The one-dimensional spin-$s\mathrm{SU}\left(2\right)$ ferromagnetic Heisenberg model, as a paradigmatic example for spontaneous symmetry breaking (SSB) with type-B Goldstone modes (GMs), is expected to exhibit an abstract fractal underlying the ground-state subspace. This intrinsic abstract fractal is here revealed from a systematic investigation into the entanglement entropy for a linear combination of factorized (unentangled) ground states on a fractal decomposable into a set of the Cantor sets. The entanglement entropy scales logarithmically with the block size, with the prefactor being half the fractal dimension of a fractal, as first noted by Castro-Alvaredo and Doyon for the spin-$1/2$ ferromagnetic Heisenberg model [Phys. Rev. Lett. 108 (2012) 120401], as long as the norm for the linear combination scales as the square root of the number of the self-similar building blocks kept at each step $k$ for a fractal, under an assumption that the maximum absolute value of the coefficients in the linear combination is chosen to be around one, and the coefficients in the linear combination are almost constants within the building blocks. Actually, the set of the fractal dimensions for all the Cantor sets forms a dense subset in the interval [0,1]. As a consequence, the ground-state subspace is separated into a disjoint union of countably infinitely many regions, each of which is labeled by a decomposable fractal. Hence, the interpretation of the prefactor as half the fractal dimension is valid for any support beyond a fractal, which in turn leads to the identification of the fractal dimension with the number of type-B GMs for the orthonormal basis states. Our argument may be extended to any quantum many-body systems undergoing SSB with type-B GMs.

In the search for quantum advantage with near-term quantum devices, navigating the optimization landscape is significantly hampered by the barren plateaus phenomenon. This study presents a strategy to overcome this obstacle without changing the quantum circuit architecture. We propose incorporating auxiliary control qubits to shift the circuit from a unitary 2-design to a unitary 1-design, mitigating the prevalence of barren plateaus. We then remove these auxiliary qubits to return to the original circuit structure while preserving the unitary 1-design properties. Our numerical simulation suggests that the proposed structure effectively mitigates the barren plateaus phenomenon. A significant finding is that the gradient of ${\theta }_{1,1}$, the first parameter in the quantum circuit, displays a broader distribution as the number of qubits and layers increases. This suggests a higher probability of obtaining effective gradients. This stability is critical for the efficient training of quantum circuits, especially for larger and more complex systems. The results of this study represent a significant advance in the optimization of quantum circuits and offer a promising avenue for the scalable and practical implementation of quantum computing technologies. This approach opens up new opportunities in quantum learning and other applications that require robust quantum computing power.

Feynman's circuit-to-Hamiltonian construction enables the mapping of a quantum circuit to a time-independent Hamiltonian. This model introduces a Hilbert space made from an ancillary clock register tracking the progress of the computation. In this paper, we explore the efficiency, or run time, of a quantum computer that directly implements the clock system. This relates to the model's probability of computation completion which we investigate at an established optimal time for an arbitrary number of gates $k$. The relationship between the run time of the model and the number of gates is obtained both numerically and analytically to be $O\left(k^{5/3}\right)$. In principle, this is significantly more efficient than the well-investigated Feynman-Kitaev model of adiabatic quantum computation with a run time of $O\left(k^4\right)$. We address the challenge which stems from the small window that exists to capture the optimal stopping time, after which there are rapid oscillations of decreasing probability amplitude. We establish a relationship for the time difference between the first and second maximum which scales as O($k^{1/3}$).

The x-ray absorption spectrum of the ${\mathrm{O}}_2^{+}$ molecular cation is measured. The ions are stored in a cryogenically cooled radiofrequency ion trap and probed by tunable synchrotron radiation. The spectrum exhibits several salient features: a three-state composite ${\pi }^{*}$ resonance at the low-energy side followed by a two-component exchange split, a highly dissociative, ${\sigma }^{*}$ resonance pulled down well below the ionization limit; and a complex valence-Rydberg high-energy part, including several resolved bands. Small structures are interpreted as correlation state satellites with leading internal or semi-internal configurations. Calculations using the restricted active space wave functions and quantum wave packet dynamics offer an overall excellent interpretation of the spectral features.

We analyze high-order harmonic generation using the asymmetric polarization gating obtained by the combination of two delayed circularly polarized counterrotating pulses with different peak amplitudes. This technique gives deeper insight into polarization gated extreme ultraviolet (XUV) generation in general, increases the control of the harmonic temporal confinement, and can be used for tuning the central frequency of the harmonic comb and optimizing the high-order harmonic generation efficiency. Experimental results clearly confirm the gate control and the XUV tunability, in agreement with a model based on the strong field approximation.

Creating crystal bilayers twisted with respect to each other would lead to large periodic supercell structures, which can support a wide range of novel electron correlated phenomena, where the full understanding is still under debate. Here, we propose a scheme to realize an interaction-induced twisted-bilayer lattice in an atomic Bose-Einstein condensate (BEC). The key idea here is to utilize the intrinsic atomic interaction to couple different layers and dynamically induce a supercell structure, distinct from the conventional wisdom to achieve the static twisted-bilayer lattices. To illustrate that, we study the dynamics of a two-component BEC and show that the intrinsic interaction effect arising from interacting bosonic ultracold atoms can dynamically induce both periodic (commensurable) and aperiodic (incommensurable) moiré structures. One of the interesting moiré-physics effects, i.e., the flat-band physics, is shown through investigating the dynamics of a wave packet of the BEC. Our proposal can be implemented using available state-of-the-art experimental techniques and leads to an alternative way to study twistronics in cold atom quantum simulators.

Generalized contextuality is the notion of nonclassicality powering up a myriad of quantum tasks, among which is the celebrated case of a two-party information processing task where classical information is compressed in a quantum channel, the parity-oblivious multiplexing (POM) task. The success rate is the standard quantifier of resourcefulness for this task, while robustness-based quantifiers are as operationally motivated and have known general properties. In this work we leverage analytical and numerical tools to estimate robustness of contextuality in POM scenarios under different types of noise. We conclude that for the 3-to-1 case, robustness of contextuality to depolarization as well as a minimization of robustness of contextuality to dephasing over all bases are good quantifiers for the nonclassical advantage of this scenario. Moreover, we obtain a general relation between robustness of contextuality to depolarization and the success rate in any $n$-to-1 POM scenario and show how it can be used to bound the number of bits encoded in this task.

The uncertainty principle is one of quantum theory's most foundational features. It underpins a quantum phenomenon called measurement incompatibility—two physical observables of a single quantum system may not always be measured simultaneously. Apart from being fundamentally important, measurement incompatibility is also a powerful resource in the broad quantum science and technologies, with wide applications to cryptography, communication, random number generation, and device-independent tasks. Since every physical system is unavoidably subject to noise, an important, yet still open, question is how to characterize the ability of noisy quantum dynamics to preserve measurement incompatibility. This work fills this gap by providing a resource theory of this ability, termed incompatibility preservability. We quantify incompatibility preservability by a robustness measure. Then, we introduce an operational task, entanglement-assisted filter game, to completely characterize both the robustness measure and the conversion of incompatibility preservability. Our results provide a general framework to describe how noisy dynamics affect the uncertainty principle's signature.

We introduce a postprocessing technique for classical shadow measurement data that enhances the precision of ground state estimation through high-dimensional subspace expansion; the dimensionality is only limited by the amount of classical postprocessing resources rather than by quantum resources. Crucial steps of our approach are the efficient identification of useful observables from shadow data, followed by our regularized subspace expansion that is designed to be numerically stable even when using noisy data. We analytically investigate noise propagation within our method, and upper bound the statistical fluctuations due to the limited number of snapshots in classical shadows. In numerical simulations, our method can achieve a reduction in the energy estimation errors in many cases, sometimes by more than an order of magnitude. We also demonstrate that our performance improvements are robust against both coherent errors (bad initial state) and gate noise in the state-preparation circuits. Furthermore, performance is guaranteed to be at least as good—and in many cases better—than direct energy estimation without using additional quantum resources, and the approach is thus a very natural alternative for estimating ground state energies directly from classical shadow data.

We analyze the performance of a quantum error-correction code subject to physically motivated noise modeled by a Lindblad master equation. We consider dissipative and coherent single-qubit terms and two-qubit crosstalk, studying how different approximations of the noise capture the success rate of a code. Focusing on the five-qubit code and adapting it to partially correct two-qubit errors in relevant parameter regimes according to the noise model, we find that a composite-channel approximation where every noise term is considered separately captures the behavior in many physical cases up to long timescales, eventually failing due to the effect of noncommuting terms. In contrast, we find that single-qubit approximations do not properly capture the error-correction dynamics with two-qubit noise, even for short times. A Pauli approximation going beyond a single-qubit channel is sensitive to the details of the noise, state, and decoder and succeeds at short timescales relative to the noise strength, beyond which it fails. Furthermore, we point out a mechanism for a Pauli model failure where it underestimates the success rate of a code even with frequent syndrome projection and correction cycles. These results shed light on the performance of error correction in the presence of realistic noise and can advance the ongoing efforts towards useful quantum error correction.

Algorithmic cooling can be used to find correlated states of many-body quantum systems. It is based on quantum circuits that perform nonunitary operations, whose implementation can be challenging on near-term quantum computers. In this work we develop a method that uses inherent qubit noise to implement nonunitary operations and algorithmic cooling. In our approach, qubit decay during quantum computation is used to simulate dissipation of auxiliary-spin bath, which cools down a simulated system towards its ground state. We test the algorithm on IBM-Q devices and demonstrate the relaxation of system spins to ferromagnetic and antiferromagnetic ordering, controlled by the definition of the system Hamiltonian. The ordering is stable as long as the algorithm is run. We are able to perform cooling and state stabilization for global systems of up to three system spins and four auxiliary spins. Our work paves the way for useful quantum simulations of many-body quantum systems on near-term quantum computers.

In ideal scenarios, charge migration (CM) moves electronic charge coherently from one molecular end to the other, with periods from several hundred attoseconds to a few femtoseconds. Here we show that a well-designed continuous-wave laser can prolongate electronic coherence by more than two orders of magnitude. This enables ultralong-lived CM. The effect is demonstrated by quantum dynamics simulations for the example of ${\mathrm{HCCI}}^{+}$ prepared in a superposition of the electronic ground and first excited states. The success is due to straightforward control of the three laser parameters, i.e., the field strength, the frequency, and the carrier envelope phase, to anchor the nuclei close to the Franck-Condon point, with equal populations of the two electronic states.

We study the breakup of positronium (Ps) by Compton scattering in the range of photon energies, where the motion of the electron and the positron remains nonrelativistic and the process is dominated by the interaction terms $\sim {\widehat{\mathit{A}}}^2$, where $\widehat{\mathit{A}}$ is the vector potential of the photon field. In this study we first compare the total cross section for this process with the total cross section for the positronium breakup by photoabsorption, showing that they become equal at the incident photon energy $\hslash {\omega }_i^{\text{Ps}}\approx 2.2$ keV and that—due to strong (and opposite) dependencies of these cross sections on the photon energy—the Compton scattering rapidly becomes by far the dominant breakup channel when the photon energy exceeds $\hslash {\omega }_i^{\text{Ps}}$. Then we explore the energy and angular spectra of electrons and positrons, which are emitted from the positronium in collisions with high-energy photons, and of the scattered photons. By analyzing the physical mechanisms, which determine the properties of the spectra, we demonstrate that in such collisions the atomic particles can be clearly subdivided into the “participator,” on which the incident photon scatters, and the “spectator,” which is not directly involved in the scattering process. The results for the positronium breakup are compared with the corresponding results for the ionization of atomic hydrogen and the similarities in these processes as well as the differences between them are discussed.

Borromean states refer to a class of bound states with special topological structures, generally thought to exist only in microscopic systems. In this paper, we investigate vortex bound states in three-component Bose-Einstein condensates using coupled Gross-Pitaevskii equations. Specifically, through the competition between two-body and three-body interactions, we identify the emergence of vortex Borromean states, where only three vortices form a stable bound state while any two-vortex subsystems remain unbound. Our theoretical analysis and numerical simulations provide a comprehensive phase diagram of the vortex Borromean states. Additionally, we uncover an unconventional topological phase—a vortex anti-Borromean state—in which two vortices bind together but separate upon the addition of a third vortex. This study highlights the complex role of three-body interactions in macroscopic systems and offers different insights into the topology and phase transitions of multicomponent vortex systems.

We theoretically investigate the influence of dynamic Coulomb interaction on optical bistability and Rabi oscillations in a driven two-level semiconductor quantum dot system under laser irradiation. Using density matrix equations derived from the Coulomb-interaction model proposed by Lu et al. [Phys. Rev. A 103, 043504 (2021)], we obtain analytical solutions for population inversion under the rotating wave approximation. Our analysis shows that the Coulomb interaction induces optical bistability, governed by a cubic equation. The thresholds and the shapes of the hysteresis loops are tunable and can be controlled by various parameters, including electron density, confinement potential, detuning, and dephasing. Additionally, our numerical simulations demonstrate the potential for achieving high-efficiency population inversion and predicting bifurcation and anharmonic regimes in Rabi oscillations under monochromatic excitation.

Advancements in x-ray sources extend the scope of light-matter interactions into the x-ray-nuclear regime. Precise temporal control of quantum phases provides fundamental insights into quantum systems and serves as a cornerstone for numerous quantum technologies. Nevertheless, achieving phase control of quantum systems with high temporal and spatial resolution remains a substantial challenge in the realm of hard x-ray quantum optics due to the ultrashort oscillation periods of photons. In this study, we propose to manipulate the magnetic properties of a thin ${}_{}{}^{57}\text{Fe}$ film using near-infrared (NIR) pulses characterized by a high repetition rate. By calculating the evolution of quantum beats, we can theoretically extract the phase information of the nuclear response. Coherence within the nuclear ensemble is preserved throughout the entire process. This control scheme achieves quantum shifts with zeptosecond precision and modulates the spectral line shape within the frequency domain. Our proposal introduces a high-resolution method for rapidly manipulating nuclear states using optical laser pulses.

We suggest an objective-axis-expansion single-integral algorithm based on the Richards-Wolf vectorial diffraction theory to calculate tight focusing of a collimated continuous-wave coherent laser beam by a high-numerical-aperture microscope objective into a planar layered microcavity. The mathematical basis of the algorithm is formed by (i) expansion of a focused beam into a linear superposition of circularly polarized vortex vector beams and (ii) expansion of the focal amplitudes of the circularly polarized vortex vector beams into power series of the focal distance coordinate $\rho$. The algorithm's computational speed is from four to seven orders of magnitude greater than that of the direct double-integral Richards-Wolf algorithm and up to two orders of magnitude greater than that of the Bluestein-method-based algorithm [Light: Sci. Appl. 9, 119 (2020)], the fastest existing method, for typical focal-plane field calculations. We show that such computational speeds are the fastest possible for focal field calculations in planes perpendicular to the microscope objective axis. These speeds are able to allow for the real-time prediction of focal fields. The accuracy of the suggested algorithm is completely controllable and unlimited. The reported computational speed enhancement is valid for three-dimensional focal field calculations as well because a three-dimensional region can be scanned slice by slice in the longitudinal direction.

The temporal evolution of the optical force density in structured membranes under ultrafast optical illumination is investigated for illustrative situations. Based on this work, it appears that it is possible to exert a pulling force on resonant structures using pulsed light. A combination of optical pulse control and nanostructured material design enables optomechanical device paradigms that allow temporal control of mechanical modes. This is of relevance in several existing areas, such as sensing and computation, and could lead to special opportunities for mechanical metamaterial concepts. This work provides insight into interactions between pulsed light and condensed matter, and motivates optomechanics experiments using ultrafast light.

We theoretically investigate the quantum correlations of nonclassical states in disordered optical waveguides with next-nearest-neighbor (second-order) coupling. We find that single-particle states from different initial positions exhibit similar behavior at specific second-order coupling strengths. At the same time, entangled bosons display correlations that are either analogous to or mirror-symmetric to those of bosons and fermions. We numerically calculate the interparticle distance probabilities of both planar and circular structures and show that their distinct boundary conditions produce unique correlation patterns. In certain cases, bosons are less likely to occupy the same site and single-particle states show asymmetric probability distributions. The effects of second-order coupling and disorder act to cancel out these nontrivial features. Nonclassical states have found numerous applications in integrated quantum photonics. Furthermore, in practical scenarios, disorder is unavoidable, and second-order coupling becomes crucial for light-matter interactions, polymer chains, magnetic materials, non-Hermitian Hamiltonians, topologically nontrivial systems, spin chains, and so on. Their combined effects across diverse physical systems and experimental platforms signify the broader importance of our work.