Symbolization is a well-established tool to transform a time series into a sequence of symbols. Here, we compare two symbolization approaches: recurrence microstate (RM), based on recurrence patterns in phase space, and symbolic dynamics (SD), derived from ordinal binary sequences. Specifically, we compare the performance of two sets of features, based on RM and SD, for parameter estimation and classification. For parameter estimation, we generate synthetic data simulated from chaotic dynamical systems with a parameter that varies in a range that is divided into ten equal bins, and for classification, we use freely available electrocardiogram (ECG) recordings from patients with four different cardiac pathologies. We train a Random Forest (RF) classifier to infer to which parameter bin a synthetic time series belongs and to which pathology an ECG recording corresponds. We find that using RM features to train the RF algorithm consistently provides higher accuracy; however, SD features encapsulate complementary information that can improve the performance. Combining the two sets of features generally enhances the performance.

We carried out nonresonant inelastic x-ray scattering measurements at the V $L_1$ edge to probe the local V $3d$ charge density in ${\mathrm{VO}}_2$ across the metal-insulator transition (MIT). Without relying on spectral calculations, we were able to integrate directly from the orientational dependence an image of the occupied $3d$ shell and extract quantitatively the orbital occupations of the V ions. We found that in the low-temperature insulating $M_1$ phase the V is highly polarized toward the $\sigma$ configuration. The orbital occupation undergoes significant redistribution upon transition into the metallic $R$ phase, leading to a more isotropic charge density. The massiveness of the orbital switching promotes the scenario in which electron correlations and lattice degrees of freedom are strongly coupled, so that the contribution of the lattice and the electronic part to the energetics must be treated on equal footing to model the MIT quantitatively.

Optical orientation enables the injection of spin-polarized electron and hole populations in III-V and group-IV semiconductors. In particular, absorption of circularly polarized light near the direct gap generates spin-oriented electrons in the conduction band with polarization up to 50%, while hole polarization, opposite to that of electrons, can reach 83%. In recent years, increasing attention has focused on the orbital angular momentum, as charge-to-orbital conversion in semiconductors has been shown to be significantly more efficient than charge-to-spin. This has opened possibilities for exerting torques on ferromagnets in a semiconductive platform and is motivating research on the generation of carrier populations with net orbital angular momentum. In this framework, here, we exploit a “full-zone” $\mathbf{k}·\mathbf{p}$ model to theoretically investigate the injection of orbital angular momentum in bulk Ge and GaAs by means of the absorption of circularly polarized photons. We show that the orbital polarization of holes considerably exceeds 100% for photon energies close to the direct gap of the semiconductors. These results offer a route for generating high orbital polarizations and suggest that semiconductors are a convenient platform for future development of orbitronic and opto-orbitronic devices.

We study time-optimal state-to-state control for two- and multiqubit operations motivated by neutral-atom quantum processors within the Rydberg blockade regime. Block diagonalization of the Hamiltonian simplifies the dynamics and enables the application of a semianalytic approach to the Pontryagin   maximum principle   (PMP) to derive optimal laser controls. We provide a general formalism for $N$ qubits. For $N=2$ qubits, we classify normal and abnormal extremals, showcasing examples where abnormal solutions are either absent or suboptimal. For normal extremals, we establish a correspondence between the laser detuning from atomic transitions and the motion of a classical particle in a quartic potential, yielding a reduced, semianalytic formulation of the control problem. Combining PMP-based insights with numerical optimization, our approach bridges analytic and computational methods for high-fidelity, time-optimal control.

We propose the quasi Monte Carlo method for linear combination of unitaries via classical postprocessing (LCU-CPP) on quantum applications. The LCU-CPP framework has been proposed as an approach to reduce hardware resources, expressing a general target operator $F\left(A\right)$ as $F\left(A\right)={\int }_{V}f\left(\mathit{t}\right)G(A,\mathit{t})d\mathit{t}$, where each $G(A,\mathit{t})$ is proportional to a unitary operator. On a quantum device, $\mathrm{Re}\left[\mathrm{Tr}\right(G(A,\mathit{t})\rho \left)\right]$ can be estimated using the Hadamard test and then combined through classical integration, allowing for the realization of nonunitary functions with reduced circuit depth. While previous studies have employed the Monte Carlo method or the trapezoid rule to evaluate the integral in LCU-CPP, we show that the quasi Monte Carlo method can achieve even lower errors. In two numerical experiments, ground-state property estimation and Green’s function estimation, the quasi Monte Carlo method achieves the lowest errors with a number of Hadamard test shots per unitary that is practical for real hardware implementations. These results indicate that quasi Monte Carlo is an effective integration strategy within the LCU-CPP framework.

Combinatorial optimization problems have wide-ranging applications in industry and academia. Quantum computers may help solve them by sampling from appropriately prepared Ansatz quantum circuits. However, current quantum computers are limited by their qubit count, connectivity, and noise. This is particularly restrictive when considering optimization problems beyond the quadratic order. Here, we introduce Ansätze based on an approximate quadratization of high-order Hamiltonians that do not incur a qubit overhead. The price paid is a loss in the quality of the noiseless solution. Crucially, these approximations yield shallower Ansätze that are more robust to noise than the standard Quantum Approximate Optimization Algorithm one. We show this through simulations with variable noise strengths. Furthermore, we also propose a noise-aware Ansatz design method for quadratic optimization problems. This method implements only a portion of the target Hamiltonian by limiting the number of layers of swap gates in the Ansatz. We find that for both problem types, under noise, our approximate implementation of the full problem structure can significantly enhance the solution quality. Our work opens a path to enhance the solution quality that approximate quantum optimization achieves on noisy hardware.

The continuous-variable (CV) Gaussian no-go theorem fundamentally limits the suppression of Gaussian displacement errors using only Gaussian gates and states. Prior studies have employed Gottesman-Kitaev-Preskill (GKP) states as ancillary qumodes to suppress small Gaussian displacement errors. However, when the displacement magnitude becomes large, inevitable lattice-crossing errors arise beyond the correctable range of the GKP state. To address this issue, we concatenate the Gaussian-noise-suppression circuit with an outer analog Steane code that corrects such occasional lattice-crossing events as well as other abrupt displacement errors. Contrary to conventional concatenation, which primarily aims to reduce logical error rates, the Steane-GKP duality in encoding provides complementary protection against displacement errors at different scales: The inner GKP layer employs non-Gaussian resources to suppress continuous Gaussian noise and reduce residual variance, while the outer analog Steane code corrects discrete lattice-crossing events that exceed the GKP correctable range. It is precisely this separation of error-mitigation roles that enables CV error correction. In contrast to prior work on concatenating GKP and repetition codes to establish error correction for discrete qubit/qudit encoding, we provide correction in the continuous encoding space. Analytical studies show that, under infinite squeezing, the concatenated code suppresses the variance of Gaussian displacement errors acting on all qumodes by up to 50%, while enabling unbiased correction of lattice-crossing errors with a success probability determined by the ratio between the residual Gaussian error standard deviation and the lattice-crossing magnitude. Even with finite squeezing, the proposed architecture still provides Gaussian-error suppression and lattice-crossing correction. Moreover, the presence of the outer analog Steane code relaxes the squeezing requirement of the inner GKP states, indicating near-term experimental feasibility. This work establishes a viable route toward fault-tolerant continuous-variable quantum computation and provides insight into the design of concatenated CV error-correcting architectures.

We present the phenomenology of the one-dimensional nonreciprocal Cahn-Hilliard model for varying nonreciprocity $\left(\alpha \right)$ and different boundary conditions. At small $\alpha$, a perturbed uniform state evolves to a defect-laden configuration that lacks global polar order. Defects are the sources and sinks of traveling waves. For a given $\alpha$, defects with a unique wave number that increases monotonically with $\alpha$ are selected. A critical threshold ${\alpha }_c$ marks the onset of a transition to states with finite global polar order. For periodic boundary conditions, above ${\alpha }_c$, the system shows traveling waves that are completely ordered. In contrast, traveling waves are incompatible with the Neumann and Dirichlet boundary conditions. Instead, for $\alpha \gtrsim {\alpha }_c$, we find fluctuating domains that show intermittent polar order, and at large $\alpha$, the system partitions into two domains with opposite polar order.

Many driven systems alternate between bursts of activity and quiescence and can become trapped in an absorbing state, such as complete inactivity in reaction-diffusion processes or extinction in predator-prey dynamics. It is generally assumed that, conditioned on survival, their long-lived (quasistationary) behavior is unique and independent of the initial condition. We show that this need not hold, even for memoryless Markov dynamics. When the configuration space fractures into multiple macroscopic communicating classes, where configurations can be reached from one another within a class but not across classes, the system retains a measurable memory of its preparation, which can directly affect the critical exponents near absorbing transitions. Using a minimal birth-death-diffusion model, we demonstrate that the quasistationary state is unique when birth processes are present, but becomes nonunique and initial-condition dependent when they are suppressed. This mechanism, arising from vanishing of interclass escape-rate ratios in thermodynamic limit, challenges the conventional universality hypothesis and suggests possibility of history-dependent critical scaling in controlled lattice or colloidal systems with tunable particle number.

Recently, there is interest in coincident “sharpening” and “learnability” transitions in monitored quantum systems. In the latter, an outside observer's ability to infer properties of a quantum system from measurements undergoes a phase transition. Such transitions appear to be related to the decodability transition in quantum error correction, but the precise connection is not clear. Here, we study these problems under one framework we call the general quantum inference problem. In cases as above where the system has a Markov structure, we say that the inference is on a quantum hidden Markov model. We show a formal connection to classical hidden Markov models and that they coincide for certain setups. For example, we prove this for those involving Haar-random unitaries and measurements. We introduce the notion of Bayes nonoptimality, where parameters used for inference differs from true ones. This allows us to expand the phase diagrams of above models. At Bayes optimality, we obtain an explicit relation between “sharpening” and “learnability” order parameters, explicitly showing that the two transitions coincide. Next, we study concrete examples. We review quantum error correction on the toric and repetition code and their mapping to two-dimensional (2D) random-bond Ising model (RBIM) through our framework. We study the Haar-random $\mathrm{U}\left(1\right)$-symmetric monitored quantum circuit and tree, mapping each to inference models that we call the planted simple symmetric exclusion process and planted xor, respectively, and expanding the phase diagram to Bayes nonoptimality. For the circuit, we deduce the phase boundary numerically and analytically argue that it is of a single universality class. For the tree, we present an exact solution of the entire phase boundary, which displays re-entrance as does the 2D RBIM. We discuss these phase diagrams, with their interpretations for quantum inference problems and rigorous arguments on their shapes.

We present a density-functional-theory (DFT) study of the effects of oxygen vacancies on the structural and electronic properties of vanadium dioxide $\left({\mathrm{VO}}_2\right)$. Our motivation is the reported suppression of the metal-insulator transition by oxygen vacancies and the lack of a clear consensus on its origin. We use the $\mathrm{DFT}+V$ method with a static intersite vanadium-vanadium interaction term, $V$, to calculate the properties of the oxygen-deficient metallic rutile and insulating monoclinic M1 phases of ${\mathrm{VO}}_2$ on the same footing. We find that oxygen vacancies induce local distortions in the M1 phase, but do not destroy the dimerization usually associated with the insulating behavior. In spite of this, we find that the M1 phase becomes metallic as a result of the partial filling of the conduction band due to a rigid-band-like doping effect.

We investigate one- and two-mode variants of the ${\mathbb{Z}}_3$-symmetric quantum Rabi model, which describe the interaction of a qutrit with one or two bosonic modes and are directly relevant for circuit-QED and spin-qudit platforms. We find a canonical transformation that allows one to obtain the spectrum of the ${\mathbb{Z}}_3$ Rabi model using perturbation theory in a magnetic field. We show that in a certain parameter regime (deep-strong coupling and a small magnetic field), the three lowest eigenstates become ${\mathbb{Z}}_3$ qutrit-boson cat states. In order to characterize these states, we introduce a joint qutrit-boson Wigner function and derive its closed-form expression for the qutrit-boson cat states. Numerical calculations across a wide range of coupling strengths show that the proposed Wigner function is a useful tool that allows one to unambiguously identify the states of the ${\mathbb{Z}}_3$ qutrit-boson cat states.

We report on a quantum state characterization method, which we call Rabi-based quantum state tomography (RQST), that we have validated on single-qubit quantum states, in particular on the electron and nuclear spins of a single nitrogen-vacancy (NV) center in diamond, demonstrating high fidelities. The difference of RQST with conventional tomography methods is in the implementation of rotation operators and construction of the density matrix from the measured datasets. We demonstrate efficient quantum state control of the electron spin at room temperature with an average fidelity of 0.995 over more than 40 measurements on different states on the Bloch sphere. Also, we apply the methodology to the dark NV nuclear spin state. The state is read via the electron spin using the C-NOT two-qubit entanglement gate and demonstrates fidelities of the same order.

Although one-dimensional classical spin chains do not exhibit phase transitions, we found that a phase transition does occur when they are coupled to a cavity photon mode. This provides the simplest exactly solvable examples demonstrating that finite-temperature superradiant phase transitions can emerge from long-range fully connected interactions mediated by photons and interactions within the material.

Optical refrigeration of solids with anti-Stokes fluorescence has been widely explored as a vibration-free cryogenic cooling technology. A minimum temperature of 87 K has been demonstrated with rare-earth-ion-doped crystals using optical refrigeration. However, the depletion of the upper-lying energy levels in the ground-state manifold hinders further cooling to below the liquid nitrogen $\left({\mathrm{LN}}_2\right)$ temperatures, restricting its applications. In this work, we introduce a Purcell-enhanced optical refrigeration method to circumvent this limitation. This approach enhances the emission of high-energy photons by coupling the emitters to an optical cavity, blueshifting the mean emission wavelength. Such Purcell-enhanced emission facilitates cooling starting from a lower-energy level in the ground-state manifold, which exhibits a higher occupation below the ${\mathrm{LN}}_2$ temperatures. Using experimentally measured optical coefficients, our theoretical analysis predicts a minimum achievable internal temperature of about 38 K for a ${\mathrm{Yb}}^{3+}:{\mathrm{YLiF}}_4$ nanocrystal near a cavity under realistic conditions. The proposed method is applicable to other rare-earth-ion-doped materials and semiconductors and will have applications in creating superconducting and other quantum devices through solid-state cooling.

We investigate quantum reservoir computing (QRC) using a hybrid qubit-boson system described by the Jaynes-Cummings (JC) Hamiltonian and its dispersive limit (DJC). These models provide high-dimensional Hilbert spaces and intrinsic nonlinear dynamics, making them powerful substrates for temporal information processing. We systematically benchmark both reservoirs through linear and nonlinear memory tasks, demonstrating that they exhibit an unusual superior nonlinear over linear memory capacity. We further test their predictive performance on the Mackey-Glass time series, a widely used benchmark for chaotic dynamics, and show comparable forecasting ability. We also investigate how memory and prediction accuracy vary with reservoir parameters and show the role of higher-order bosonic observables and time multiplexing in enhancing expressivity, even in minimal spin-boson configurations. Our results establish JC- and DJC-based reservoirs as versatile platforms for time-series processing and as elementary units that overcome the setting of equivalent qubit pairs and offer pathways toward tunable, high-performance quantum machine learning architectures.

We develop a general framework for classifying fermionic dynamical systems with measurements using symmetry and topology. We introduce two complementary classification schemes based on the Altland-Zirnbauer tenfold way: (1) the many-body evolution operator (mEO) symmetry class, which classifies fermionic dynamics at the many-body level and naturally extends to interacting dynamics, and (2) the single-particle transfer matrix symmetry class, which classifies free-fermion dynamics at the single-particle level and connects to Anderson localization physics. In the free-fermion limit, we show that these two frameworks are equivalent via a dynamical bulk-boundary correspondence: The topology of the dynamical system's spacetime bulk determines the topology of the area-law-entangled steady-state ensemble living on its temporal boundary. Next, we prove that symmetry-invariant, postselection-free Gaussian measurements are realizable in only four of the ten mEO classes (A, AI, BDI, D); the remaining six require either postselection or interacting (non-Gaussian) measurements. Building on these results, we construct general postselection-free topological adaptive circuits that realize topological dynamical phases in any spatial dimension for the four admissible mEO classes. These circuits simultaneously provide a protocol for preparing and stabilizing free-fermion topological states in all ten symmetry classes. As a concrete demonstration, we construct and simulate $2+1\mathrm{d}$ adaptive circuits that realize mEO-class-A topological dynamics, steering toward a steady-state ensemble of Chern insulators in $\mathcal{O}\left(1\right)$ circuit depth. Finally, we numerically characterize topological phase transitions, dynamical domain-wall modes, and robustness to coherent noise, identifying finite error thresholds at which trajectory-resolved and trajectory-averaged quantities undergo distinct phase transitions.

We have extended the two-color bicircular approach for generating chiral XUV radiation via high-harmonic generation by combining femtosecond driving laser fields with 1:3 frequency ratio of wavelengths 1200 and 400 nm. With optimized driving-field intensities, we produced highly chiral spectra in which the vast majority of harmonics sharing the same helicity constitute the vast majority of spectral content. We support these experimental finding with a numerically comprehensive analytical model that describes the propensity (selection) rules for emission of circularly polarized high harmonics. We identify and confirm the rules responsible for the contrast between the allowed odd harmonics of orders $4q+1$ and $4q-1$ ($q$ an integer), which posses opposite helicities, as well as the complete prohibition of even-order harmonics in the high-harmonic spectra. We further apply these rules to explain the spectral shape and ellipticity of the emitted odd harmonics as functions of both the intensity and the ellipticity of the driving-field components. Using XUV polarimetry, we retrieved full Stokes vector, confirming achieved ellipticities higher than 0.9.