The Heisenberg microscope provides a powerful mental image of the measurement process of quantum mechanics (QM), attempting to explain the uncertainty relation through an uncontrollable backaction from the measurement device. However, Heisenberg's proposed backaction uses features that are not present in the QM description of the world, and according to Bohr not present in the world. Therefore, Bohr argues, the mental image proposed by Heisenberg should be avoided. Later developments by Bell and Kochen-Specker show that a model that contains the features used for the Heisenberg microscope is in principle possible but must necessarily be nonlocal and contextual. In this paper we will reexamine the measurement process within a restriction of QM known as Stabilizer QM (SQM), that still exhibits, for example, Greenberger-Horne-Zeilinger nonlocality and Peres-Mermin contextuality. The reexamination will use a recent extension of SQM, the Contextual Ontological Model (COM), where the system state gives a complete description of future measurement outcomes reproducing the quantum predictions, including the mentioned phenomena. We will see that the resulting contextual Heisenberg microscope backaction can be completely described within COM, and that the associated randomness originates in the initial state of the pointer system, exactly as in the original description of the Heisenberg microscope. The presence of contextuality, usually seen as prohibiting ontological models, suggests that the contextual Heisenberg microscope picture could perhaps be enabled in general QM.

A discrete time crystal (DTC) is an out-of-equilibrium phase of quantum matter that exhibits broken discrete time-translation symmetry, manifested through a robust subharmonic response to periodic driving. Such phases are of interest for quantum memory and fault-tolerant quantum operations. However, conventional DTCs are typically fragile in the presence of environmental dissipation. Here, we propose and experimentally demonstrate a DTC phase in a noninteracting system whose stability is instead enabled by environmental decoherence. The lifetime of this DTC is independent of the initial state and system size, while exhibiting a nontrivial dependence on the driving frequency. Using nuclear magnetic resonance spectroscopy, we realize this phase experimentally and find excellent agreement with theoretical predictions. This environment-assisted discrete time crystal represents a distinct nonequilibrium phase, naturally described within a Liouvillian framework, and offers a promising route toward robust time-crystalline behavior in open quantum systems.

Quantum channel simulation has profound physical significance and essentially imitates the behavior of another quantum channel using free operations and resource states, revealing the minimum resources needed to realize a target channel. However, the deterministic channel-simulation process is not always successful. Therefore, it is necessary to study probabilistic channel simulation. In this paper, we study probabilistic channel simulation under the framework of magic (nonstabilizerness) resource theory. First, we give the upper and lower bounds of the maximal success probability of channel simulation under completely stabilizer-preserving operations. Furthermore, as an example, we give the number of copies of different pure magic states needed to simulate the amplitude-damping channel. We also give the semidefinite programming (SDP) to calculate the maximal success probability when the magic states are mixed resource states. Finally, we also study the maximal success probability of channel simulation under completely positive-Wigner-preserving operations and give the corresponding SDP.

Universal quantum computers require fault-tolerant logical qudits, as qudits naturally align with the simulation of multilevel physical systems. Here we present a general framework and working examples for encoding fault-tolerant logical qudits in finite-dimensional spin systems. We construct distance-3 codewords, distance-5 codewords, and general ($2t+1$)-distance codes that can be implemented using a single physical qudit or a small number of coupled qudits for higher distances while requiring a Hilbert-space dimension significantly smaller than conventional constructions based on multiple logical qubits. Logical operations and error-correction protocols can be implemented with polynomial scaling in the number of elementary operations. We further discuss schematic designs for physical implementation and required single-gate fidelities, which are compatible with current spin qudit platforms. This strategy provides a resource-efficient path toward realizing fault-tolerant logical qudits in finite multilevel physical systems.

Bound entanglement, a weak, yet resourceful, form of quantum entanglement, remains notoriously hard to detect and construct. We address this here by leveraging symmetric random induced states, where positive partial transpose (PPT) bound entanglement arises naturally under partial tracing when proper parameters are selected. We investigate the probability of finding PPT bound entanglement in symmetric random induced states constructed via two methods: partial tracing of symmetric multiqubit pure states, on the one hand, and tracing out a qudit ancilla, on the other hand. For $N>3$ qubits, we demonstrate that bound entanglement naturally emerges under optimal parameters, with a probability of occurrence very close to 1. We show that the two methods produce different varieties of PPT bound entangled states and identify the contexts in which each method offers distinct advantages. These methods provide a versatile toolkit for the generation of large families of random PPT bound entangled states without complex numerical optimization.

Quantum entanglement has long been recognized as an important resource for quantum sensing. In this work, we demonstrate the use of multiple-quantum solid-state NMR for quantum sensing by creating, manipulating, and detecting large clusters of correlated nuclear spins. We show that such clusters can sensitively detect pulse-width jitters in radio-frequency control fields at the level of tens of nanoseconds. By analyzing the response of high-order quantum coherences to these control-field jitters, we investigate the critical interplay between the enhanced sensitivity offered by large coherence orders, their relative distributions, and their varying susceptibility to decoherence. We further demonstrate that, even within a nonuniform distribution of coherence orders, there exists an optimal maximum coherence order that maximizes sensing efficiency. To support our interpretation, we supplement the experimental results with a simplified numerical model that estimates the corresponding quantum Fisher information. These results support the solid-state NMR platform as a valuable testbed for investigating many-body quantum metrology protocols.

Momentum-space close coupling calculations of electron scattering require removal of spurious and unphysical solutions. We demonstrate here that removal of these solutions involve regulator operators that enforce Pauli exclusion selection rules in addition to removing spurious solutions. The form of a regular operator for e-H scattering has already been established, but a general extension to the multielectron case has been elusive. Here we present a general method for scattering on multielectron targets, atoms, or molecules, ensuring that the scattering solutions obey Pauli-exclusion selection rules. The regulator operator is obtained by finding the null space vectors of the $N+1$ electrons of the projectile and target atom scattering system. We demonstrate that this general procedure reduces to the e-H result and provide examples for He- and Li-like targets as well as guidance for implementation.

We present a systematic theoretical study on angular and polarization properties of the prominent $4f\to 3d$ characteristic lines in Ni- to Ga-like gold ions (${\mathrm{Au}}^{51+}$ to ${\mathrm{Au}}^{48+}$), excited by electron impact over a wide range of impact energies. Calculations are performed within the framework of density matrix theory, utilizing the multiconfigurational Dirac-Hartree-Fock and relativistic distorted-wave approaches to obtain excitation energies, cross sections, alignment parameters, and, particularly, the angular anisotropy and linear polarization of the emitted lines. Our results reveal that these lines are strongly anisotropic and linearly polarized, at a level readily observable with current x-ray spectrometers. These characteristics exhibit a pronounced dependence upon the impact energy, peaking near 4 keV, and a strong sensitivity to the ion charge state: lines of ${\mathrm{Au}}^{51+,49+}$ ions are significantly more anisotropic and polarized than those from ${\mathrm{Au}}^{50+,48+}$ ions at comparable energies. The distinct dependencies on electron energy and ion charge state suggest that accurate measurements of these line features could provide a potential diagnostic for determining electron energy and ion species in high-temperature fusion gold plasmas.

We investigate rotational state changes in a single collision of diatomic molecular ions, polar or apolar, with an atomic ion. Rotational state changes may occur since the angular degree of freedom of the molecular ions interacts with the electric field due to the atomic ion. Thanks to the very different time and energy scales of translational and rotational motion, we may treat the collision classically and describe only the rotations quantum mechanically. We first investigate a number of example systems numerically and then derive closed-form approximations for the rotational excitation per collision, depending on the scattering energy and the molecular parameters. These findings provide the basis for estimating the accumulated rotational excitation in sympathetic cooling of molecular ions by laser-cooled atomic ions [J. M. Berglund et al., Phys. Rev. A 113, 042817 (2026)] which involves many single collisions.

Sympathetic cooling of molecular ions through the Coulomb interaction with laser-cooled atomic ions is an efficient tool to prepare translationally cold molecules without, ideally, affecting the internal state of the molecular ions. However, the electric field due to the Coulomb interaction may induce rotational transitions that change the purity of initially quantum state prepared molecules. Here, we use estimates of rotational state changes in single collisions of diatomic ions with atomic ions [J. M. Berglund, M. Drewsen, and C. P. Koch, Phys. Rev. A 113, 042816 (2026)] to determine the overall rotational excitation accumulated over the sympathetic cooling. Considering two different experimental scenarios, that of a molecular ion cotrapped with a single atomic ion and a molecular ion immersed in a Coulomb crystal of atomic ions, we also estimate the cooling time.

We report on efficient rovibrational state-selective loading of single ${\mathrm{H}}_2{}^{+}$ molecular ions into a cryogenic linear Paul trap using ($2+1$) resonance-enhanced multiphoton ionization (REMPI). The ${\mathrm{H}}_2{}^{+}$ ions are created by resonant two-photon excitation of ${\mathrm{H}}_2$ molecules from the $X{}^1{\mathrm{\Sigma }}_g^{+}$ state to the $E,F{}^1{\mathrm{\Sigma }}_g^{+}$ state, followed by nonresonant one-photon ionization. The ions are produced from ${\mathrm{H}}_2$ residual gas and sympathetically cooled by a cotrapped, laser-cooled ${}^9{\mathrm{Be}}^{+}$ ion. By tuning the wavelength of the REMPI laser, we observe the loading of single ${\mathrm{H}}_2{}^{+}$ ions via the (${\nu }^{\prime }=0, L^{\prime }=0,1,2$) rovibrational levels of the $E,F{}^1{\mathrm{\Sigma }}_g^{+}$ intermediate state. We measure the success probability for the production of ${\mathrm{H}}_2{}^{+}$ in the (${\nu }^{+}=0, L^{+}=1$) state via the (${\nu }^{\prime }=0, L^{\prime }=1$) level to be $85\left(6\right)\%$ by quantum logic spectroscopy (QLS) of the hyperfine structure of this rovibrational state. Furthermore, we load an ${\mathrm{H}}_2{}^{+}$ ion via the (${\nu }^{\prime }=0, L^{\prime }=2$) level and confirm its rovibrational state is (${\nu }^{+}=0, L^{+}=2$) by QLS. We perform QLS probes on the ion over $19\mathrm{h}$ and observe no decay of the rotationally excited state. Our work demonstrates an efficient state-selective loading mechanism for single-ion, high-precision spectroscopy of hydrogen molecular ions.

We consider tunnel ionization of atomic argon in a femtosecond-laser pulse of intensity ${10}^{21}–{10}^{22}{\mathrm{W}/\mathrm{cm}}^2$, aiming to investigate the relativistic dynamics and radiation of photoelectrons released from their parent ions inside the laser focus. Radiation of such electrons accelerated along the laser-field propagation direction appears to have moderate power but can be considerably enhanced by a collision with a relatively weak counterpropagating laser pulse. Using the theory of laser-induced tunneling in atoms and ions and that of nonlinear Thomson scattering, we demonstrate that angular distributions and the spectra of emitted photons can serve as a probe of the peak intensity in the focus. The angular distribution of emitted radiation in the plane of polarization and propagation of the ionizing laser beam appears narrow and peaked around an intensity-dependent angle. The sensitivity of angular distributions and spectra of emitted photons to the peak intensity of the ionizing laser pulse can be used as an additional tool for in situ atomic diagnostics of high-power laser beams.

We investigate a non-Hermitian quantum battery based on the Su-Schrieffer-Heeger (SSH) lattice, charged through a parity-time ($\mathcal{PT}$)-symmetric protocol that alternates gain and loss between the two sublattices. The interplay between lattice topology and non-Hermiticity gives rise to both bulk and edge exceptional points (EPs), which govern the charging dynamics. In the topological regime, an edge-state EP appears at a smaller gain-loss strength than the bulk thresholds and gives rise to an additional edge-broken regime absent in the trivial configuration. This topology-specific spectral structure is reflected in the charging dynamics, where the topological phase exhibits more favorable transient and long-time performance in the representative non-Hermitian regimes considered here. We further examine the corresponding Lindblad dynamics, identifying the non-Hermitian model as the conditional no-jump description of the same gain-loss processes. The Lindblad results show that the topological advantage remains visible at the level of stored energy, extractable work, and extractable fraction under unconditional open-system evolution. These findings demonstrate that topology constitutes a genuine physical resource for enhancing the performance of quantum batteries.

Nelson's stochastic mechanics formulates quantum dynamics as a real-time conservative diffusion process in which a particle undergoes Brownian-like motion with a fluctuation amplitude fixed by Planck's constant. While being mathematically equivalent to the Schrödinger formulation, this approach provides an alternative dynamical framework that enables the study of time-resolved quantities that are not straightforwardly defined within the standard operator-based approach. In the present work, Nelson's stochastic mechanics is employed to investigate tunneling-time statistics for bound states in double-well potentials. Using first-passage-time theory within this framework, both the mean tunneling time, $\overline{\tau }$, and the full probability distribution, $p\left(\tau \right)$, are computed. The theoretical predictions are validated through extensive numerical simulations of stochastic trajectories for two representative potentials. For the square double-well potential, analytical expressions for $\overline{\tau }$ are derived and are shown to be in excellent agreement with simulations. In the high-barrier limit, the results reveal a direct relation between the stochastic-mechanical and quantum-mechanical tunneling times, expressed as ${\tau }_{\mathrm{QM}}=(\pi /2)\overline{\tau }$, where ${\tau }_{\mathrm{QM}}$ corresponds to half the oscillation period of the probability of finding the particle in either well. This relation is further confirmed for generic double-well systems through a WKB analysis. As a concrete application, the inversion dynamics of the ammonia molecule is analyzed, yielding an inversion frequency of approximately 24 GHz, in close agreement with experimental observations. These results highlight the potential of stochastic mechanics as a conceptually coherent and quantitatively consistent framework for analyzing tunneling phenomena in quantum systems.

In the stabilizer formalism of quantum computation, the stabilizer states and Clifford gates serve as classical objects since the Gottesman-Knill theorem asserts that any quantum circuit with these elements can be simulated efficiently by classical means. To achieve genuine quantum computation, the magic resource (i.e., nonstabilizer state or non-Clifford gate) is necessary. The quantum $T$ gates are identified as fundamental operations in the paradigm $\text{Clifford}+T$. Among many quantifiers of the magic resource of quantum states, two basic and simple ones are the $L^1$ norm of the characteristic function (Fourier transform) and Wigner negativity. When the magic resource is quantified by the $L^1$ norm, the quantum $T$ gate is optimal (for generating the magic resource from stabilizer states) among all diagonal gates in any prime dimensional system. When the magic resource is quantified by Wigner negativity, the qutrit $T$ gate on ${\mathbb{C}}^3$ is optimal among all diagonal gates, and it remains open whether the quantum $T$ gates are also optimal in other prime dimensional systems. Considering the operational significance of Wigner negativity in quantum computation, in this work, we investigate the optimal diagonal gates for generating Wigner negativity in the ququint system ${\mathbb{C}}^5$. In sharp contrast with the qutrit case ${\mathbb{C}}^3$, we demonstrate that the ququint $T$ gate is suboptimal. Through theoretical analysis and numerical calculations, 500 distinct ququint diagonal gates are identified as optimal for generating Wigner negativity, which surpass the ququint $T$ gate. All these gates are Clifford equivalent, exhibit special symmetries, and lie outside the Clifford hierarchy. We further explore the optimal gates in a family of diagonal gates lying in the Clifford hierarchy, revealing that, while the ququint $T$ gate is not globally optimal, it can still generate considerable Wigner negativity.

We present a unitary-based gradient formulation for variational quantum algorithms (VQAs) that applies to general differentiable cost functions defined by a parametrized quantum circuit composed of Pauli-generated rotations. The gradient is obtained directly from the underlying unitary evolution, without assuming a specific expectation-value form of the cost function. The resulting expressions can be accessed on quantum hardware using the Hadamard and Hilbert-Schmidt tests. We demonstrate the method in variational quantum compilation, where it yields stable and accurate gradient estimates. This unitary-based framework therefore provides a broadly applicable and hardware-compatible tool for gradient evaluation in VQAs.

We develop a hydrodynamic description for the driven-dissipative dynamics of the entanglement negativity, which quantifies the genuine entanglement in mixed-state systems. We focus on quantum quenches in fermionic and bosonic systems subject to linear dissipation, as described by quadratic Lindblad master equations. In the spirit of hydrodynamics, we divide the system into mesoscopic cells. At early times, correlations are generated in each cell by the unitary component of the evolution. Correlations are then transported across different cells via ballistic quasiparticle propagation, while simultaneously evolving under the action of the environment. We show that in the hydrodynamic limit the negativity can be reconstructed from the correlations between the independently propagating quasiparticles. We benchmark our approach considering quenches from both homogeneous and inhomogeneous initial states in the Kitaev chain, the tight-binding chain, and the harmonic chain in the presence of gain or loss dissipation.

High-fidelity quantum state transfer over lossy and thermally populated channels is a major challenge for quantum information processing in quantum networks. Here, we propose a dark-mode-based protocol for high-fidelity quantum state transfer between two distant microwave cavities coupled via a thermal waveguide. By dynamically shaping the microwave cavity-waveguide couplings, the transmission path of quantum information is confined to a decoherence-free subspace, enabling robust transfer even in the presence of thermal photons and waveguide loss. The core mechanism of the protocol is that the dynamical modulation induces an additional effective dissipation channel, which destructively interferes with the waveguide-mediated coupling, thereby realizing genuine dark-mode immunity. Numerical simulations confirm the protocol's robustness and identify key parameters governing fidelity. We also discuss the feasibility of noise-immune quantum communication over experimentally relevant distances. Our work provides a pathway for long-distance quantum network construction and practical applications of future quantum computing systems.

Generative modeling is one of the most promising applications of quantum machine learning, yet training and deploying quantum generative models (QGMs) on near-term hardware remains effectively intractable due to prohibitive gradient estimation and implementation costs. We propose a resource-efficient approach based on shallow instantaneous quantum polynomial-time (IQP) circuits that circumvents these bottlenecks by leveraging efficient classical training while retaining the guarantee of sampling hardness. To validate this approach, we formalize graph generation as a hierarchy of physical correlations, allowing us to map abstract data features—such as edge density and bipartiteness—directly to the quantum observables required to learn them. We validate our protocol through demonstrations both on real hardware (from 28 to 153 qubits) and simulations (28 qubits). Results show that while global structural features exhibit significant degradation beyond 91 qubits, our models achieve high-precision reproduction of local correlations, even up to 153 qubits. These findings establish shallow IQP circuits as a robust, scalable candidate for generative tasks on current noisy intermediate-scale quantum (NISQ) devices.

The verification of quantum entanglement is essential for quality control in quantum communication. In this work we propose an efficient protocol to directly verify the two-qubit entanglement of a known target state through a single-expectation-value measurement. Our method provides exact entanglement quantification using the concurrence measure without performing quantum state tomography. We prove the existence of a unitary transformation that drives a known initial state of a two-qubit system to a designated final state, where the trace over a chosen observable directly yields the concurrence of the initial state. Furthermore, we implement an optimal control process of that transformation and demonstrate its effectiveness through numerical simulations. We also show that this process is robust to environmental noise. Our approach offers advantages in directly verifying entanglement with low circuit depth, making it suitable for industrial-scale quality control of entanglement generation. Our results presented here provide mathematical justification for our earlier computational experiments.