Investigating localization properties of interacting disordered systems plays a crucial role in understanding thermalization and its absence in closed quantum systems. However, simulating such systems on classical computers is challenging due to their complexity. In this work we propose a method to realize $S=1/2$ and 1 quantum spin models with quasiperiodic interactions using Rydberg atoms by utilizing the high tunability of the atoms' spatial positions. We also perform numerical calculations and show that these models host a many-body critical regime, which differs from the ergodic and many-body localized regimes.

Hexagonal optical lattices, emulating graphene and hexagonal boron nitride (h-BN) structures, provide a versatile platform for exploring strongly correlated quantum matter. Using continuous-space exact diagonalization and quantum Monte Carlo simulations, we investigate the phase diagrams of ultracold bosons in honeycomb and h-BN lattices. For the honeycomb lattice, we find significant deviations from the standard Bose-Hubbard model even for strong lattice amplitudes. We observe suppressed Mott insulator lobes and the absence of higher-order insulating phases, which we attribute to strong density-assisted tunneling effects. In the h-BN case, a rich phase diagram emerges, featuring multiple Mott lobes with various sublattice occupations, driven by the interplay of lattice asymmetry, interactions, and particle filling. Our results highlight the necessity of continuous-space treatments for capturing the full complexity of bosonic quantum phases in hexagonal geometries, paving the way for experimental realizations with ultracold atoms and further theoretical work.

Polygon resonators are promising candidates for nanomechanical applications due to their compact architecture and high force sensitivity. Here, we develop a polygon-specific analytical model for perimeter modes by coupling the flexural motion of the polygon sides to tether torsion governed by a stress-modified Timoshenko-Gere equation. The model captures finite-wavelength torsional phase accumulation beyond the conventional short-tether approximation, revealing tether-length-dependent resonances and bending-torsion hybridization. Comparisons with finite-element-method simulations show good agreement in the quasi-one-dimensional regime, while identifying the onset of deviations associated with neglected torsional deformation of the polygon sides. The model therefore provides a useful analytical tool for interpreting and optimizing high-quality-factor ($Q$) polygon resonators for cavity optomechanics and precision sensing.

The manipulation of microscale objects using midinfrared light has recently opened a new direction in optical manipulation, enabling the separation of materials according to their chemical species. Here, we report an enhanced midinfrared optical force exerted on silica micro- and nanoparticles, which can be attributed to light reflection when the laser wavelength is slightly blue-detuned from the siloxane absorption peak. In other words, the wavelength is tuned into the Reststrahlen band between the transverse optical (TO) and longitudinal optical (LO) phonon modes of the siloxane bonds. Translational motion of various microparticles in an evanescent field generated by two midinfrared lasers (8.9 and 9.3 $\mu \mathrm{m}$ lasers) was compared: the 9.3 $\mu \mathrm{m}$ laser excites at the siloxane-bond absorption peak (TO phonon mode), whereas the 8.9 $\mu \mathrm{m}$ laser is blue-detuned from it, falling within the Reststrahlen band. The velocity of silica particles at 8.9 $\mu \mathrm{m}$, especially for nanoparticles, was found to be higher than that at 9.3 $\mu \mathrm{m}$, despite the lower absorbance at 8.9 $\mu \mathrm{m}$. The analytical evaluation of the optical force using the dipole approximation for nanoparticles shows a consistent enhancement of the optical force under blue-detuned conditions, where the phase difference between the incident electric field and the induced polarization is $\pi /2$. From the above evaluation, we conclude that enhanced optical force originates from localized surface phonon polariton excitation within the Reststrahlen band.

Quantum optomechanical STIRAP (Stimulated Raman Adiabatic Passage) is investigated for a system of two mechanical modes coupled to an optical mode. We show analytically that in a system without loss, fractional STIRAP can generate a mechanical Bell state from a single-phonon Fock state of one of the mechanical modes with the other mechanical mode in the vacuum state, and a product state from a coherent state. Relative phases between Fock basis components in the final state of STIRAP are determined by the phonon-number parity of the initial state. Furthermore, the system is numerically studied to determine the effects of dissipation, and it is concluded that high-fidelity entanglement can be achieved via fractional STIRAP using state-of-the-art cryogenic cooling and mechanical devices. Finally, an interferometric protocol using time-reversed fractional STIRAP is proposed to quantify entanglement between two mechanical modes.

We investigated the spectral properties of squeezed light generated via parametric down-conversion in the high-gain regime, considering both unapodized and apodized dispersion-engineered waveguides. The gain-dependent evolution of these states is examined starting from the low-gain regime, which includes both highly correlated and nearly uncorrelated cases. For the unapodized configuration, our simulated results show a monotonic increase in spectral purity with gain, whereas for some of the apodized configuration, they exhibit a nonmonotonic dependence, initially decreasing and then recovering at higher gain. By combining Schmidt-mode analysis with a group-velocity-based interpretation, we explain why different dispersion conditions exhibit distinct gain-dependent behavior, specifically that rapid purification occurs when the pump group velocity lies between those of the signal and idler. Our study shows that the evolution of spectral purity is governed primarily by the underlying dispersion of the waveguide. These results demonstrate that dispersion engineering and parametric gain can be jointly exploited to tailor the spectral-mode structure of squeezed-light sources, enabling their optimization for a broad range of quantum applications.

Highly efficient transfer of quantum resources including quantum excitations, states, and information on coupled bosonic networks is an important task in quantum physics and quantum information science. Here we propose a bipartite-graph framework to characterize quantum excitation transfer in coupled bosonic networks. This is achieved by diagonalizing the intermediate subnetwork between the sender and the receiver to construct a bipartite-graph configuration, and hence this treatment can be understood from the viewpoint of network deformation. We examine the covariance matrix of the coupled bosonic networks in both the original and bipartite-graph representations. In particular, we investigate quantum excitation transfer in both the finite and infinite intermediate-normal-mode cases and show the dependence of the transfer efficiency on the network configurations and system parameters. We find the bounds of maximally transferred excitations for various network configurations and reveal the underlying physical mechanisms. We also discover that the dark-mode effect will degrade the excitation transfer efficiency. Our findings provide a new insight for the design and optimization of networks in physics, information theory, and complex system science.

We study a surface-state electron on liquid helium in a tilted magnetic field. The tilt couples the cyclotron ladder to the vertical Rydberg-like subbands of the same electron and thereby realizes a self-coupled Landau-subband Hamiltonian. In the far-detuned regime, the cyclotron line acquires a state-dependent shift described by standard second-order perturbation theory. The resulting expression identifies the cyclotron resonance as a direct probe of the dynamical polarizability of the vertical ladder. The theory is intrinsically multilevel. Exact diagonalization confirms a broad microwave window in which sizable state-dependent cyclotron shifts are expected while the system remains dispersive.

The theoretical efficiency of classical shadow tomography is predicated on a perfect Haar-random unitary ensemble, yet this mathematical ideal remains physically unattainable in near-term hardware. Here, we report the experimental characterization of a hardware-induced systematic error floor on integrated photonic processors: an operational Hardware Horizon, where the reconstruction error undergoes a sharp crossover. While the error initially obeys the predicted statistical scaling $\mathcal{O}\left(M^{-1/2}\right)$ in a variance-dominated regime, it abruptly saturates at a floor determined by the spectral distortions of the realized unitary group, marking a transition to a bias-dominated regime. By deriving a phenomenological error model, we decouple the competing mechanisms of static coherent spectral distortion and dynamic decoherence, demonstrating that this device-specific noise floor imposes a systematic saturation limit that statistical accumulation cannot overcome. These findings establish that the utility of shadow tomography on NISQ (noisy intermediate-scale quantum) hardware is defined by a specific scaling law involving hardware parameters, necessitating active compensation strategies to bridge the gap between theoretical purity and the noisy reality of integrated photonics.

We investigate single-photon scattering in a waveguide quantum electrodynamics system in both the Markovian and the non-Markovian regimes, where a giant $\mathrm{\Lambda }$-type atom is coupled to two waveguides via different atomic transitions at two separated points. The phases of coupling strengths between the giant atom and waveguides are considered. In the Markovian regime, with a proper choice of phases, including the phases accumulated by photons traveling between coupling points and phase difference between two coupled channels, the incident photons can be manipulated to undergo elastic scattering (frequency-preserving) or inelastic scattering (frequency-converting) process. The frequency conversion with unit efficiency can be achieved and the condition of the optimal frequency conversion is identified. Furthermore, we show that asymmetric frequency conversion can also be achieved by phase control. In addition, our numerical simulations demonstrate that the present scheme shows significant robustness under the influence of moderate experimental parameter errors. In the non-Markovian regime, the scattering spectra show more complicated line shapes and become very sensitive to changes in detuning. More interestingly, under specific conditions, non-Markovianity can induce frequency conversion that cannot occur in the Markovian regime. Multiple narrow asymmetric scattering windows are further obtained, which provides more possibilities for studying asymmetric frequency conversion at off-resonant conditions. Our results may have potential applications in designing quantum devices involving giant atoms.

Prime factorization on quantum processors is typically implemented either via circuit-based approaches such as Shor's algorithm or through analog methods based on adiabatic, annealing, or variational techniques. While Shor's algorithm demands high-fidelity quantum gates, Hamiltonian optimization schemes, with prime factors encoded as degenerate ground states, generally require substantial classical postprocessing to determine control parameters of the driving field. We propose a measurement-based feedback approach that iteratively steers a quantum system towards the target ground state. Akin to an all-quantum implementation, the present approach completely bypasses the computationally expensive classical optimization of the control parameters. As a proof of principle, we experimentally factor the biprime 551 using a three-qubit nuclear magnetic resonance quantum register and numerically analyze the robustness of the method against control-field errors. We further demonstrate scalability by numerically implementing the FALQON factorization of larger biprimes 9167 and 2 106 287 using 5 and 9 qubits, respectively.

Implementing time-evolution operators in shallow quantum circuits is important for quantum simulations. The standard method of Trotterization requires a large number of gates to achieve practical accuracy. Variational quantum simulation (VQS) is an algorithm that calculates the time evolution of a quantum state and can be executed with shallower circuits than Trotterization. However, the operator obtained by VQS evolves only a fixed initial state and is not the time-evolution operator itself. In this paper, we propose variational quantum operator simulation (VQOS), a method to realize time-evolution operators in shallow quantum circuits. This method is based on the variational principle for operators and does not require the implementation of the desired Trotter decomposition of the time-evolution operator. We performed numerical simulations of the VQOS algorithm and successfully implemented the time-evolution operator for closed systems in a quantum circuit that is up to five times shallower than the Trotterization. By providing a more practical way to implement time-evolution operators, VQOS increases the applicability of near-term quantum computers.

The destruction of Aharonov-Bohm (AB) caging by interaction and the emergence of interaction-induced chiral currents in flux lattices are two paradigmatic examples of interaction-driven quantum transport. While various mechanisms, such as bound-state formation and chiral spectral imbalance, have been proposed, a unifying physical picture remains elusive. Here, we employ the concept of evolution-path symmetry (EPS) and its interaction-induced breaking as a framework to understand interaction-induced delocalization in flux lattices. EPS is defined as the invariance of a path's contribution under combined geometric and phase transformations. We demonstrate that in a $\pi$-flux rhombic lattice, interactions break the EPS present in the noninteracting limit by modifying the phase accumulation of many-body paths, thereby lifting the destructive interference responsible for AB caging. Furthermore, we apply this framework to explain interaction-induced chiral transport in flux ladders, where interactions break the phase relationship between symmetric paths, leading to a nonvanishing chiral current. Our work establishes EPS as a powerful tool for understanding transport phenomena beyond conventional eigenstate analysis.

The mean-field yrast spectrum of an SU(2)-symmetric two-component Bose gas confined to a ring geometry is known to exhibit an intricate nonanalytic structure that is absent in single-component systems. In particular, due to the interplay between the species concentration and the atomic interactions, a sequence of plane-wave states can emerge as yrast states at fractional values of the angular momentum per particle. This behavior stands in sharp contrast to the single-component case, where plane-wave states occur only at integer angular momenta. In this paper, we investigate how the structure of the yrast spectrum in a two-component Bose gas is modified by interaction asymmetry. By numerically solving the coupled Gross-Pitaevskii equations for propagating soliton states, we compute the mean-field yrast spectrum, and in particular, determine the critical curves associated with the emergence of various plane-wave yrast states. We find that both the behavior of these critical curves and the mechanisms by which plane-wave yrast states arise depend sensitively on the relative strengths of the inter and intracomponent interactions. When the intracomponent interaction is weaker, the plane-wave yrast states replace soliton states through a continuous evolution, as in the SU(2)-symmetric case, although the conditions for their existence become more restrictive. In contrast, when the intracomponent interaction is stronger, plane-wave yrast states may emerge by overtaking soliton states via branch crossings, and their stability is significantly enhanced. Our results have important implications for the existence and stability of persistent currents in asymmetric, two-component Bose gases.

The expressions of the eigenfunctions of the Hawton photon position operator in configuration space are derived for several classes of wave function, including the Riemann-Silberstein and Landau-Peierls cases. Although these eigenfunctions have a simple form in momentum space, the explicit characterization of their representations in configuration space is rather more involved. We provide closed expressions of these eigenfunctions in terms of linear combinations of the complete elliptic integrals $K\left(\kappa \right)$ and $E\left(\kappa \right)$ with modulus $\kappa$ depending on trigonometric functions of the polar angle. We show that they diverge not only at the value $\mathit{q}$ of the position eigenvalue but also on a plane containing $\mathit{q}$ and that they decay as inverse powers of the distance from $\mathit{q}$.

We investigate bipartite entanglement in qubit hypergraph states across an arbitrary fixed bipartition. Using the real equally weighted representation, the Schmidt rank across the cut can be computed as the real rank of a phase-cleaned cross-cut sign matrix. Whereas graph states admit an exact cut-rank rule, because the cross-cut phase is purely bilinear, hypergraph states typically contain higher-degree cross-cut interactions, for which the cut-rank rule fails. Our approach certifies entanglement by fixing a single computational-basis assignment on a subset of qubits, thereby selecting a submatrix on an active slice. When this restriction removes all higher-degree cross-cut residues, the remaining cross-cut phase becomes bilinear up to cut-local terms. We call the resulting submatrices residual-free bilinear cores and show that they yield an exponential Schmidt-rank lower bound in terms of the ${\mathbb{F}}_2$ rank of an exposed core matrix. We further give a combinatorial sufficient condition, phrased as a disjoint bridge matching, that guarantees large full-rank cores for structured sparse controlled-controlled-Z-type bridge patterns. This condition is sufficient rather than necessary: it is meant to identify a checkable regime where the certificate is provably strong, while the accompanying search-and-verify procedure can certify residual-free cores beyond the explicit matching pattern whenever the verification test succeeds.

We show an explicit $N$-qubit protocol involving one-axis-twisted spin squeezed states that allows for simultaneous phase and dephasing strength estimation with precision that asymptotically matches fundamental quantum metrological bounds. The relevance of the protocol goes beyond this particular model since any uncorrelated noise quantum metrological model that allows for, at most, constant asymptotic quantum enhancement, can be reduced to this problem via an appropriately tailored quantum error-correction procedure.

As quantum systems expand in size and complexity, manual qubit characterization and gate optimization will be a nonscalable and time-consuming venture. Physical qubits have to be carefully calibrated because quantum processors are very sensitive to the external environment, with control hardware parameters slowly drifting during operation, affecting gate fidelity. Currently, existing calibration techniques require complex and lengthy measurements to independently control the different parameters of each gate and are unscalable to large quantum systems. Therefore, fully automated protocols with the desired functionalities are required to speed up the calibration process. This paper aims to propose single-qubit calibration of superconducting qubits under continuous weak measurements from a real physical experimental settings point of view. We propose a real-time optimal estimator of qubit states, which utilizes weak measurements and Bayesian optimization to find the optimal control pulses for gates' design. Our numerical results demonstrate a significant reduction in the calibration process, obtaining a high gate fidelity. Using the proposed estimator, we estimated the qubit state with and without measurement-induced noise and the estimation error between the qubit state and the estimator state is less than $2\%$. With this setup, we drive an approximated $\pi$ pulse with final fidelity of $99.28\%$. This shows that our proposed strategy is robust against the presence of measurement and environmental noise and can also be applicable for the calibration of many other quantum computation technologies.

Cluster states are multipartite entangled states that are maximally connected and resilient to decoherence, making them valuable resources for quantum information processing. Continuous-variable (CV) cluster states have been extensively investigated for such applications. Here we present a pulsed protocol for generating CV cluster states in a phononic quantum network composed of phonon waveguides, mechanical resonators, and optical cavities. A key feature of this architecture is its modular design, where pairs of mechanical modes serve as building blocks with only local, tunable interactions between mechanical and cavity modes. We characterize the generated cluster states through the average nullifier of the CV modes. Our numerical results show that high-quality CV cluster states can be generated with moderate squeezing parameters, whereas strong squeezing and the resulting large phonon occupations can degrade the cluster states in the presence of finite dissipation. We further show that, under moderate squeezing and dissipation, the average nullifier can decrease with increasing system size $N$, demonstrating the scalability of the proposed scheme. As a direct application, we demonstrate that distant mechanical modes can be entangled through local measurements.