward physically relevant solutions and improving convergence stability. We benchmark the PINN against a traditional local gradient-based solver for a range of monochromatic, few-cycle, bichromatic, elliptical, and bicircular fields, demonstrating robust recovery of the dominant complex ionization times over wide parameter ranges. The network naturally tracks changes in ionization event dominance as laser parameters are varied, enabling continuous exploration of regimes where conventional solvers require repeated manual initialization. This renders it much less sensitive to initial guesses than conventional solvers. Using the PINN-derived solutions, we compute coherent ATI photoelectron momentum distributions and show that the symmetries of the driving fields are reflected in both the saddle-point structure and the resulting spectra. These results establish PINNs as a promising computational framework for semiclassical strong-field calculations and provide a foundation for extending machine-learning solvers to Coulomb-corrected models or to more complex strong-field processes, such as rescattered ATI for which the SPEs are highly nonlinear and the presence of multiple closely spaced solutions makes conventional Newton-type root finding highly sensitive to initial guesses, which hinders systematic investigations across laser-parameter spaces, particularly for tailored fields. The present method is transferable to other research areas in which similar saddle-point equations are solved.