Short-time approximations and path integrals may be dominated by high-energy or large-field contributions, especially for singular interactions, motivating regulators that suppress such contributions while remaining removable. We show that smooth regulators of this kind can arise as conditional maps generated by interference in coherently controlled, postselected superpositions of time evolutions. In quantum mechanics, a Gaussian superposition of short-time translations produces a Gaussian energy filter that renders time-sliced kernels well behaved for singular potentials while recovering the target unitary dynamics when the regulator is removed and in the continuum limit. We also discuss a related momentum-space regulator obtained by coherently smearing a kinetic prefactor. In scalar quantum field theory, local Gaussian smearing of the quartic coupling induces a positive local ${\varphi }^8$ term in the Euclidean action, providing a symmetry-compatible large-field stabilizer. We derive short-time error bounds, analyze multistep success probabilities, and discuss how the construction can be used as a removable regulator together with conventional ultraviolet regularization.

We studied the longitudinal and transverse magnetoresistance of helical magnets, MnSi and ${\mathrm{Mn}}_{1-x}{\mathrm{Co}}_x\mathrm{Si}$, at temperatures between 1.8 and 100 K and in magnetic fields up to 9 T. The helical and conical phases of MnSi show a negative response to low applied magnetic fields at 1.8 and 4 K, which is obviously a result of suppressing weak magnetic fluctuations. However, in the field-induced phase at low temperature, the magnetoresistance of MnSi becomes positive and anisotropic, indicating the action of the Lorentz force. All substances exhibited negative longitudinal and transverse magnetoresistance at temperatures above 4 K, which is most likely related to the suppression of spin fluctuations by the magnetic field. Note that in contrast to our finding, the longitudinal magnetoresistance of ferromagnetic metals was found to be positive. The unique positive and anisotropic magnetoresistance of pure MnSi at low temperatures (1.8 and 4 K) in the induced ferromagnetic phase shows effective suppression of fluctuations by the magnetic field. The significant difference in behavior between pure MnSi and doped MnSi lies in the specifics of the latter material, which forms a sort of helical fluctuation cloud and reveals quantum critical properties at low temperatures. The observed isotropic magnetoresistance in MnSi and ${\mathrm{Mn}}_{1-x}{\mathrm{Co}}_x\mathrm{Si}$ at higher temperatures can tentatively be attributed to the shortening of the mean free path of electrical carriers due to scattering on magnetic fluctuations and impurities, which results in a suppression of Lorentz force effects.

Topological quantum computation, featuring qubits built out of anyonic excitations known as Majorana zero modes (MZMs), have long presented an exciting route toward scalable quantum computation. Recently, the advent of altermagnetic materials has presented a pathway toward localized MZMs on the boundary of two-dimensional materials, consisting of an altermagnetic film, subject to a superconducting proximity effect from a superconducting substrate. In this work, we demonstrate the possibility for an altermagnet-superconductor heterostructure, to not only harbor MZMs, but also freely manipulate their position along the topological boundary of the material, via rotation of the Néel vector. Using this mechanism, on a square platform, we utilize a time-dependent method to simulate the Z gate via braiding, and then extend this to a larger H junction, where we implement the $\sqrt{\mathrm{X}}$ and $\sqrt{\mathrm{Z}}$ gates on a single-qubit system. Further, this structure is eminently scalable to many-qubit systems, thus providing the essential ingredients toward universal quantum computation.

OpenAI’s reasoning model o3-mini-high was used to carry out an exact analytic study of one-dimensional ferrimagnetic site- and bond-decorated $q$-state Potts models. We demonstrate that the finite-temperature ultranarrow phase crossover (UNPC), driven by a hidden “half-ice, half-fire” state recently discovered in the $q=2$ case (Ising model), persists for $q>2$. Moreover, we identify unique features for $q>2$, including the dome structure in the field-temperature phase diagram, and for large $q$ a secondary high-temperature UNPC to the fully disordered paramagnetic state. As the UNPC quickly approaches a genuine transition by enhancing $J$, the interaction between the backbone spins, two distinct behaviors emerge: In the site-decorated Potts model, $T_0$ is independent of $J$ and thus remains unchanged (Type-I UNPC), and in the bond-decorated Potts model with $q>2$, $T_0$ depends on $J$ and quickly shifts toward a finite temperature as $J$ increases (Type-II UNPC). These results establish a versatile framework for engineering controlled fast state-flipping switches in low-dimensional systems. Our nine-dan artificial intelligence (AI)-contribution framework assigns AI the meritorious status of AI-co-led discovery in this work.

We explicitly show that the quantum teleportation protocol can be employed to completely reconstruct arbitrary two- and three-qubit density matrices. We also extend the present analysis to $n$-qubit density matrices. The only quantum resources needed to implement the teleportation-based quantum state tomography protocol are the ability to make Bell measurements and the ability to prepare a few different single-qubit states to be teleported from Alice to Bob.

Optical tomograms can be envisaged as patterns. The Wasserstein generative adversarial network (WGAN) algorithm provides a platform to train the machine to compare patterns corresponding to input and generated tomograms. Using a deep-learning framework with two convolutional neural networks and WGAN, we have trained the machine to generate tomograms of Fock states, coherent states (CSs), and the single-photon added CS (1-PACS). The training process was continued until the Wasserstein distance between the input and output tomographic patterns levelled off at a low value. The mean photon number, variances, and higher moments were extracted directly from the generated tomograms, to distinguish between different Fock states and also between the CS and the 1-PACS, without using an additional classifier neural network. The robustness of our results has been verified using two error models and also with different colormaps that define the tomographic patterns. We have examined whether the training program successfully reflected some of the findings in a recent experiment in which state reconstruction was carried out to establish that the fidelities between an amplified CS, an optimal CS, and a 1-PACS were close to unity, over a range of parameter values. By training the machine to reproduce tomograms corresponding to these specific states, and comparing the mean photon numbers of these states obtained directly from the tomograms, we have established that the variations in these observables reflect the experimental trends. State reconstruction from tomograms could be challenging, in general, since the Hilbert space associated with quantized light is large. The tomographic approach provides a viable alternative to detailed state reconstruction. Our work demonstrates the use of machine learning to generate optical tomograms from which the states can be directly characterized.

We present a general formalism for performing a time-dependent Bogoliubov analysis of a dynamically unstable Bose-Einstein condensate, which extends the quasiparticle projection method of Morgan et al. [Phys. Rev. A 57, 3818 (1998)] to cases with a complex spectrum. By introducing the proper left eigenvectors associated with each regime, we construct a biorthogonal basis. While the usual Bogoliubov normalization $\langle u|u\rangle -\langle v|v\rangle =1$ may not hold in this basis, it still allows for a complete mode decomposition and an accurate reconstruction of arbitrary perturbations over time. This approach extends the applicability of the Bogoliubov framework beyond the stable regime, providing a consistent analysis of the time evolution of unstable condensates. As a proof of concept, we apply the method to a one-dimensional condensate with attractive interactions, which is dynamically unstable and evolves into nonstationary localized structures seeded by small perturbations. Overall, the present method provides a complete and robust mode expansion that remains meaningful beyond the linear regime and useful for characterizing the macroscopic development of instabilities.

Entangled free electrons constitute a key missing resource for quantum electron optics, with direct relevance to nonclassical electron probes, collective radiation, and quantum-enhanced electron-matter spectroscopy. We propose a heralded protocol for generating Bell pairs of spatially separated free electrons by transferring entanglement from an atomic two-level-system (TLS) pair to electronic energy-sideband degrees of freedom. Local resonant electron-TLS exchange converts a delocalized atomic excitation into a delocalized electronic sideband excitation, and a projective TLS measurement certifies successful Bell-pair generation. A self-contained input-output theory establishes the conditional transfer map, the heralding probability, and the relation between the initial atomic resource and the heralded electronic entanglement. Full-Hamiltonian simulations confirm the robustness of the protocol against detuning, pulse shaping, and counterrotating corrections, with the dominant beyond-rotating-wave approximation effects identified as a Bloch-Siegert-type shift and weak leakage outside the target manifold. The results establish a quantitative route to certifiable entangled free electrons and provide a foundation for integrating stationary quantum resources into nonclassical quantum electron optics.

The halide double perovskite ${\mathrm{Cs}}_2{\mathrm{AgBiBr}}_6$ has been proposed as a potential replacement for organic halide perovskites for photovoltaic applications. Further investigation of its dielectric response, optical properties, and structural stability is thus warranted. ${\mathrm{Cs}}_2{\mathrm{AgBiBr}}_6$ exhibits a well-documented structural phase transition at 120 K but indications for an additional lower-temperature ($\sim 40$ K) phase transition have also been reported. On the basis of measurements of the specific heat capacity, temperature-dependent powder x-ray diffraction, low-frequency capacitance, and infrared reflectivity, we clarify the previously reported splitting of phonon modes in the Raman spectrum at $\sim 40\mathrm{K}$ as due to a subtle structural phase transition from the tetragonal $I4$/$m$ structure to a monoclinic $P{12}_1$/$n1$ crystal structure. The infrared-active vibrational modes are experimentally investigated in the three structural regimes. In the cubic structure at room temperature, the four infrared-active modes are observed at 135, $\sim 85$, 55, and $\sim 25{\mathrm{cm}}^{-1}$. As the symmetry reduces to tetragonal, a minute splitting of these modes is found; however, below 40 K additional mode splitting is observed, indicating a further reduction in symmetry.

A realistic model of a projective quantum measurement is presented that provides a physical justification for the collapse postulate without invoking the macroscopic nature of a detector. The analysis adopts a minimally realist interpretation of the formalism, in which objective reality is ascribed only to quantum states associated with definite, empirically accessible physical properties. It is shown that objective state reduction arises from an irreversible microscopic process, enforced by appropriate boundary conditions, while the subsequent amplification stage merely reveals, at the macroscopic scale, the randomly selected measurement outcome.

The material ${\mathrm{ZrTe}}_5$ exhibits distinct topological phases, including a Weyl semimetal (WSM) phase, characterized by a chiral anomaly and in-plane Hall effect, and a three-dimensional quantum Hall (3D QH) phase. The relationship between these phases remains poorly understood. This work systematically explores their connection in ${\mathrm{ZrTe}}_5$ through rotatable, pressure-dependent measurements. At ambient pressure, both phases are observed; the WSM phase requires strong spontaneous electronic polarization, while the 3D QH phase appears when polarization is fully suppressed, with the characteristic resistivity peak temperature $T_{\text{p}}\sim 90\mathrm{K}$. Under applied pressure, ferroelectric polarization diminishes, weakening the WSM phase and its associated nontrivial Hall signals. Concurrently, $T_{\text{p}}$ rises dramatically from 2 K at ambient pressure to 70 K at 2.2 GPa, approaching the expected regime for the 3D QH phase. These findings clarify the conditions underlying the WSM and 3D QH phases and suggest that exploring the 3D QH phase at even higher pressures is a promising direction for future research.

We interpret the $B$-lattice flavor framework as a compositeness hierarchy: all three fermion generations are elementary chiral fields, but third-generation Yukawa couplings are undressed ($Q=0$), while lighter generations acquire their Yukawa couplings through chains of spin-0 subconstituents (“hops”) whose depth is counted by the ${\mathbb{Z}}_9$ discrete gauge symmetry. The ${\mathbb{Z}}_9$ charge admits a two-index decomposition $q_9\mapsto (a,b)$ that identifies two hop species ($\alpha , \beta$) and organizes all fundamental scales from $v_{\mathrm{EW}}$ to $M_{\mathrm{Pl}}$ on a “ninths ladder” $\mathrm{\Lambda }\times {\epsilon }^{n/9}$. The lattice structure yields the Cabibbo-Kobayashi-Maskawa and Pontecorvo-Maki-Nakagawa-Sakata mixing parametrizations (with all mixing exponents expressible as charge differences $\mathrm{\Delta }Q$ dressed by a universal Fritzsch-Xing phase shift of $\pm 1/9$), a seesaw benchmark $m_3\simeq 51$ meV, the axion mass window $m_a\sim 7$–$12\mu \mathrm{eV}$, and the prediction $tan\beta \simeq 10$–16 (from the chain internal factor combined with the Dine-Fischler-Srednicki-Zhitnitsky-II two-Higgs-doublet structure), all from two parameters ($\mathrm{\Lambda }$ and $\epsilon =14/75$). Generation-dependent Peccei-Quinn charges restore the axion-photon coupling ($C_{a\gamma }\simeq 0.6$–1.0) from “back to invisible” suppression. An illustrative UV realization in terms of hypercolor-confined scalars communicated to the standard model by a gauge-invariant messenger chain is presented as an existence proof.

We propose a technique to investigate multipartite entanglement in the symmetric subspace. Our approach is to map an $N$-qubit symmetric state onto a bipartite symmetric state of higher local dimension. We show that this mapping preserves separability and allows to characterize the entanglement of the original multipartite state. In particular, we establish a connection between the border rank and the Schmidt rank, and derive lower bounds on entanglement measures. Finally, we reveal the existence of entangled symmetric subspaces, where all bipartite states are entangled.

Despite the success of the spin-thermalized assumption in explaining hyperon spin polarizations in relativistic heavy-ion collisions, challenges begin to arise especially at lower collision energies. The present study compares the nucleon spin polarization during the collision process and at the freeze-out stage from a nonrelativistic spin-dependent transport model with spin-thermalized approaches in intermediate-energy heavy-ion collisions, where the relativistic effect and the temperature gradient have shown to be unimportant. It is found that both the global and local spin polarizations are largely overestimated from spin-thermalized approaches, compared to those generated by the spin-orbit mean-field potential in transport simulations.

Transformer models contain substantial internal redundancy arising from coordinate-dependent representations and continuous symmetries, in model space and in head space, respectively. While recent approaches address this by explicitly breaking symmetry, we propose a complementary framework based on symmetry reduction. We reformulate representations, attention mechanisms, and optimization dynamics in terms of invariant relational quantities, eliminating redundant degrees of freedom by construction. This perspective yields architectures that operate directly on relational structures, providing a principled geometric framework for reducing parameter redundancy and analyzing optimization.

Using numerically exact diagrammatic Monte Carlo simulations in the two-electron (single-bipolaron) sector, we explore the impact of long-range Coulomb repulsion on the dilute-limit Berezinskii-Kosterlitz-Thouless transition temperature $T_c$ of bipolarons on a two-dimensional square lattice. We study the bond Su-Schrieffer-Heeger model, in which bond phonons modulate the electron hopping. In the absence of long-range repulsion, this model was shown to support small, light bipolarons with a comparatively high transition temperature [C. Zhang, J. Sous, D. R. Reichman, M. Berciu, A. J. Millis, N. V. Prokof’ev, and B. V. Svistunov, Bipolaronic high-temperature superconductivity, Phys. Rev. X 13, 011010 (2023)]. Here, we find that long-range Coulomb repulsion suppresses the optimal $T_c$ but leaves it appreciable over a broad parameter window, including the adiabatic regime $\omega /t=0.5$ at a representative Coulomb strength $V=U/10$ (with $U$ the on-site repulsion). Our results provide controlled single-bipolaron inputs for dilute-limit $T_c$ estimates in the presence of long-range repulsion.

We explore the helical quantum two-body problem, i.e., two repulsively Coulomb interacting particles confined to move along a helix. The effective potential possesses a tunable number of potential wells superimposed on the repulsive Coulomb interaction that can be varied by changing the ratio of the pitch and radius of the helix. The anharmonicity of these wells depends crucially on this ratio and on the order of the well, which can also be seen by analyzing the individual wells’ energy eigenvalue spacing. Our main focus is the investigation of the quantum dynamics of differently prepared wave packets that scatter from the multiwell potential landscape. We show that there exists a rich pattern-forming transient evolution that depends also on the number of bound states of the individual wells. We demonstrate how the multiple wells leave their fingerprints in the dynamics leading, among others, to oscillatory structures on different spatial scales, the formation of beats, and pulsed emission from single well localized wave packets due to their intrawell dynamics.

The magnetoconductance of ${\mathrm{Ti}}_3{\mathrm{C}}_2{\mathrm{T}}_x$ MXene thin films under both perpendicular and parallel magnetic fields is systematically investigated to elucidate how finite thickness impacts weak localization (WL). In thicker films ($\sim 700\mathrm{nm}$), the magnetoconductance is nearly orientation independent, indicating a three-dimensional (3D) regime. In contrast, thinner films ($\lesssim 70\mathrm{nm}$) exhibit pronounced angle-dependent WL, consistent with two-dimensional (2D) behavior. Notably, in some of these thinner films, a small negative magnetoconductance is also detected at low temperatures in parallel fields—a hallmark of weak antilocalization arising from spin-orbit coupling. By fitting the 2D data in both orientations, the key transport parameters are extracted, including an effective thickness of around 12 nm (smaller than the physical thickness) and dephasing lengths. These findings deepen the understanding of quantum interference in MXenes and lay the groundwork for harnessing their tunable dimensionality and spin-orbit effects in emerging electronic and spintronic applications.

The transition to synchrony in the Kuramoto model of globally coupled phase oscillators with a uniform distribution of natural frequencies is discontinuous. We extend the theory of this transition to the Kuramoto-Sakaguchi model, taking into account a phase shift in coupling. In the thermodynamic limit, we derive dependencies of the order parameters on the coupling strength and the phase shift, and describe two transitions from disorder to partial synchrony and from partial synchrony to complete synchrony. In all cases, the first transition is discontinuous, although for phase shifts close to $\pi /2$, the jump is exponentially small. We also discuss which properties of the transition hold for distributions close to the uniform one.