Coherent states offer a promising path for near-term quantum computing due to their inherent protection against bit-flip noise. However, their large photon numbers can be challenging for numerical simulation. This paper introduces an effective model, representing coherent-state quantum annealing using spin-$1/2$ degrees of freedom. We demonstrate that this model yields accurate predictions for realistic experimental settings and can therefore serve as a practical tool for optimizing future quantum hardware.

Linear optical quantum computation (LOQC) offers a promising platform for quantum information processing, but its scalability is fundamentally constrained by the probabilistic nature of nonlocal entangling gates. Qudit circuit compression schemes mitigate this issue by encoding multiple qubits onto qudits. However, these schemes become inefficient when only a subset of the encoded qubits is required to participate in the nonlocal entangling gate, leading to an exponential increase in the number of nonlocal gates. In this paper, we address this bottleneck by demonstrating the existence of multilevel control-$Z$ (CZ) operations for qudits encoded in multiple spatial modes in LOQC. Unlike conventional two-level CZ gates, which act only on a single pair of modes, multilevel CZ gates impart a conditional phase shift for an arbitrarily chosen subset of the spatial modes. We present two explicit linear optical schemes that realize such operations, illustrating a fundamental trade-off between prior information about the input quantum state and the physical resources required. The first scheme is realized with a constant success probability of $1/8$ independent of the qudit dimension using a single nonlocal entangling operation, at the cost of input state dependence. Our second scheme provides a fully state-independent realization, akin to a standard quantum gate, reducing the number of nonlocal gates to $\mathcal{O}(2^{r_1}+2^{r_2})$ as compared to the existing bound of $\mathcal{O}\left(2^{r_1+r_2}\right)$ where $r_1$ and $r_2$ are the number of qubits to be removed as controls in the qudits. The success probability of the realization is $\frac{1}{2}{\left(\frac{1}{8}\right)}^{2^{r_1}+2^{r_2}}$. When combined with qudit circuit compression schemes, our results improve upon a key scalability limitation and significantly improve the efficiency of LOQC architectures.

Parity-nonconserving (PNC) effects in atoms produced by $Z$-boson exchange between the electron and the nucleus grow rapidly with the nuclear charge $Z$. If a hypothetical additional $Z^{\prime }$ boson is light, however, its contribution does not exhibit the same strong enhancement with $Z$. As a result, the ratio of the low-mass $Z^{\prime }$ contribution to the Standard Model $Z$-boson contribution increases rapidly with decreasing $Z$, in fact faster than $1/Z^2$. Hydrogen has a further important advantage: its theoretical description is substantially cleaner than that of heavy atoms, allowing a more accurate interpretation of experimental results. For these two reasons, hydrogen and deuterium PNC experiments may provide an especially favorable setting in which to disentangle a possible $Z^{\prime }$ contribution from the Standard Model background. In this paper we calculate the ratio of the $Z^{\prime }$-boson contribution, for arbitrary $Z^{\prime }$ mass, to the Standard Model $Z$-boson contribution to parity violation in hydrogen and deuterium, including both nuclear-spin-independent and nuclear-spin-dependent interactions.

Recent advancements in the field of quantum simulation have significantly expanded the potential for applications, particularly in the context of lattice gauge theories (LGTs). Maintaining gauge invariance throughout a simulation remains a central challenge, especially for large-scale non-Abelian LGTs with dynamical matter, which are particularly complex in terms of engineering for experiments. Gauge-symmetry breaking is inevitable in established rishon-based schemes for alkaline-earth-like atoms (AELAs) and controlling the magnitude of its effect is an open challenge. Here we first construct a minimal model to quantum simulate non-Abelian LGTs ensuring that the gauge constraints are met and explicitly derive their unambiguous non-Abelian nature. Second, we present a proposal for a gauge protection scheme using native interactions in AELAs enabling the simulation of toy models of non-Abelian $U\left(2\right)$ LGTs with dynamical fermionic matter in $(2+1)$ dimensions on large scales. Due to the simplicity of the gauge protection mechanism, based on a Zeeman shift in combination with superexchange interactions, our scheme can be naturally included in other rishon-based quantum simulation protocols. Third, we extend our approach to a fully scalable, hybrid digital-analog simulator for $U\left(N\right)$ LGTs based on Rydberg AELA with variable rishon number. The proposed general mechanism for gauge protection provides a promising path towards the simulation of non-Abelian LGTs relevant to particle physics.

Optically levitated dielectric objects are promising for precision force, acceleration, torque, and rotation sensing due to their extreme environmental decoupling. While many levitated optomechanics experiments employ spherical objects, for some applications nonspherical geometries offer advantages. For example, rod-shaped or dumbbell-shaped particles have been demonstrated for torque and rotation sensing, and high-aspect-ratio plate-like particles can exhibit reduced photon recoil heating and may be useful for high-frequency gravitational wave detection or as high-bandwidth accelerometers. To achieve optimal sensitivity, cooling, and quantum control in these systems, it is beneficial to achieve optimal displacement detection using scattered light. We describe and numerically implement a method based on Fisher information that is applicable to suspended particles of arbitrary geometry. We demonstrate the agreement between our method and prior methods employed for spherical particles, in both the Rayleigh and Lorentz-Mie regimes. As practical examples, we analyze the optical detection limits of an optically levitated high-aspect-ratio disk-like dielectric object and a rod-shaped object for configurations recently realized in experimental work.

The theoretical description of broadband, multimode quantum pulses undergoing a second-order ${\chi }^{\left(2\right)}$-nonlinear interaction can be quite intricate due to the large dimensionality of the underlying phase space. However, in many cases only a few broadband (temporal) modes are relevant before and after the nonlinear interaction. Here we present an efficient framework to calculate the relation between the quantum states at the input and output of a nonlinear element in their respective relevant modes. Since the number of relevant input and output modes may differ, resulting in an open quantum system, we introduce the generalized Bloch-Messiah decomposition (GBMD), reducing the description to an equal number of input and output modes. The GBMD enables us to calculate the multimode Wigner function of the output state by convolving the rescaled Wigner function of the reduced input quantum pulse with a multivariate Gaussian phase-space function. We expand on this result by considering two examples: a parametric amplification of a broadband Fock state in the infrared frequencies and a THz-to-optical frequency up-conversion of a pulsed two-mode squeezed vacuum state. We investigate the effect, the convolution and thermalization due to entanglement breakage have on the output Wigner function by calculating the von Neumann entropy of the output Wigner function. The methods presented here can be used to optimize the amplification or frequency conversion of broadband quantum states, opening an avenue to the generation and characterization of optical quantum states on ultrafast timescales.

Time-dependent density-functional theory (TDDFT) is a central tool for studying the dynamical electronic structure of molecules and solids, yet aspects of its mathematical foundations remain insufficiently understood. In this work, we revisit the foundations of TDDFT within a finite-dimensional setting by developing a general geometric framework for Schrödinger dynamics subject to prescribed expectation values of selected observables. We show that multiple natural definitions of such constrained dynamics arise from the underlying geometry of the state manifold. The conventional TDDFT formulation emerges from demanding stationarity of the action functional, while an alternative, purely geometric construction leads to a distinct form of constrained Schrödinger evolution. This alternative dynamics may provide a more mathematically robust route to TDDFT and may suggest alternative strategies for constructing nonadiabatic approximations. Applying the theory to interacting fermions on finite lattices, we derive Kohn-Sham schemes in which the density constraint is enforced via an imaginary potential or, equivalently, a nonlocal Hermitian operator. Numerical illustrations for the Hubbard dimer demonstrate the behavior of these approaches.

We introduce the spin coherence scale as a measure of quantum coherence for spin systems, generalizing the quadrature coherence scale (QCS) previously defined for quadrature observables. This SU(2)-invariant measure quantifies the off-diagonal coherences of a quantum state in angular momentum bases, weighted by the classical distinguishability of the superposed states. It serves as a witness of nonclassicality, provides both upper and lower bounds on the Hilbert-Schmidt distance to the set of classical (spin coherent) states, and bounds the Wigner negativity of a spin state. We demonstrate that many hallmark properties of the QCS carry over to the spin setting, including its links to noise susceptibility of a state and moments of quasiprobability distributions and its experimental realizability with a two-copy scheme. The spin coherence scale has direct implications for quantum metrology in the guise of rotation sensing. We also generalize the framework to SU($n$) systems, identifying the unique SU($n$)-invariant depolarization channel and outlining a broad, Lie-algebraic approach to defining and characterizing the properties of coherence scale beyond harmonic oscillators.

Quantum steering ellipsoids (QSEs) provide a geometric representation, within the Bloch picture, of all possible states to which one qubit can be steered through measuring another correlated qubit. However, in realistic settings, quantum systems are inevitably coupled to their environment, resulting in decoherence and degradation of the QSEs. Here, by investigating how local dissipative environments coupled to each qubit affect the quantum steering, we find that the geometry of each party's QSEs is closely tied to the non-Markovian effect and the formation of a bound state in the energy spectrum of the total qubit-environment system. The bound state provides the ability and the non-Markovian effect provides the dynamical way for preserving the QSEs. We systematically examine the characteristics of QSEs under three distinct scenarios, i.e., two-sided bound states, one-sided bound states, and no bound state, revealing a diverse range of steering types. Our work establishes quantum reservoir engineering as a tunable strategy for protecting and controlling quantum steering in open systems, offering a practical pathway toward robust steering-based quantum technologies.

Isotope shift, a systematic error arising from the alkali polarization field generated by the spin-exchange collisions between the Xe and alkali-metal atoms, has been observed in many ${}^{129}\mathrm{Xe}-{}^{131}\mathrm{Xe}$ comagnetometer studies. This isotope shift constitutes a major source of systematic error that ultimately limits the measurement precision and long-term stability of comagnetometers. In this work we present a comprehensive analysis of how a spatially inhomogeneous alkali polarization field induces the isotope shift through the diffusion motion of Xe atoms. We identify two primary physical mechanisms responsible for the isotope shift: the mismatch of the wall relaxation rates and the large difference of the gyromagnetic ratios between ${}^{129}\mathrm{Xe}$ and ${}^{131}\mathrm{Xe}$ spins. Focusing on the alkali polarization field produced by a Gaussian pump beam, we perform detailed analytical and numerical evaluations of the magnitude and stability of the isotope shift. These results offer practical guidance for optimizing the experimental working point, thereby enhancing the absolute accuracy and long-term stability of ${}^{129}\mathrm{Xe}-{}^{131}\mathrm{Xe}$ comagnetometers and nuclear magnetic resonance gyroscopes.

Coherent control of electronic ring currents enables the steering of optomagnetic responses on femtosecond timescales. However, most existing schemes confine these currents to the molecular plane, effectively constraining the electronic angular momentum (EAM) vector to a fixed direction. Here, we demonstrate three-dimensional control of the time-dependent EAM in benzene. By engineering a coherent superposition involving the ground state and three dipole-allowed excited states within the ${}^1{E}_{1u}(X,Y)$ and ${}^1{A}_{2u}\left(Z\right)$ manifolds, we show that both the magnitude and spatial orientation of the electronic flux and EAM vector $\langle \mathbf{L}\rangle \left(t\right)$ can be continuously steered. We identify three characteristic dynamical regimes: (i) steady axial alignment, (ii) single-axis reversal, and (iii) the conical precession of $\langle \mathbf{L}\rangle \left(t\right)$. These predictions are corroborated by dissipative quantum dynamics simulations using the Lindblad master equation. Our findings establish that coherence across multiple electronic states unlocks controllable degrees of freedom for the EAM vector, demonstrating proof-of-principle three-dimensional optomagnetic sculpting in benzene and suggesting possible criteria for identifying other candidate polyatomic systems.

The dynamical generation of quantum resources, such as many-body entanglement, Bell correlations, or spin squeezing, can be achieved via one-axis twisting (OAT) dynamics, which require all-to-all couplings. However, current digital and analog quantum simulation platforms natively provide short-range or power-law couplings that decay too quickly for this purpose. We demonstrate that two spin-1/2 chain models—a staggered nearest-neighbor XXX chain and a long-range XXZ chain—develop an effective OAT nonlinearity when projected onto the symmetric sector. We show that these dynamics generate metrologically useful spin-squeezed states and Greenberger-Horne-Zeilinger coherences that ensure violation of many-body Bell inequalities. We confirm the accuracy of this mapping by comparing it to the exact dynamics and demonstrate that the generated correlations can be read out using a single probe qubit. The resulting dynamics can be simulated with analog and digital quantum simulators.

We extend Gleason's theorem to the two-dimensional Hilbert space of a qubit by invoking the standard axiom that describes composite quantum systems. The tensor-product structure allows us to derive density matrices and Born's rule for $d=2$ from a simple requirement: the probabilities assigned to measurement outcomes must not depend on whether a system is considered on its own or as a subsystem of a larger one. In line with Gleason's original theorem, our approach assigns probabilities only to projection-valued measures, while other known extensions rely on considering more general classes of measurements. This extension of Gleason's theorem to two-dimensional systems is shown to remain valid for some foil theories of quantum theory.

Electromagnetically induced transparency (EIT) enables coherent light-matter storage, forming the basis of photonic quantum memories that are essential for scalable quantum networks and distributed quantum computing. However, accelerating the storage process violates the adiabatic condition, resulting in the excitation of the lossy intermediate state and a reduction in writing efficiency. We propose and numerically investigate a high-speed, high-fidelity quantum storage scheme by incorporating a shortcut-to-adiabaticity technique based on counterdiabatic (CD) driving. By introducing a precisely engineered auxiliary field into a conventional EIT system, our protocol significantly shortens the writing time beyond the conventional adiabatic limit while effectively suppressing the transient population of the lossy intermediate state. Furthermore, our scheme demonstrates strong flexibility in pulse design, remaining effective across different temporal profiles of both the control and signal fields. It also exhibits robustness against imperfections in the CD drive. Even with imperfect single-photon writing and nonideal Rydberg blockade, the scheme retains clear advantages, maintaining high storage performance and overcoming the intrinsic speed-fidelity tradeoff of traditional EIT protocols. These features pave the way for fast and robust quantum devices suitable for high-throughput quantum repeaters and advanced quantum information processing.

Various methods have been explored to prepare the spin-adapted ground state—the lowest energy state within the Hilbert space constrained by externally specified values of the total spin magnitude and the spin-$z$ component. In such problem settings, nonvariational methods incorporate penalty terms into the original Hamiltonian to enforce the desired constraints. Such additional terms would require a quartic number of gates in terms of the number $n_{\text{spin}}$ of spins when naively implemented. To circumvent this computationally intensive scaling, this paper proposes a nonvariational procedure to obtain the spin-adapted ground states that requires only quadratic scaling. The proposed method consists of two stages: the first stage is to prepare a spin-magnitude adapted state and the second stage is postprocessing for the desired $S_z$. By separating into two stages, the procedure achieves the desired spin-adapted ground state while reducing the number of penalty terms from $O\left(n_{\text{spin}}^4\right)$ to $O\left(n_{\text{spin}}^2\right)$. We conducted numerical experiments for spin-1/2 Heisenberg ring models and manganese trimer systems. The results confirmed the effectiveness of our method, demonstrating a significant reduction in gate complexity and validating its practical usefulness.

We propose a general class of open fermionic models where quadratic Liouvillians governing the dissipative dynamics feature analytically characterized higher-order exceptional points (EPs). Invoking the formalism of third quantization, we show that, among the multiple EPs of Liouvillian, an EP with its order approaching the system size arises as the dominant modes of the system at long times, leading to a gapless Liouvillian spectrum. By introducing perturbations, in the form of many-body quantum-jump processes, these higher-order EPs break down, leading to finite Liouvillian gaps with fractional power-law scalings. While the power-law scaling is a signature of the higher-order EP, its explicit form is sensitively dependent on the many-body perturbation. Finally, we discuss the long-time dynamics which can serve as detectable signals for the higher-order Liouvillian EPs.

We employ an all-particle multireference Fock-space relativistic coupled-cluster theory to compute the ionization potential, excitation energy, transition rate, and hyperfine structure constants associated with the $7s^2{}^1{S}_0\to 7s7p{}^3{P}_1$ and $7s^2{}^1{S}_0\to 7s7p{}^1{P}_1$ transitions in nobelium (No). Using our state-of-the-art calculations in conjunction with available experimental data [S. Raeder et al., Phys. Rev. Lett. 120, 232503 (2018)], we extract the values of nuclear magnetic dipole ($\mu$) and electric quadrupole ($Q$) moments for ${}^{253}\mathrm{No}$. Further, information on nuclear deformation in even-mass isotopes is extracted from the isotope shift calculations. Moreover, we employ a perturbed relativistic coupled-cluster theory to compute the ground-state electric dipole polarizability of No. In addition, to assess the accuracy of our calculations, we compute the ionization potential and dipole polarizability of lighter homolog ytterbium (Yb). To account for strong relativistic and quantum electrodynamical (QED) effects in No, we incorporate the corrections from Breit interaction, vacuum polarization, and self-energy in our calculations. The contributions from triple excitations in coupled cluster is accounted perturbatively. Our calculations reveal a significant contribution of $\approx 10\%$ from the perturbative triples to the transition rate of the $7s^2{}^1{S}_0\to 7s7p{}^3{P}_1$ transition. The largest cumulative contribution from $\mathrm{Breit}+\mathrm{QED}$ is observed to be $\approx 4\%$, to the magnetic dipole hyperfine structure constant of the $7s7p{}^1{P}_1$ state. Our study provides a comprehensive understanding of atomic and nuclear properties of nobelium with valuable insights into the electron-correlation and relativistic effects in superheavy elements.

The three-level $5S_{1/2}\text{−}5P_{3/2}\text{−}5D_{5/2}$ cascade transition of ${}^{87}\mathrm{Rb}$ is widely used as a reference for optical frequency standards based on two-photon spectroscopy, implemented with either single-color excitation at 778 nm or two-color excitation at 780 and 776 nm. Although primarily exploited as a clock transition, its relatively large scattering rate enables significant radiation pressure. Here we theoretically investigate two-color laser cooling based on this optical clock transition. Using a semiclassical model, we calculate the radiation force, damping and diffusion coefficients, and equilibrium temperatures as a function of laser detunings and intensities. We show that sub-Doppler temperatures, below the Doppler limit of the $5S_{1/2}\text{−}5D_{5/2}$ transition, can be achieved with a weak probe field at 780 nm and a strong coupling field at 776 nm. We further demonstrate that, under appropriate cooling conditions, the ac Stark shift of the clock transition can be strongly reduced or canceled through suitable choices of laser detunings and power ratios. These results suggest a route toward incorporating laser cooling directly into two-color rubidium optical clocks using the same interrogation lasers, potentially improving stability while minimizing experimental complexity.