In recent years, graph neural networks have achieved notable success in processing complex structured data. However, traditional graph neural networks still face challenges in capturing long-range dependencies and higher-order structural information within graphs. To address these limitations, we propose two physics-informed graph neural network architectures based on the continuous time quantum walk-inspired complex graph convolution mechanism to accomplish the small-node and large-node classification tasks. Specifically, node features are mapped into the complex domain and subsequently propagated through a continuous time quantum walk, which enables effective capture of intricate spatial correlations across the graph topology. Furthermore, the framework incorporates complex-valued activation functions and complex weight update strategies, thereby enhancing both the nonlinear modeling capacity and training stability of the model. Experimental results on protein structure datasets show that the proposed methods consistently outperform standard graph convolutional networks and other state-of-the-art approaches in terms of classification accuracy and convergence speed, thus demonstrating the promise of quantum-inspired complex domain graph convolution for handling highly structured data.

Quantum key distribution (QKD) provides information-theoretic security grounded in the fundamental laws of physics. Nevertheless, practical imperfections can introduce side channels that expose QKD systems to quantum hacking, especially passive attacks that are inherently difficult to detect. In this study, we experimentally and theoretically investigate the upper limit of the backflash attack—a representative passive side-channel threat. Using a fully equipped fiber-based QKD receiver, we demonstrate the feasibility of the attack and reveal its limited capability in distinguishing quantum states. We further develop a theoretical framework to quantify the maximum distinguishability achievable by an eavesdropper, taking into account the broadband spectral nature of backflash photons. The analysis shows that Eve can extract effective key information from at most 95.7% of the backflash photons. Based on these findings, we evaluate the secure key rate of a decoy-state Bennett-Brassard 1984 (BB84) QKD system under backflash attack. Our results provide a quantitative assessment of the vulnerability of QKD systems to backflash emissions and offer a general methodology to evaluate the practical security of QKD systems.

Characterizing complexity and criticality in quantum systems requires diagnostics that are both computationally tractable and physically insightful. We apply a measure of quantum state complexity for $n$-qubit systems, defined as the divergence between the Shannon or von Neumann entropy of the computational basis distribution and the second-order Rényi entropy. This quantity has already been used earlier termed as structural entropy and it is particularly powerful as the Rényi entropy is directly related to state purity, linear entropy, and the inverse participation ratio, providing a clear physical grounding. While other Rényi orders could be used, the second order offers a deep and established connection to these key physical quantities. We first validate the measure in canonical noise channels, showing it peaks at the boundary between quantum and classical regimes. We then demonstrate its power in many-body physics. For systems exhibiting a many-body localization transition, including deformed random matrix ensembles and a disordered Heisenberg spin chain, the complexity measure reliably signals the crossover from integrable or localized to quantum-chaotic or ergodic phases. Crucially, the maximum complexity occurs in the nonergodic yet extended states at the transition, precisely capturing the critical region where the system is neither fully localized nor thermalized. Furthermore, within the chaotic phase, the measure correlates with the survival probability of local excitations, revealing a spectrum of thermalization properties. Our results establish that the entropic complexity is a simple, versatile, and effective probe for identifying nontrivial quantum regimes and transitions giving a new and alternative insight into such systems.

A compelling application of quantum computers with thousands of qubits is quantum simulation. Simulating fermionic systems is both a problem with clear real-world applications and a computationally challenging task. To simulate a system of fermions on a quantum computer, one has to first map the fermionic Hamiltonian to a qubit Hamiltonian. The most popular such mapping is the Jordan-Wigner encoding, which suffers from inefficiencies caused by the high weight of some encoded operators. As a result, alternative local encodings have been proposed that solve this problem at the expense of a constant factor increase in the number of qubits required. Some such encodings possess local stabilizers, i.e., Pauli operators that act as the logical identity on the encoded fermionic modes. A natural error mitigation approach in these cases is to measure the stabilizers and discard any run where a measurement returns a −1 outcome. Using a high-performance stabilizer simulator, we classically simulate the performance of a local encoding known as the Derby-Klassen encoding and compare its performance with the Jordan-Wigner encoding and the ternary tree encoding. Our simulations use more complex error models and significantly larger system sizes (up to $18\times 18$) than in previous work. We find that the high sampling requirements of postselection methods with the Derby-Klassen encoding pose a limitation to its applicability in near-term devices and call for more encoding-specific circuit optimizations.

We present a theoretical study of the Wichmann and Kroll correction to the one-loop vacuum polarization (VP) to all orders in $\alpha Z$. We consider electronic, muonic, and antiprotonic atoms for a wide range of nuclear charge numbers and explicitly investigate the influence of finite nuclear size effects and different nuclear models. Moreover, we place special emphasis on circular Rydberg states in the exotic atoms as they have recently attracted interest as a tool to perform isolated tests of strong-field QED. We find that the higher-order vacuum polarization is strongly enhanced in exotic atoms and remains large enough in highly excited Rydberg states that an accurate treatment is crucial for the analysis of upcoming spectroscopy experiments such as antiProtonic Atom X-ray spectroscopy (PAX). Moreover, our calculations show that the VP contribution to the Lamb shift in these exotic Rydberg states has almost no dependence on the structure of the nucleus.

Calculations of fitting parameters, describing electrostatic potentials $U\left(r\right)$ and atomic densities $\rho \left(r\right)$ in a simple analytical form, are presented for neutral atoms with the nuclear charges $Z=93$–120. The data are obtained based on calculations of wave functions in the relativistic Dirac-Fock-Slater approximation with the extended distribution of the nuclear charge. The $U\left(r\right)$ and $\rho \left(r\right)$ functions are approximated by the sum of three Yukawa potentials with six fitting parameters as has been done for $Z=1–92$ by other authors.

We numerically investigate the ground-state phases and quench dynamics of spin-orbit coupled spin-1 Bose-Einstein condensates with ferromagnetic and antiferromagnetic interactions. For finite Rabi coupling, the system exhibits zero-momentum, elongated zero-momentum, and stripe phases, while in the zero-Rabi coupling limit the superstripe wave phases emerge. Varying the attractive density-density ($c_0$) and spin-exchange ($c_2$) interactions induces the transition from stripe and superstripe phases to the elongated zero-momentum phase, characterized by miscibility and polarization. The condensate remains miscible in the zero-momentum phase and partially miscible for the elongated, stripe, and superstripe phases. Quenching in Rabi coupling stabilizes the condensate, while spin-orbit coupling quenching leads to fluctuations or the formation of complex patterns, with the stripe phase exhibiting the vanishing of the zeroth spin component over time. Our results may offer valuable insights into the engineering of complex quantum phases in ultracold atomic gases.

We perform free-fall experiments with a charge-neutral, optically levitated nanoparticle. This is achieved using an optical tweezer that can be rapidly toggled on and off and vertically displaced, enabling the particle to be released and recaptured after each free fall. The particle is insensitive to electric fields due to its charge neutrality, and during free evolution, is not subject to photon recoil heating. We achieve free-fall durations of up to $0.25\mathrm{ms}$ and observe a nearly 200-fold increase in the particle's position uncertainty at recapture. The current limit on the free-fall time arises from the performance of the initial cooling step. By implementing linear feedback techniques and reducing the background pressure, we expect to perform millisecond-scale free-fall experiments in an ultrahigh vacuum, opening new opportunities for generating large delocalizations of levitated objects.

In this work we investigate nonreciprocal interactions in waveguide-based systems within the non-Markovian regime. We show that by designing the coherent interaction between two spatially separated small atoms in the form of steplike modulations and by properly balancing the strengths of coherent and waveguide-induced dissipative interactions, it is possible to achieve a highly efficient unidirectional interaction between these two atoms. The resulting asymmetric instantaneous population distributions arise purely from the mathematical structure of the system and are influenced by multiple factors, including the time delay, phase, amplitude of the coherent interaction, and form of the steplike modulations. We further extend our analysis to giant-atom systems with various topological configurations. Our results reveal that, unlike in the case of small atoms, energy not only can be transferred asymmetrically between two giant atoms but also can be preserved without decay in the long-time limit under appropriate conditions. By incorporating temporal effects, this work provides a valuable reference for exploring long-distance unidirectional energy exchange in waveguide-based systems.

The field of force sensing in hybrid optomechanical systems is pivotal for developing quantum technologies. Achieving sensitivity that surpasses the standard quantum limit (SQL) is a central goal, but this is often hindered by practical limitations such as operating power and thermal noise. In this theoretical work, we investigate how qubit-oscillator coupling and Kerr nonlinearity can be harnessed to overcome these challenges. We demonstrate that while each nonlinearity can independently enable surpass-SQL sensitivity, their joint effect significantly enhances performance, widening the detection bandwidth and substantially increasing robustness to thermal fluctuations. Our detailed analysis reveals that these two nonlinear mechanisms act as distinct tools for quantum noise reduction. Qubit-oscillator coupling is effective at suppressing both back-action and shot noise, whereas Kerr nonlinearity provides a powerful, yet frequency-localized suppression of these noise components. Our findings establish this hybrid system as a promising platform for developing highly sensitive and robust quantum sensors capable of operating under less-than-ideal conditions.

Retrieving classical information from quantum systems is central to quantum information processing. As a more general task than quantum state discrimination, which focuses on identifying the exact state, quantum state exclusion only requires ruling out options, revealing fundamental limits of information extraction from quantum systems. In this work, we study the limits and protocols of conclusive exclusion for quantum states generated by group actions, establishing explicit criteria for when such exclusion is possible. For systems with complex symmetries, including finite and compact Lie groups, we derive a sufficient condition for conclusive exclusion based on the initial state's amplitudes and the group's structure. As applications to special groups such as Abelian groups, we establish necessary and sufficient conditions for conclusive state exclusion and generalize the Pusey-Barrett-Rudolph result to a wider range of scenarios. Finally, we explore zero-error communication via conclusive exclusion of quantum states and derive a lower bound on the feedback-assisted and no-signaling-assisted zero-error capacity of classical-quantum channels generated by group actions.

The level of adiabaticity determines many properties of time-dependent quantum systems. However, a reliable and easy-to-apply criterion for checking and tracking it remains an open question, especially for complex many-body systems. Here, we test techniques based on recently proposed metrics to characterize and track adiabaticity quantitatively. We investigate the time evolution of x-ray photoemission in metals, which exhibits a strongly out-of-equilibrium character, a continuum of energies, and the Anderson orthogonality catastrophe—a nightmarish scenario for this type of test. Our results show that the metrics-based methods remain valid. In particular, we demonstrate that the natural local density distance can not only track adiabaticity but also provide information not captured by the corresponding Bures or trace distances regarding the system's dynamics. In the process, we derive a simple analytical solution that accurately describes the evolution of a tight-binding chain with a time-dependent localized scattering potential for an extensive range of parameters, and we establish an explicit upper limit for this local density distance in terms of the trace distance. We also demonstrate that, for x-ray photoemission, the quantum adiabatic criterion, as commonly used, fails to predict and track adiabaticity. The local particle density is typically much more straightforward to compute than the corresponding quantum state and is experimentally measurable; this makes the tested method extremely appealing.

Strong symmetries enforce nontrivial quantum entanglement patterns on the stationary states of symmetric open quantum dynamics. Specifically, noncommuting conserved quantities lead to long-range quantum entanglement even for infinite-temperature mixed states within fixed symmetry sectors. Leveraging the commutant algebra framework, we show that for any bipartition of such states, regardless of their geometry, various bipartite entanglement measures—including exact and asymptotically exact entanglement costs and squashed entanglement, which are generally intractable for a generic many-body mixed state—can be exactly computed. In particular, we focus on strongly symmetric maximally mixed states arising from the Temperley-Lieb model, which features quantum Hilbert-space fragmentation with exponentially large (in system size) non-Abelian commutants. We find that while both the logarithmic negativity and the "exact" entanglement cost for equal-size bipartitions scale with the volume of the system, the entanglement of formation, squashed entanglement, entanglement cost, and distillable entanglement exhibit subextensive scaling. We relate this separation in entanglement measures to a parametric difference between the entanglement costs of exact and asymptotically exact state preparations and infer it to be a consequence of a particular pattern of quantum Hilbert-space fragmentation.

The discrimination of coherent states is a crucial component in quantum communication with continuous variables, especially in quantum key distribution protocols (CV-QKD), which rely on the ability to distinguish among different coherent states to establish a shared secret key between two parties. Here, we propose and analyze a strategy for distinguishing among $N$ phase-symmetric coherent states, which optimally takes unambiguous discrimination (UD) to the deterministic regime, at the inevitable cost of having nonzero probability of error. Despite the disturbance introduced by the separation map used in the UD process, we show that for $N>2$, the “failure” states of UD retain residual information about the original input states, which can be further used for discrimination. Rather than discarding inconclusive outcomes as in conventional UD, we show that the “failure” states of UD can be optimally recycled by performing a sequential minimum-error discrimination (MED). This strategy, which we call information recycling (IR), combines the benefits of both MED and optimal UD: It always provides conclusive results while allowing for a subset of those results to be error-free, which are identifiable by an ancillary system. We characterize the disturbance introduced by the state separation map by the infidelity between input and failure states, demonstrating that it lower bounds the error probability in the recycling stage. Furthermore, in the low-amplitude regime (relevant for long-distance CV-QKD applications) we show that the state separation achieves significant success while introducing relatively low disturbance to the input states after failed events. Our results open up additional possibilities for adaptive and sequential discrimination protocols in continuous-variable settings, and could potentially be used in the design of next-generation receivers in quantum communication.

Dick noise, arising from aliasing of local-oscillator (LO) fluctuations through dead time, limits the stability of leading optical lattice clocks. We propose a multiple-excitation protocol that implements coherence buffering: Most atoms are shelved in protected Zeeman manifolds, and controlled deexcitation releases fresh subensembles for sequential clock-transition interrogations within a single preparation. This timelike multiplexing raises the effective duty cycle without lengthening the interrogation beyond the coherence limit or shortening the fixed dead time. Sensitivity-function analysis shows a train of lobes in time and suppression of low-order Fourier components $g^{\prime }\left(m\right)$ that couple most strongly to LO flicker ($1/f$) noise. Incorporating the quantum projection noise–limited atom number, coherence limited $T_i$, and reservoir loss, we find a nonmonotonic optimum in the achievable interrogation count versus LO stability; for representative flicker levels ${\sigma }_0\in [4\times {10}^{-16},8\times {10}^{-15}]$, the Dick-noise contribution is reduced by approximately $2.4–5.65\mathrm{dB}$. Time-domain Monte Carlo simulations using synthesized $1/f$ noise agree with the analytical predictions, and a noise decomposition based on experimentally reported power-law LO-noise parameters shows a nearly constant flicker fraction (approximately equal to $0.89$) across interrogation numbers. More broadly, shelving-deexcitation coherence buffering is a portable “prepare once, interrogate many'' primitive for quantum sensors, simulators, and processors.

Native multiqubit gates could be essential for bridging the gap from current noisy devices to future utility-scale quantum computers, as they can substantially reduce circuit depth for near-term applications on noisy devices and may also lower the physical overhead of fault-tolerant quantum computation. Here we introduce a scalable protocol for implementing native multicontrolled gates on fluxonium qubits, supporting an arbitrary number of control qubits ($N>1$) while remaining compatible with existing single- and two-qubit gate realizations. Our approach leverages engineered interactions in noncomputational state manifolds to enable qubit-state selective transitions, which is activated for the direct implementation of $\left(C^{\otimes N}\right)Z$ gates. We show that in square lattices with fluxonium qubits, $CCZ, CCCZ$, and $CCCCZ$ gates with errors around 0.01 (0.001) are achievable, with gate lengths of $50\left(100\right)\text{ns}, 100\left(250\right)\text{ns}$, and $150\left(300\right)\text{ns}$, respectively. Looking forward, integrating these native multicontrolled gates with primitive single- and two-qubit gate sets within a single quantum processor could significantly enhance flexibility in circuit synthesis and offer a promising alternative pathway toward utility-scale quantum computing.

Vacuum fluctuations are known to be responsible for dispersion attraction forces, and in more general and dynamical approaches, for friction forces. In this paper, we study a system of two neutral atomic oscillators, rotating around each other, and calculate friction forces linear in their angular velocity. This system requires a precise and complete understanding of the radiation reaction effect, both on the dipolar dynamics and on the atomic center of mass. We treat the nonretarded (short range) and retarded (long range) regimes at zero or finite temperature. At very long distances, the individual thermal friction, known since the work of Einstein and Hopf, is retrieved as the dominant contribution. The model also allows for a calculation of the attractive forces in the above regimes as presented in a companion paper. The two main results are the nontrivial absence of linear friction at zero temperature, at any distance range, as long as the dipolar approximation holds, and a new, thermally activated interatomic dissipation.

Fluctuation-induced dispersion forces between atoms or molecules are known to show different regimes, depending on interatomic distances and temperature. They were generally developed in two kinds of models, alternatively considering quantum fluctuations of matter or fluctuating electromagnetic fields of the vacuum. In this paper, we present a comprehensive study of van der Waals attraction forces between two neutral atoms, in which we retrieve nonretarded (short range), retarded (long range) and finite-temperature dispersion forces, connecting continuously all regimes. This approach also permits a general calculation of vacuum friction presented in a companion paper.

We describe a novel mechanism of charged particles confinement by a rapidly oscillating magnetic field. It relies on the renowned dynamical stabilization phenomenon and provides a foundation for a new class of the magnetic traps. The dynamical magnetic confinement of charges and spin magnetic moments has a number of remarkable properties which make it a promising alternative to the existing techniques in a wide range of physical problems.