Periodic driving is a powerful tool to generate exotic topological phases without static counterparts, such as the anomalous chiral edge modes from bulk bands with zero Chern number and topological $\pi$ modes exhibiting period-doubled dynamics. Recently, a new class of Floquet topological mode, namely, the $\pi /2$ mode, which carries four-period periodicity and has potential applications in quantum computing, was proposed based on a square-root method and realized in an acoustic system. Here we propose a laser-written waveguide array lattice to realize topological $\pi /2$ modes in photonics. Our photonic model simulates a square-root periodically driven Su-Schrieffer-Heeger model and has a rich phase diagram allowing for the coexistence of conventional zero, $\pi$ modes, and the new $\pi /2$ modes. Through numerical simulations of the wave equation, we uncover the unique four-period evolution feature of the $\pi /2$ modes. Our model, which only contains four waveguides per unit cell and two driving steps, is easy to implement with current fabrication techniques and may find applications in quantum optics.

Perturbative master equations are essential for modeling open quantum systems but often exhibit late-time divergences when environmental correlations decay algebraically. In this work, we analyze the time-convolutionless (TCL) master equation expanded to order ${\mathrm{TCL}}_{2n}$ and demonstrate that, while van Kampen's cumulants suppress early-time secular growth, they ultimately diverge at long times. To overcome this, we introduce a resummation technique based on the Hadamard trick, which incorporates time integrals directly into the bath's spectral density via elementwise multiplication. This approach establishes a maximum expansion order, $n_{\text{max}}=\lceil s+1\rceil$, and defines a precision limit of the asymptotic states of $O\left({\lambda }^{2\lceil s\rceil }\right)$, where $s$ is the power-law exponent and $\lambda$ is the weak-coupling constant. The resummed master equation features renormalized Bohr frequencies that capture decoherence and spectral overlap effects. In the unbiased spin-boson model, this results in an inflation of the generator at a temperature-independent rate equal to the decoherence rate ${\nu }_2$ and a finite validity time $t_L\approx (s+1)/{\nu }_2$. For exponentially decaying correlations, the method recovers a proper Markovian limit below a critical coupling threshold.

We present direct experimental verification of quantum coherence for a set of quantum states in a basis-independent manner. We find that the theory of quantum coherence for a set of quantum states matches our experimental results perfectly and can be applied to protocols such as the 1984 protocol of Bennett and Brassard (BB84) and quantum secure direct communication. Using a Sagnac interferometer, we experimentally quantify the quantum coherence for two sets of experimental states. Moreover, we introduce an application of set coherence, illustrating that the states employed in the BB84 protocol exhibit maximal set coherence. Our results pave the way for wider applications of quantum coherence for a set of quantum states, including quantum key distribution protocols and probabilistic quantum cloning.

In this paper, the laser-driven three-dimensional vibration excitation dynamics of ${\mathrm{N}}_2\mathrm{Ar}$ dimer are simulated using the full time-dependent wave-packet simulation method. The three-dimensional vibrational wave functions are obtained first by solving the Schrödinger equation involving the rotation of ${\mathrm{N}}_2$, vibration of ${\mathrm{N}}_2$-Ar, and intermolecular interaction. The solved vibration wave functions have both the angular quantum number $m$ and the symmetric or antisymmetric properties with respect to the ${\mathrm{N}}_2$-Ar axis. The theoretical calculation shows that laser-induced molecular vibrational excitation needs to satisfy the selection rules of nonresonant Raman processes. Two modes of excitation are further distinguished as follows: (1) $\mathrm{\Delta }m=\pm 2$ and the symmetry does not change; here, the van der Waals bond will be strengthened. (2) $\mathrm{\Delta }m=\pm 1$ and the symmetry is reversed; here, the dimer will be partially excited into a linear structure. Our results point out that the ${\mathrm{N}}_2\mathrm{Ar}$ initially located in the ground vibrational state mainly prefers the excitation of mode (1), but the one located in the first excited state will undergo two modes of excitation simultaneously.

Configurable arrays of optically trapped Rydberg atoms are a versatile platform for quantum computation and quantum simulation, also allowing controllable decoherence. We demonstrate theoretically that they also enable proof-of-principle demonstrations for a technique to build models for open quantum dynamics using machine learning with artificial neural networks, recently proposed by Mukherjee et al. [Quantum Sci. Technol. 10, 02LT01 (2025)]. Using the outcome of quantum transport through a network of sites that correspond to excited Rydberg atoms, the multistage neural-network algorithm successfully identifies the number of atoms (or nodes in the network) and, subsequently, their location. It further extracts an effective interaction Hamiltonian and decoherence operators induced by the environment. To probe the Rydberg array, one initiates dynamics repeatedly from the same initial state and then measures the transport probability to an output atom. Large datasets are generated by varying the position of the latter. Measurements are required in only one single basis, making the approach complementary to, e.g., quantum process tomography. Due to steeply increasing requirements for training data size, the present implementation appears best suited for networks of just a few sites. The cold-atom platform discussed in this article can be used to explore the performance of the proposed protocol when training the neural network with simulation data but then applying it to construct models based on experimental data.

We propose a postselected amplification scheme for phase-shift measurement of optical coherent states when passing through the Mach-Zehnder interferometer (MZI). Different from the usual weak-value-amplification (WVA) formulation, the which-path states of the MZI cannot be described as subsystem states entangled with two optical coherent states. However, we obtain the same phase amplification result of the usual WVA in the Aharonov-Albert-Vaidman limit but, beyond this limit, the result is essentially different. We explicitly carry out the amplified phase shift, which can be extracted out from the field-quadrature measurement in the dark port of the MZI. We also evaluate the performance quality of the proposed scheme and analyze the technical advantages by considering possible errors in the quadrature measurement.

Graph states are computationally powerful quantum states with many applications, including use as resource states for measurement-based quantum computing (MBQC). We demonstrate construction of graph states on a Rydberg atom quantum analog simulator. We show how an always-on interaction can be used to simultaneously entangle all Rydberg atoms into a graph state. We construct and implement many-body computational order parameters for graph states using nonlocal measurement-based logic operations in the Clifford group. The order parameters measure the efficacy of entanglement to allow MBQC on graph states of any size. We parametrize finite-size scaling of these order parameters. Our results define a route to efficiently test computational power in quantum devices.

Multiply charged ions with a single hole in closed shells are being extensively used to study relativistic and quantum electrodynamic (QED) effects due to the suppression of electron correlations in such systems. Here, we report measurements of the fine-structure splitting in the ground configuration $3d^9$ of Co-like ions of Yb, Re, Os, and Ir performed with an electron beam ion trap. Extensive relativistic many-body perturbation theory and multiconfiguration Dirac-Hartree-Fock calculations were executed with account of high-order QED contributions. It is found that those advanced calculations very well agree with the present accurate measurements of the $3d^9 {}^2{D}_{3/2}{-}^2{D}_{5/2}$ splittings. Comparisons with other theoretical works and experiments are presented as well.

Spin polarization in the multiphoton ionization of the HI molecule with intense 395 nm, circularly polarized laser pulses is investigated theoretically. To this end, we numerically solve the time-dependent Schrödinger equation in the basis of spherical spinors employing the time-dependent single-center method. We investigate the influence of the ionizing-pulse parameters, such as peak intensity, time envelope, and duration, as well as molecular orientation in space on the computed spin polarization of photoelectrons emitted by the multiphoton ionization of HOMO, HOMO-1, and HOMO-2 states of the molecule.

We explore the energy spectrum and eigenstates of two-component atomic Fermi superfluids with tunable pairing interactions in the presence of spin-dependent ultralong-range Rydberg molecule (ULRM) potentials, within the Bogoliubov–de Gennes formalism. The attractive ULRM potentials lead to local-density accumulation, while their difference results in a local polarization potential and induces the in-gap Yu-Shiba-Rusinov (YSR) states whose energies lie below the bulk energy gap. A transition from equal population to population imbalance occurs as the pairing strength falls below a critical value, accompanied by the emergence of local Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)–like states characterized by out-of-phase wave functions and lower energies compared to the YSR states. The negative contribution emanating from the FFLO-like states also causes a sign change in the gap function within the ULRM potentials. Depending on the Rydberg excitation, the transition towards population imbalance can be on either the BCS or the Bose-Einstein condensation side of the Fermi superfluid. Additionally, spin-polarized bound states arise along with oscillatory “clumpy states” to compensate for the local-density difference. We discuss possible experimental realizations of the composite Rydberg-atom–Fermi-superfluid system.

We investigate the in- and out-of-equilibrium phenomena of a rotational impurity—specifically, a linear molecule—coupled to a nonconventional environment, a helium nanodroplet. By employing a Lee-Low-Pines-like transformation combined with a multireference configuration approach, we self-consistently account for the molecule's backaction on the superfluid bath and accurately capture the complex entanglement between the molecule's rotational degrees of freedom and the bath excitations. Our findings reveal that in the ground state, the impurity induces a density defect in the superfluid bath, giving rise to two novel types of excited states: (a) attractive angulon states, analogous to bound states in photonic crystals and Yu-Shiba-Rusinov bound states in superconductors, localized within the density defect region, and (b) long-lived repulsive angulon states in dilute environments. Rotational spectroscopy demonstrates a crossover from repulsive to attractive angulon states as the bath density increases. This work paves the way for exploring novel nonequilibrium phenomena of quantum impurities in interacting environments.

We present a scheme to generate maxon and roton solitons via the maxon and roton excitations of a Rydberg-dressed Bose-Einstein condensate (BEC). We show that the strong, long-range Rydberg-Rydberg interaction between Rydberg atoms can drastically alter the linear excitation spectrum of the quasiparticles (phonons) on the homogeneous background of the BEC, which displays obvious maxon-roton character and can be tuned actively by adjusting the strength of the Rydberg-Rydberg interaction and Rydberg blockade radius. We also show that the system supports both bright maxon and dark roton solitons if the center wave numbers of excited wave packets are chosen respectively to be those of the maxon and roton. Moreover, we corroborate that both the maxon and roton solitons are dynamical stable during the evolution if system parameters are kept in the domain where the homogeneous background of the BEC is modulationally stable. The results reported are beneficial not only for understanding the physical property of Rydberg-dressed BECs, but also for creating and actively manipulating new types of nonlinear matter-wave excitations in cold atomic gases.

As is well known, unital Pauli maps can be eternally non-CP-divisible. In contrast, here we show that in the case of nonunital maps, eternal non-Markovianity in the nonunital part is ruled out. In the unital case, the eternal non-Markovianity can be obtained by a convex combination of two dephasing semigroups, but not all three of them. We study these results and ramifications arising from them.

Probabilistic cellular automata with deterministic updating are discrete quantum systems. They are characterized by a probability distribution over initial configurations. We employ the quantum formalism for an investigation of random probabilistic cellular automata for which the properties of the deterministic updating are randomly distributed over space and time. We are interested in a possible continuum limit for a very large number of cells or space points. We consider bits with two colors, moving to the left or right on a linear chain. At randomly distributed scattering points they change direction and color. A numerical simulation reveals the typical features of quantum systems. We find particular initial probability distributions which reemerge periodically after a certain number of time steps, as produced by the periodic evolution of energy eigenstates in quantum mechanics. Using a description in terms of wave functions allows us to introduce statistical observables for momentum and energy. They characterize the probabilistic information without taking definite values for a given bit configuration, with a conceptual status similar to temperature in classical statistical thermal equilibrium. Conservation of energy and momentum are essential ingredients for the understanding of the evolution of the stochastic probabilistic automata. This evolution resembles in some aspects a single Dirac fermion in two dimensions with a generalized random potential.

We investigate how local distinguishability can restrict global properties of states shared between two parties. We begin exploring how nonlocality becomes limited by local state discrimination and observe a nontrivial tradeoff between Clauser-Horne-Shimony-Holt (CHSH) violation and success probability of local discrimination. We extend our findings to bounding the maximally entangled state fidelity and global observables such as the energy. Our results show that local state discrimination can become a powerful tool to limit global behaviors, e.g., from entangled adversaries in quantum cryptography.

The ability to route quantum states between arbitrary nodes in a multinode network is one of the many facets required to build future large-scale quantum computing devices. Quantum routing can be implemented based on chiral dynamics, while their related research stays in three-node networks. In this paper, we give the target Hamiltonian for realizing chiral dynamics in arbitrary $N$-node networks. Based on the derived Hamiltonian, we present key features of chiral state transfer in multinode spin and bosonic networks. For the realistic implementation of the required Hamiltonian, we propose a modulation scheme to generate the matched effective Floquet Hamiltonian. Furthermore, we numerically simulate the multinode chiral dynamics with realistic parameters in superconducting circuits, and the results clearly show multinode chiral state transfer. Our work provides a universal and fundamental framework for understanding chiral dynamics in multinode networks. These findings will stimulate quantum state transfer, quantum routing, and nonreciprocal circulators in multinode networks.

Surface codes have gained widespread popularity as quantum error-correction codes due to their unique structural feature that encoders and decoders can be implemented by leveraging interactions between physically neighboring qubits. The implementational advantage of surface codes has driven extensive research into decoding algorithms for surface codes, aimed at improving error-rate performance and/or reducing decoding complexity. In this paper, we propose a low-complexity postprocessing algorithm that effectively resolves failures of a syndrome-based belief-propagation (SB-BP) decoder for surface codes. In particular, we carefully analyze the topological structure of surface codes and present a method for selecting reliable qubits, enabling efficient recovery operator identification through a simple syndrome matching technique with a lookup table. Furthermore, we present an efficient way to construct lookup tables tailored to the proposed postprocessing algorithm. Numerical results demonstrate that the proposed postprocessing algorithm requires substantially reduced complexity as compared to that of a competing postprocessing algorithm, the ordered statistics decoding in the depolarizing error model, while providing the same logical error-rate (LER) performance. It is also demonstrated that the combination of SB-BP decoding and the proposed postprocessing algorithm outperforms minimum weight perfect matching, a more computationally expensive decoding algorithm, in terms of LER and threshold at drastically reduced complexity.