Quantum speed limit characterizes the fastest rate at which a quantum system can evolve in the quantum-state space. It plays a significant role in the search for more efficient quantum control technologies. The previous work demonstrated that, within a stochastic quantum dynamical framework for open quantum systems, the quantum speed limit bound can be geometrically established via the evolution of the joint system-environment state. However, its explicit expression and tightness are generally unknown. In this paper, going beyond the usual Born-Markovian approximation, we provide a unified scheme to derive the exact expression of the quantum speed limit for a general discrete-variable open quantum system. More importantly, we demonstrate that the quantum speed limit based on the joint system-environment state can be tighter than that obtained from the traditional convolutionless master equation approach. Enriching the characterization schemes of the quantum speed limit, our result may have potential applications for some quantum manipulation tasks in practical noisy situations.

Practical large-scale quantum computation requires both efficient error correction and robust implementation of logical operations. Three-dimensional (3D) color codes are promising candidates for fault-tolerant quantum computation due to their transversal non-Clifford gates, but efficient decoding remains challenging. In this work, we extend previous decoders for two-dimensional color codes [S.-H. Lee et al., Quantum 9, 1609 (2025)], which are based on the restriction of the decoding problem to a subset of the qubit lattice, to three dimensions. Including boundaries of 3D color codes, we demonstrate that the 3D restriction decoder achieves optimal scaling of the logical error rate and a threshold value of 1.55(6)% for code-capacity bit- and phase-flip noise, which is almost a factor of 2 higher than previously reported for this family of codes [N. Delfosse, Phys. Rev. A 89, 012317 (2014); S. Turner et al., arXiv:2003.11602]. We furthermore present qCodePlot3D, a python package for visualizing two-dimensional and 3D color codes, error configurations, and decoding paths, which supports the development and analysis of such decoders. These advancements contribute to making 3D color codes a more practical option for exploring fault-tolerant quantum computation.

Estimating the fidelity between an unknown quantum state and a fixed target is a fundamental task in quantum information science. Direct fidelity estimation (DFE) enables this without full tomography by sampling observables according to a target-dependent distribution. However, existing approaches face notable trade-offs. Grouping-based DFE achieves strong accuracy for small systems but suffers from exponential scaling, and its applicability is restricted to Pauli measurements. In contrast, classical-shadow-based DFE offers scalability but yields lower accuracy on structured states. In this work, we address these limitations by developing two classes of operator-aware shadow importance sampling algorithms using informationally overcomplete positive operator-valued measures. Instantiated with local Pauli measurements, our algorithm improves over the grouping-based algorithms for Haar-random states. For structured states such as the Greenberger-Horne-Zeilinger (GHZ) and W states, our algorithm also eliminates the exponential memory requirements of previous grouping-based methods. Numerical experiments confirm that our methods achieve state-of-the-art performance across Haar-random, GHZ, and W targets.

Electron tunneling through a potential barrier is a salient quantum effect behind multiple practical applications such as, for example, in electronics and scanning tunneling microscopy. Often considered within the quasistatic picture, where the tunneling current flows through the system in response to an applied dc field, electron tunneling can be brought into the realm of ultrafast phenomena when triggered by the electric field of a short optical pulse. Ultrafast scanning tunneling microscopy thus emerges as a result of the combination of the ultimate spatial and temporal resolution, offering unprecedented perspectives for studying electron and phonon dynamics at surfaces. In this work, using the time-dependent density-functional theory, we address the electron tunneling triggered by short (single-cycle and several-cycle) optical pulses in narrow metallic gaps under conditions relevant for actual experiments. We identify photon-assisted tunneling with one-photon, two-photon, and higher-order-photon absorption, and discuss the effect of the tunneling barrier, applied bias, and strength of the optical field on the transition from photon-assisted tunneling (weak optical fields) to the optical-field emission at strong optical fields. Numerical single-electron calculations and an analytical strong-field theory model are implemented to gain deeper insights into the results of the time-dependent density-functional theory calculations. Additionally, our parameter-free calculations allow us to retrieve and explain recent experimental results on optically induced transport in narrow metallic gaps under an applied dc bias.

We present the experimental detection of signatures of coherent three-body interactions, often masked by stronger two-body effects, through nonequilibrium spin dynamics induced by controllably quenching lattice-confined spinor gases. Three-body interactions are precisely characterized through both real-time and frequency-domain analyses of the observed dynamics. Our results, well described by an extended Bose-Hubbard model, further demonstrate the importance of three-body interactions for correctly determining atom distributions in lattice systems and have applications in quantum sensing via spin singlets. The techniques demonstrated in this work can be directly applied to other atomic species, offering a promising avenue for future studies of higher-body interactions with broad relevance to strongly interacting quantum systems.

The evolution of quantum gases, released from traps, is studied through hydrodynamics, both analytically and numerically, in one and two dimensions. In particular, we demonstrate the existence of long time self-similar solutions of the Euler equations, for the density and velocity fields, and derive the scaling exponents as well as the scaling functions. We find that the expanding gas develops a shock-like front and the size of the cloud grows in time as a power law. We relate the associated exponent to that appearing in the corresponding equation of state of the quantum gas. Furthermore, we study the relaxation dynamics of a trapped quantum gas and show that the resulting steady state is in excellent agreement with that derived analytically. Our hydrodynamic approach is versatile and can be used to unravel several other far-from-equilibrium collective phenomenon of extreme nature, relevant to the growing experimental interests in quantum gases.

We develop a systematic theoretical approach to incorporate the effects of a static white-noise disorder into the BCS-BEC crossover near the critical temperature $T_c$ of the superfluid transition. Starting from a functional-integral formulation in momentum-frequency space, we derive an effective thermodynamic potential that fully accounts for Gaussian fluctuations of the order-parameter field and its coupling to the disorder potential. The effective action, expanded to second order in both the disorder potential and the bosonic field, naturally involves third- and fourth-order terms arising from the logarithmic expansion near $T_c$. By providing a controlled description of pairing fluctuations and disorder effects, this formalism correctly recovers the well-established BCS and BEC limits. This ensures a consistent physical foundation for analyzing the entire BCS-BEC crossover, effectively anchoring the intermediate regime between these two analytically robust end points. The approach applies equally to continuum and lattice systems and provides a natural framework for generalizations to multiband models.

We present a theoretical model for a transversally driven Bose-Einstein condensate coupled to an optical cavity. We focus on the interplay between different coherent couplings, which can trigger a structural phase transition, known as the superradiant phase transition. Our approach, based on band-structure theory and a mean-field description, enables a comprehensive analysis of the nature of the system's excited modes, precursing the phase transitions. By incorporating dissipative couplings, intrinsic to these systems, we find non-Hermitian phenomena such as the coalescence of crossing precursor modes and the emergence of exceptional points. The general formulation of our model allows us to explain the role of an angle between the transverse pump and the cavity deviating from ${90}^{\circ }$. This offers us a unified perspective on the plethora of different implementations of such systems.

In trapped Bose-Einstein condensates, interaction quenches, which are abrupt changes of the interaction strength typically implemented via Feshbach tuning, are a practical and widely used protocol to address far-from-equilibrium collective modes. Using both numerical Gross-Pitaevskii and analytical schemes we study these interaction-quench-induced collective modes in a harmonically trapped two-dimensional Bose-Einstein condensate contrasting the behavior found at low and high energies. In the low-lying regime, we characterize realistic circumstances in which there is a breakdown of the expected scale invariance so that the collective excitations follow hydrodynamic theory instead of the predictions given by SO(2,1) conformal symmetry. In the high-energy regime, we focus on important trap effects associated with acoustic oscillations, which have been of interest experimentally. This comprehensive analysis of the collective excitations in trapped two-dimensional Bose-Einstein condensates is experimentally accessible. Through their frequencies and damping, this reflects an important built-in spectroscopy of such many-body states.

We demonstrate the formation of Floquet doublons in the periodically driven extended non-Hermitian two-particle Bose-Hubbard model, where in the strong interaction limit an artificial manipulation of two-photon tunneling can lead to topological phase transitions. Meanwhile, both the trivial and the topological nontrivial doublon states are gapless in the low-frequency driving regime, and nontrivial topological features can be identified via the extraordinary peaks of the inverse participation ratio. In the high-frequency limit, the time-independent effective Hamiltonian is analytically obtained via the Magnus expansion, where through the transfer matrix approach we illustrate the remarkable phenomenon that the skin localization center of Floquet doublons can be turned to different sides upon changing the driving frequency, the two-particle interaction strength, or the amplitude of two-photon tunneling despite the single-boundary favored localization induced by the fixed nonreciprocal tunneling. Finally, we present that such Floquet doublons with abnormal skin localization will not penetrate to continuum due to the existence of pronounced energy gaps.

Superradiant Raman scattering of rubidium atoms was explored in the experiment [Bohnet et al., Nature (London) 484, 78 (2012)] to prove the concept of superradiant laser. However, a careful analysis of the experiment indicates that the reported distorted pulse is different from what is expected for a superradiant pulse, and the displayed spectrum seems to be broader than what is expected from the theory. To resolve these inconsistencies, we have gone beyond the effective theory employed in the experimental paper by treating the rubidium atoms as three-level systems, and coupling them with a dressed laser and an optical cavity. Our simulations show that the distorted pulse is caused by a dynamical dispersive coupling introduced by Raman-induced population transfer, and the broader spectrum is shifted due to AC Stark shift effect of the dressing laser. Our study establishes not only the consistency between the results in this experiment and those in other superradiant experiments, but also suggests that a further experiment might be required to verify the narrow spectrum of superradiant laser through the Raman transition.

Waveguide quantum electrodynamics (wQED) has become a central platform for studying collective light-matter interactions in low-dimensional photonic environments. While conventional wQED systems rely on uniform chirality or reciprocal emitter-waveguide coupling, we propose a structured wQED framework, where the coupling directionality of each emitter can be engineered locally to control excitation transport in an atom-nanophotonic interface. For different combinations of patterned coupling directionalities of the emitters, we identify four representative configurations that exhibit distinct dynamical behaviors: centering, wave-like, leap-frog, and dispersion excitations. Spectral analysis of the effective non-Hermitian Hamiltonian reveals that these dynamics originate from interferences among subradiant eigenmodes. Variance analysis further quantifies the spreading of excitation as functions of interatomic spacing and global chirality, showing tunable localization-delocalization transitions. Including nonguided losses, we find that the transport characteristics remain robust for realistic coupling efficiencies ($\beta \ge 0.99$). These results establish structured wQED as a practical route to manipulate excitation localization, coherence, and transport through programmable directionality patterns, paving the way for controllable subradiant transport and chiral quantum information routing.

One-axis-twisting (OAT) interaction is a pivotal resource for manipulating quantum states of atomic ensembles, enabling spin squeezing, atomic-cat-state generation, and weak-phase amplification. Current implementations of OAT dynamics predominantly rely on the Tavis-Cummings model of light-atoms coupling; however, this approach inevitably introduces an additional Stark term that entangles the light with the atoms, which compromises the unitarity of OAT evolution and thereby degrades the OAT-based control precision. Here we propose a scheme based on a driven Tavis-Cummings model to achieve near-unitary OAT evolution. We demonstrate that both constant and time-varying driving of an atoms-cavity hybrid system can realize near-unitary OAT evolution, albeit with distinct coupling strength. Furthermore, when atomic dissipation is taken into account, we find that the time-varying-driving scheme exhibits superior resistance to decoherence. Our approach is broadly applicable to a variety of atomic platforms, including cold atoms, trapped ions, and nitrogen-vacancy centers.

We derive relativistic Maxwell-Bloch equations for potential applications in astronomical environments, where various radiative processes are known to occur, including the maser action and Dicke's superradiance. We show that for both phenomena a radiating system's response is preserved at different relative velocities between the system's rest frame and the observer, while the relevant timescales and the radiation intensity transform as expected from relativistic considerations. We verify that the level of coherence between groups of emitters traveling at different speeds is unchanged in all reference frames. We also derive relativistic versions of the maser equations applicable in the steady-state regime.

Contextuality is a defining feature that separates the quantum from the classical descriptions of physical systems. Within the marginal-scenario framework, noncontextual models are characterized by the existence of a single joint probability distribution consistent with all measurable contexts, while contextual models violate this condition. Building on this approach, we introduce a general method to analyze contextuality in terms of stochastic linear maps that effectively model invasive measurements on an otherwise classical statistics. These maps transform probabilities within the noncontextuality polytope, which includes all classical probabilities, into probabilities that may lie outside the polytope, while preserving the compatibility structure of the scenario at hand. We derive general consistency conditions that such maps must satisfy to represent admissible invasive measurements, and we fully identify them for a paradigmatic example of contextuality for a single three-level quantum system. Furthermore, we introduce a quantifier of contextuality based on the minimal invasiveness required to reproduce a given probability distribution, which offers a distinct approach on how to evaluate the degree of contextuality in a general scenario.

The Lindblad equation determines the time evolution of the density operator of open quantum systems. While valid for any system size, its use is, in practice, restricted to prototype and surrogate models with the aim of tackling specific aspects of the overall quantum complexity of a multiatomic system. Path integral molecular dynamics (PIMD) instead provides static and dynamical quantum statistical averages of physical observables for systems in equilibrium composed of up to thousands of atoms over timescales up to nanoseconds, under the condition that short-time quantum coherence is not relevant for the properties of interest. PIMD relies on the well-established technique of molecular dynamics with its associated classical trajectories. However, it cannot describe a direct time evolution of a system and its convergence to a stationary state in situations out of equilibrium. In this work we analyze the link between the Lindblad equation and PIMD; specifically, we will discuss how PIMD can actually be used to calculate the time evolution of ensemble-averaged physical observables and their convergence to a stationary state for situations out of equilibrium, bypassing the need for explicitly solving the Lindblad equation. Yet, at the same time, the Lindblad equation and PIMD are linked to one another through a formal relation of equivalence, which provides an argument for the consistency of PIMD results, namely, the positivity of the density operator at any time. A numerical study of a prototype system, which is of interest in chemical physics, will be used to showcase the method.

Counterfactual reasoning plays a crucial role in exploring hypothetical scenarios, by comparing some consequent under conditions identical except as results from a differing antecedent. David Lewis' well-known analysis evaluates counterfactuals using a hierarchy of desiderata. These were, however, built upon a deterministic classical framework, and whether it could be generalized to indeterministic quantum theory has been an open question. In this article, we propose a formalism for quantum counterfactuals in which antecedents are measurement settings. Unlike other approaches, it nontrivially answers questions such as, “Given that a photon-detector, observing an atom's fluorescence, clicked at a certain time, what would a field-quadrature detector have measured, if it had been used instead?”

The surface code is one of the leading quantum error correction codes for realizing large-scale fault-tolerant quantum computing (FTQC). One major challenge in realizing surface-code-based FTQC is the extremely large number of qubits required. To mitigate this problem, fusing multiple code words of the surface code into a densely packed configuration has been proposed. It is known that by using dense packing, the number of physical qubits required per logical qubit can be reduced to approximately three-fourths compared to simply placing surface-code patches side by side. Despite its potential, concrete deformation procedures and quantitative error-rate analyses have remained largely unexplored. In this work, we present a detailed code-deformation procedure that transforms multiple standard surface-code patches into a densely packed, connected configuration, along with a conceptual microarchitecture to utilize this dense packing. We also propose a cnot gate scheduling for stabilizer measurement circuits that suppresses hook errors in the densely packed surface code. We performed circuit-level Monte Carlo noise simulation of densely packed surface codes using this gate scheduling. The numerical results demonstrate that as the code distance of the densely packed surface code increases and the physical error rate decreases, the logical error rate of the densely packed surface code becomes lower than that of the standard surface code. Furthermore, we find that only when employing hook-error-avoiding syndrome extraction can the densely packed surface code achieve a lower logical error rate than the standard surface code, while simultaneously reducing the space overhead.