Papers

Topological quantum field theory (TQFT) provides a unifying framework for describing topological phases of matter and for constructing quantum error-correcting codes, playing a central role across high-energy physics, condensed matter, and quantum information. A central challenge is to formulate topological order on lattices and to extract the properties of topological excitations from microscopic Hamiltonians. In this work, we construct new classes of lattice gauge theories as Pauli stabilizer models, realizing a wide range of TQFTs in general dimensions. We develop a lattice description of extended excitations and systematically determine their generalized statistics. Our main example is the (4+1)D fermionic-loop toric code, obtained by condensing the $e^2m^2$-loop in the (4+1)D $\mathbb Z_4$ toric code. We show that the loop excitation exhibits fermionic loop statistics: the 24-step loop-flipping process yields a phase of $-1$. Our Pauli stabilizer models realize all twisted 2-form gauge theories in (4+1)D, the higher-form Dijkgraaf-Witten TQFT classified by $H^5(B^2G,U(1))$. Beyond (4+1)D, the fermionic-loop toric codes form a family of $\mathbb Z_2$ topological orders in arbitrary dimensions, realized as explicit Pauli stabilizer codes using $\mathbb Z_4$ qudits. Finally, we develop a Pauli-based framework that defines generalized statistics for extended excitations in any dimension, yielding computable lattice unitary processes to detect nontrivial statistics. For example, we propose anyonic membrane statistics in (6+1)D, as well as fermionic membrane and volume statistics in arbitrary dimensions. We construct new families of $\mathbb Z_2$ topological orders: the fermionic-membrane toric code and the fermionic-volume toric code. In addition, we demonstrate that $p$-dimensional excitations in $2p+2$ spatial dimensions can support anyonic $p$-brane statistics for only even $p$.

We study a periodically driven macrospin system with anisotropic long-range interactions and collective dissipation, described by a Lindblad master equation. In the thermodynamic limit ($N\to\infty$), a mean-field treatment yields classical equations of motion, whose dynamics are characterized via the maximal Lyapunov exponent (MLE). Focusing on the thermodynamic limit, we map out chaotic, quasiperiodic, and periodic phases via bifurcation diagrams, MLEs, and Fourier spectra of evolved observables, identifying classic period-doubling bifurcations and fractal boundaries in the regions of attractors. Finite-size quantum simulations in the Dicke basis reveal that while both quantum and classical systems exhibit diverse dynamical phases, finite-size effects suppress some behaviors present in the thermodynamic limit. The sign of $\lambda_{\mathrm{max}}$ serves as a key indicator of convergence between quantum and classical dynamics, which agree over timescales up to the Lyapunov time. Analysis of the density matrix shows that convergence occurs only when its nonzero elements are sharply localized. However, the nonconvergence does not imply a fundamental difference between quantum and classical dynamics: in chaotic regimes, although the evolution orbits of quantum and classical systems show significant differences, quantum evolution becomes mixed and diffusively explores the Hilbert space, signaling quantum chaos, which can be confirmed by the delocalized nature of the density matrix.

The emergence of statistical mechanics from quantum dynamics is conventionally understood through quantum chaos, the Eigenstate Thermalization Hypothesis (ETH), and canonical typicality, which together explain the thermal behavior of local observables in quantum many-body systems. We provide a distinct mechanism in which, for a quantum many-body system under strong random perturbation, the chaotic behavior of the system's eigenvectors and a constraint on the total energy directly generate a canonical ensemble for the entire system. The canonical ensemble occurs as the first moment of the Porter-Thomas distribution of the system's chaotic eigenstates, and the constraint on the total energy sets the temperature in the ensemble. This yields canonically distributed expectation values without invoking ETH, a microcanonical ensemble, or a subsystem-bath partition for local and global observables. We numerically demonstrate the mechanism for the 1D transverse-field Ising model by showing canonically distributed eigenstate projectors and spin-spin correlators with distinctive temperature dependence of the correlation length. An implementation of this thermalization approach on a quantum computer can be utilized for thermal state preparation.

Randomness generation through quantum-chaotic evolution underpins foundational questions in statistical mechanics and applications across quantum information science, including benchmarking, tomography, metrology, and demonstrations of quantum computational advantage. While statistical mechanics successfully captures the temporal averages of local observables, understanding randomness at the level of higher statistical moments remains a daunting challenge, with analytic progress largely confined to random quantum circuit models or fine-tuned systems exhibiting space-time duality. Here we study how much randomness can be dynamically generated by generic quantum-chaotic evolution under physical, non-random Hamiltonians. Combining theoretical insights with numerical simulations, we show that for broad classes of initially unentangled states, the dynamics become effectively Haar-random well before the system can ergodically explore the physically accessible Hilbert space. Both local and highly nonlocal observables, including entanglement measures, equilibrate to their Haar expectation values and fluctuations on polynomial timescales with remarkably high numerical precision, and with the fastest randomization occurring in regions of parameter space previously identified as maximally chaotic. Interestingly, this effective randomization can occur on timescales linear in system size, suggesting that the sub-ballistic growth of Renyi entropies typically observed in systems with conservation laws can be bypassed in non-random Hamiltonians with an appropriate choice of initial conditions.

Tomographic measurements are the standard tool for characterizing quantum states, yet they are usually regarded only as means for state reconstruction or fidelity measurement. Here, we show that the same Pauli-basis measurements (X, Y, Z) can be directly employed for the certification of nonlocality at no additional experimental cost. Our framework allows any tomographic data - including archival datasets – to be reinterpreted in terms of fundamental nonlocality tests. We introduce a generic, constructive method to generate tailored Bell inequalities and showcase their applicability to certify the non-locality of states in realistic experimental scenarios. Recognizing the stabilizer nature of the considered operators, we analyze our inequalities in the context of witnessing quantum magic - a crucial resource for quantum computing. Our approach requires Pauli measurements only and tests the quantum magic solely through the resources present in the state. Our results establish a universal standard that unifies state tomography with nonlocality certification and its application to quantum magic witnessing, thereby streamlining both fundamental studies and practical applications.

Symmetry-protected topological (SPT) phases in interacting bosonic systems have been widely explored, with many realizations emerging from the interplay of interactions, lattice geometry, and occupancy constraints. Here we investigate a dimerized bosonic lattice model with a local parity coupling and demonstrate that it supports a rich phase diagram containing topological phases at various fillings. Using density matrix renormalization group simulations, we identify two distinct topological regimes absent in the purely dimerized limit: an SPT phase at half filling stabilized by positive parity coupling and a paired-boson topological phase at unit filling, stabilized by negative parity coupling. While the latter is adiabatically connected to a trivial phase and is not symmetry protected in the conventional sense, it exhibits nontrivial topological signatures associated with paired bosons in the constrained Hilbert space. Our results establish local parity coupling as a useful framework for understanding and characterizing topological phases in one-dimensional bosonic systems.

The adaptive derivative-assembled problem-tailored variational quantum eigensolver (ADAPT-VQE) provides a promising approach for simulating highly correlated quantum systems on quantum devices, as it strikes a balance between hardware efficiency, trainability, and accuracy. Although ADAPT-VQE avoids many of the shortcomings of other VQEs, it is sometimes hindered by a phenomenon known as gradient troughs. This refers to a non-monotonic convergence of the gradients, which may become very small even though the minimum energy has not been reached. This results in difficulties finding the right operators to add to the ansatz, due to the limited number of shots and statistical uncertainties, leading to stagnation in the circuit structure optimization. In this paper, we propose ways to detect and mitigate this phenomenon. Leveraging the non-commutative algebra of the ansatz, we develop heuristics for determining where to insert new operators into the circuit. We find that gradient troughs are more likely to arise when the same locations are used repeatedly for new operator insertions. Our novel protocols, which add new operators in different ansatz positions, allow us to escape gradient troughs and thereby lower the measurement cost of the algorithm. This approach achieves an effective balance between cost and efficiency, leading to faster convergence without compromising the low circuit depth and gate count of ADAPT-VQE.

The continuous matrix product state (cMPS) ansatz is a promising numerical tool for studying quantum many-body systems in continuous space. Although it provides a clean framework that allows one to directly simulate continuous systems, the optimization of cMPS is known to be a very challenging task, especially in the case of multi-component systems. In this work, we have developed an improved optimization scheme for multi-component cMPS that enables simulations of bosonic quantum mixtures with substantially larger bond dimensions than previous works. We benchmark our method on the two-component Lieb-Liniger model, obtaining numerical results that agree well with analytical predictions. Our work paves the way for further numerical studies of quantum mixture systems using the cMPS ansatz.

A common challenge in superconducting quantum circuits is the trade-off between strong coupling and computational subspace integrity. We present Mathieu control, which uses a non-resonant two-photon drive to create a selective nonlinear frequency shift. This shift modifies interactions while preserving qubit states, enabling continuous tuning of the ZZ coupling, including full suppression, and integrating single- and two-qubit gates with low leakage. For a qubit-coupler-qubit device, it allows independent ZZ control, facilitating a programmable Heisenberg (XXZ) Hamiltonian. Extended to a five-qubit chain, the system can be reconfigured to simulate dynamics of quantum magnetic phases. Mathieu control thus provides a framework for high-fidelity quantum logic and programmable simulation.

Since an n-qubit circuit consisting of CNOT gates can have up to $\Omega(n^2/\log{n})$ CNOT gates, it is natural to expect that $\Omega(n^2/\log{n})$ Toffoli gates are needed to apply a controlled version of such a circuit. We show that the Toffoli count can be reduced to at most n. The Toffoli depth can also be reduced to O(1), at the cost of 2n Toffoli gates, even without using any ancilla or measurement. In fact, using a measurement-based uncomputation, the Toffoli depth can be further reduced to 1. From this, we give two corollaries: any controlled Clifford circuit can be implemented with O(1) T-depth, and any Clifford+T circuit with T-depth D can be controlled with T-depth O(D), even without ancillas. As an application, we show how to catalyze a rotation by any angle up to precision $\epsilon$ in T-depth exactly 1 using a universal $\lceil\log_2(8/\epsilon)\rceil$-qubit catalyst state.

A parity-time (PT) transition is a spectral transition characteristic of non-Hermitian generators; it typically occurs at an exceptional point, where multiple eigenvectors coalesce. The concept of a PT transition has been extended to Markovian open quantum systems, which are described by the GKSL equation. Interestingly, the PT transition in many-body Markovian open quantum systems, the so-called Lindbladian PT (L-PT) phase transition, is closely related to two classes of exotic nonequilibrium many-body phenomena: continuous-time crystals and non-reciprocal phase transitions. In this review, we describe the recent advances in the study of L-PT phase transitions. First, we define PT symmetry in three distinct contexts: non-Hermitian systems, nonlinear dynamical systems, and Markovian open quantum systems, highlighting the interconnections between these frameworks. Second, we develop mean-field theories of L-PT phase transitions for collective-spin systems and for bipartite bosonic systems with particle-number conservation. Within these classes of models, we show that L-PT symmetry can induce a breaking of continuous time-translation symmetry down to a discrete one, leading to persistent periodic dynamics. We further demonstrate that the L-PT phase transition point is typically a critical exceptional point, where multiple collective excitation modes with zero excitation spectrum coalesce. These findings establish an explicit connection to continuous-time crystals and non-reciprocal phase transitions. Third, going beyond the mean-field theory, we analyze statistical and quantum properties, such as purity and quantum entanglement indicators of time-independent steady states for several specific models with the L-PT symmetry. Finally, we discuss future research directions for L-PT phase transitions.

This work presents a Python framework named after the General Equation of Quantum Image Encoding (GEQIE). The framework creates the image-encoding state using a unitary gate, which can later be transpiled to target quantum backends. The benchmarking results, simulated with different noise levels, demonstrate the correctness of the already implemented encoding methods and the usability of the framework for more sophisticated research tasks based on quantum image encodings. Additionally, we present a showcase example of Cosmic Web dark-matter density snapshot encoding and high-accuracy retrieval (PCC = 0.995) to demonstrate the extendability of the GEQIE framework to multidimensional data and its applicability to other fields of research.

Thermodynamic uncertainty relations (TURs) bound the precision of currents by entropy production, but quantum transport of noncommuting (non-Abelian) charges challenges standard formulations because different charge components cannot be monitored within a single classical frame. We derive a process-level matrix TUR starting from the operational entropy production $\Sigma = D(\rho'_{SE}\|\rho'_S\!\otimes\!\rho_E)$. Isolating the experimentally accessible bath divergence $D_{\mathrm{bath}}=D(\rho'_E\|\rho_E)$, we prove a fully nonlinear, saturable lower bound valid for arbitrary current vectors $\Delta q$: $D_{\mathrm{bath}} \ge B(\Delta q,V,V')$, where the bound depends only on the transported-charge signal $\Delta q$ and the pre/post collision covariance matrices $V$ and $V'$. In the small-fluctuation regime $D_{\mathrm{bath}}\geq\frac12\,\Delta q^{\mathsf T}V^{-1}\Delta q+O(\|\Delta q\|^4)$, while beyond linear response it remains accurate. Numerical strong-coupling qubit collisions illustrate the bound and demonstrate near-saturation across broad parameter ranges using only local measurements on the bath probe.

Intracavity absorption spectroscopy (ICAS) is a well-established technique for detecting weak absorption signals with ultrahigh sensitivity. Here, we extend this concept to magnetometry using nitrogen-vacancy (NV) centers in diamond. We introduce laser intracavity absorption magnetometry (LICAM), a concept that is in principle applicable to a broader class of optical quantum sensors, including optically pumped magnetometers. Using an electrically driven, edge-emitting diode laser that operates self-sustainably, we show that LICAM enables highly sensitive magnetometers operating under ambient conditions. Near the lasing threshold, we achieve a 475-fold enhancement in optical contrast and a 180-fold improvement in magnetic sensitivity compared with a conventional single-pass geometry. The experimental results are accurately described by a rate-equation model for single-mode diode lasers. From our measurements, we determine a projected shot-noise-limited sensitivity in the $\mathrm{pT}\,\mathrm{Hz}^{-1/2}$ range and simulate that, with realistic device improvements, shot-noise limited sensitivities down to the $\mathrm{fT}\,\mathrm{Hz}^{-1/2}$ scale are attainable.

Uncertainty is a fundamental and important concept in quantum mechanics. In this work, using the technique in matrix theory, we propose an uncertainty relation of four observables and show that the uncertainty constant is tight. It is argued that this method can deal with the several known uncertainty relations for two, three and four observables in a unified way. The result is also compared with other uncertainty relations of four observables.

We extend the Worldline Monte Carlo approach to computationally simulating the Feynman path integral of non-relativistic multi-particle quantum-mechanical systems. We show how to generate an arbitrary number of worldlines distributed according to the (free) kinetic part of the multi-particle quantum dynamics and how to simulate interactions between worldlines in the ensemble. We test this formalism with two- and three-particle quantum mechanical systems, with both long range Coulomb-like interactions between the particles and external fields acting separately on the particles, in various spatial dimensionality. We extract accurate estimations of the ground state energy of these systems using the late-time behaviour of the propagator, validating our approach with numerically exact solutions obtained via straightforward diagonalisation of the Hamiltonian. Systematic benchmarking of the new approach, presented here for the first time, shows that the computational complexity of Wordline Monte Carlo scales more favourably with respect to standard numerical alternatives. The method, which is general, numerically exact, and computationally not intensive, can easily be generalised to relativistic systems.

Distributed quantum computing architectures require high-performance quantum interconnects between quantum information processing units, while previous implementations have been fundamentally limited by transmission line losses. Here, we demonstrate a low-loss interconnect between two superconducting modules using an aluminum coaxial cable, achieving a bus mode quality factor of 1.7e6. By employing SNAIL as couplers, we realize inter-modular state transfer in 0.8 {\mu}s via a three-wave mixing process. The state transfer fidelity reaches 98.2% for quantum states encoded in the first two energy levels, achieving a Bell state fidelity of 92.5%. Furthermore, we show the capability to transfer high-dimensional states by successfully transmitting binomially encoded logical states. Systematic characterization reveals that performance constraints have shifted from transmission line losses (contributing merely 0.2% infidelity) to module-channel interface effects and local Kerr nonlinearities. Our work advances the realization of quantum interconnects approaching fundamental capacity limits, paving the way for scalable distributed quantum computing and efficient quantum communications.

Scaling quantum computing beyond a single device requires networking many quantum processing units (QPUs) into a coherent quantum-HPC system. We propose the Modular Entanglement Hub (ModEn-Hub) architecture: a hub-and-spoke photonic interconnect paired with a real-time quantum network orchestrator. ModEn-Hub centralizes entanglement sources and shared quantum memory to deliver on-demand, high-fidelity Bell pairs across heterogeneous QPUs, while the control plane schedules teleportation-based non-local gates, launches parallel entanglement attempts, and maintains a small ebit cache. To quantify benefits, we implement a lightweight, reproducible Monte Carlo study under realistic loss and tight round budgets, comparing a naive sequential baseline to an orchestrated policy with logarithmically scaled parallelism and opportunistic caching. Across 1-128 QPUs and 2,500 trials per point, ModEn-Hub-style orchestration sustains about 90% teleportation success while the baseline degrades toward about 30%, at the cost of higher average entanglement attempts (about 10-12 versus about 3). These results provide clear, high-level evidence that adaptive resource orchestration in the ModEn-Hub enables scalable and efficient quantum-HPC operation on near-term hardware.

The performance and scalability of semiconductor quantum-dot (QD) qubits are limited by electrostatic drift and charge noise that shift operating points and destabilize qubit parameters. As systems expand to large one- and two-dimensional arrays, manual recalibration becomes impractical, creating a need for autonomous stabilization frameworks. Here, we introduce a method that uses the full network of charge-transition lines in repeatedly acquired double-quantum-dot charge stability diagrams (CSDs) as a multidimensional probe of the local electrostatic environment. By accurately tracking the motion of selected transitions in time, we detect voltage drifts, identify abrupt charge reconfigurations, and apply compensating updates to maintain stable operating conditions. We demonstrate our approach on a 10-QD device, showing robust stabilization and real-time diagnostic access to dot-specific noise processes. The high acquisition rate of radio-frequency reflectometry CSD measurements also enables time-domain noise spectroscopy, allowing the extraction of noise power spectral densities, the identification of two-level fluctuators, and the analysis of spatial noise correlations across the array. From our analysis, we find that the background noise at 100~$\mu$\si{\hertz} is dominated by drift with a power law of $1/f^2$, accompanied by a few dominant two-level fluctuators and an average linear correlation length of $(188 \pm 38)$~\si{\nano\meter} in the device. These capabilities form the basis of a scalable, autonomous calibration and characterization module for QD-based quantum processors, providing essential feedback for long-duration, high-fidelity qubit operations.

We investigate the quantum correlations in an axially symmetric hybrid qubit-qutrit system subjected to different noisy environments. We first introduce a physical model and analyze its Hamiltonian structure, emphasizing the role of hybrid dimensionality and axial symmetry. The effects of decoherence are then examined under two local noise mechanisms, namely dephasing and phase-flip channels, acting on the qubit and qutrit subsystems in both symmetric and asymmetric configurations. Quantum correlations are quantified using negativity to capture entanglement and quantum discord based on linear entropy to characterize more general nonclassical correlations. Our results show that both thermal fluctuations and phase noise lead to a monotonic degradation of quantum correlations, with increasing temperature accelerating coherence loss and inducing entanglement sudden death at finite temperatures. While negativity vanishes abruptly under sufficiently strong noise, quantum discord persists beyond the entanglement threshold, revealing residual quantum correlations in mixed states. We further demonstrate that asymmetric noise configurations significantly enhance the robustness of both entanglement and discord by partially shielding coherence in the less affected subsystem. A comparative analysis reveals that phase-flip noise is more destructive than pure dephasing, leading to faster suppression of quantum correlations.

Recent advances in time-resolved cathodoluminescence have enabled ultrafast studies of single emitters in quantum materials with femtosecond temporal resolution. Here, we develop a quantum theory modeling the dynamics of free electrons interacting with quantum emitters in arbitrary initial states. Our analysis reveals that a free electron can induce transient coherent oscillations in the populations when the system is initially prepared in a coherent superposition of its states. Moreover, the electron energy spectrum exhibits a clear signature of the quantum coherence and sensitivity to the transition frequency of the emitter. These coherence effects manifest themselves as oscillations in the zero-loss peak of the spectral energy-loss probability. Our findings pave the way for characterization of quantum-coherent dynamics of individual quantum emitters by electron-probes.

Spatially entangled photon pairs (biphotons) generated by spontaneous parametric down-conversion offer unique opportunities for quantum imaging, but image-plane biphoton correlations are difficult to observe with camera-based detectors. Previous camera-based biphoton imaging experiments have relied on photon-counting detection, which necessitates operation deep in the photon-sparse regime and requires extremely low dark rates. Here, we demonstrate the detection of spatial biphoton joint probability distributions in both the image plane and the pupil plane (also termed "near-field plane" and "far-field plane" respectively) using a conventional scientific CMOS camera operated in linear mode. We work at mesoscopic intensity levels, corresponding to a photon flux approximately four orders of magnitude higher than typical photon-counting approaches. From the measured image- and pupil plane correlations, we observe position and momentum correlations consistent with an EPR-type entanglement witness. A tailored correlation analysis suited for image plane imaging suppresses detector artifacts and intensity fluctuations, enabling acquisition with significantly fewer frames. Our results demonstrate that spatially entangled-light imaging can be performed efficiently with standard imaging hardware, extending quantum imaging techniques beyond the photon-counting regime.

Pure-state manifestations of geometric phase are well established and have found applications across essentially all branches of physics, yet their generalization to mixed-state regimes remains largely unexplored experimentally. The Uhlmann geometric phase offers a natural extension of pure-state paradigms and can exhibit a topological character. However, observation of this invariant is impeded by the incompatibility between Uhlmann parallel transport and Hamiltonian dynamics, as well as the difficulty of preparing topologically nontrivial mixed states. To address this challenge, we report an experimentally accessible protocol for directly measuring the mixed-state topological invariant. By engineering controlled nonunitary dynamics in a photonic quantum walk, we prepare topologically nontrivial mixed states from a trivial initial state. Furthermore, by machine-learning the full density matrix in momentum space, we directly extract the quantized geometric phase of the nontrivial mixed states. These results highlight a geometric phase framework that naturally extends to open quantum systems both in and out of thermal equilibrium.

We investigate the quantum Mpemba effect in a dissipative Dicke model, which consists of a spin-1/2 ensemble coupled to a bosonic mode, which in turn is coupled to a bosonic bath. We derive a sufficient criterion for occurrence of the quantum Mpemba effect, characterized by quantum coherence, in this model. We introduce the phenomenon of role reversal in the Mpemba effect, wherein changes in the system parameters invert the relaxation ordering of a given pair of initial states that exhibit the Mpemba effect, causing the faster-relaxing state to become slower and vice versa. We find the existence of role reversal in Mpemba effect for this Dicke model using different relaxation measures, including differential quantum coherence and entanglement, and trace distance, between the time-evolved and steady states.

Floquet engineering offers an unparalleled platform for realizing novel non-equilibrium topological phases. However, the unique structure of Floquet systems, which includes multiple quasienergy gaps, poses a significant challenge to classification using conventional analytical methods. We propose a novel unsupervised machine learning framework that employs a kernel defined in momentum-time ($\boldsymbol{k},t$) space, constructed directly from Floquet-Bloch eigenstates. This approach is intrinsically data-driven and requires no prior knowledge of the underlying topological invariants, providing a fundamental advantage over prior methods that rely on abstract concepts like the micromotion operator or homotopic transformations. Crucially, this work successfully reveals the intrinsic topological characteristics encoded within the Floquet eigenstates themselves. We demonstrate that our method robustly and simultaneously identifies the topological invariants associated with both the $0$-gap and the $\pi$-gap across various symmetry classes (1D AIII, 1D D, and 2D A), establishing a robust methodology for the systematic classification and discovery of complex non-equilibrium topological matter.

We argue that Hopf-algebra deformations of symmetries – as encountered in non-commutative models of quantum spacetime – carry an intrinsic content of $operator$ $entanglement$ that is enforced by the coproduct-defined notion of composite generators. As a minimal and exactly solvable example, we analyze the $U_q(\mathfrak{su}(2))$ quantum group and a two-qubit realization obtained from the coproduct of a $q$-deformed single-spin Hamiltonian. Although the deformation is invisible on a single qubit, it resurfaces in the two-qubit sector through the non-cocommutative coproduct, yielding a family of intrinsically nonlocal unitaries. We compute their operator entanglement in closed form and show that, for Haar-uniform product inputs, their entangling power is fully determined by the latter. This provides a concrete mechanism by which non-commutative symmetries enforce a baseline of entanglement at the algebraic level, with implications for information dynamics in quantum-spacetime settings and quantum information processing.

Sampling tasks have been successful in establishing quantum advantages both in theory and experiments. This has fueled the use of quantum computers for generative modeling to create samples following the probability distribution underlying a given dataset. In particular, the potential to build generative models on classically hard distributions would immediately preclude classical simulability, due to theoretical separations. In this work, we study quantum generative models from the perspective of output distributions, showing that models that anticoncentrate are not trainable on average, including those exhibiting quantum advantage. In contrast, models outputting data from sparse distributions can be trained. We consider special cases to enhance trainability, and observe that this opens the path for classical algorithms for surrogate sampling. This observed trade-off is linked to verification of quantum processes. We conclude that quantum advantage can still be found in generative models, although its source must be distinct from anticoncentration.

We construct holonomic quantum gates for qubits that are encoded in the near-degenerate vibrational $E$-doublet of a deformable three-body system. Using Kendall's shape theory, we derive the Wilczek–Zee connection governing adiabatic transport within the $E$-manifold. We show that its restricted holonomy group is $\mathrm{SU}(2)$, implying universal single-qubit control by closed loops in shape space. We provide explicit loops implementing a $\pi/2$ phase gate and a Hadamard-type gate. For two-qubit operations, we outline how linked holonomic cycles in arrays generate a controlled Chern–Simons phase, enabling an entangling controlled-$X$ (CNOT) gate. We present a Ramsey/echo interferometric protocol that measures the Wilson loop trace of the Wilczek–Zee connection for a control cycle, providing a gauge-invariant signature of the non-Abelian holonomy. As a physically realizable demonstrator, we propose bond-length modulations of a Cs($6s$)–Cs($6s$)–Cs($nd_{3/2}$) Rydberg trimer in optical tweezers and specify operating conditions that suppress leakage out of the $E$-manifold.

We solve the static isoperimetric problem underlying the Mandelstam-Tamm bound. Among one-dimensional confining potentials with a fixed spectral gap, we prove that the harmonic trap is the unique maximizer of the ground-state position variance. As a consequence, we obtain a sharp geometric quantum speed-limit bound on the position-position component of the quantum metric, and we give a necessary-and-sufficient condition for when the bound is saturated. Beyond the exact extremum, we establish quantitative rigidity. We control the Thomas-Reiche-Kuhn spectral tail and provide square-integrable structural stability for potentials that nearly saturate the bound. We further extend the analysis to magnetic settings, deriving a longitudinal necessary-and-sufficient characterization and transverse bounds expressed in terms of guiding-center structure. Finally, we outline applications to bounds on static polarizability, limits on the quantum metric, and benchmarking of trapping potentials.

Double perovskites containing 4d–4f interactions provide a platform to study complex magnetic phenomena in correlated systems. Here, we investigate the magnetic ground state and quasiparticle excitations of the fascinating double perovskite system, Ba$_2$DyRuO$_6$, through Time of flight (TOF) neutron diffraction (TOF), inelastic neutron scattering (INS), and theoretical modelling. The compound Ba$_2$DyRuO$_6$ is reported to exhibit a single magnetic transition, in sharp contrast to most of the other rare-earth (R) members in this family, A$_2$RRuO$_6$ (A = Ca/Sr/Ba), which typically show magnetic ordering of the Ru ions, followed by R-ion ordering. Our neutron diffraction results confirm that long-range antiferromagnetic order emerges at $T_\mathrm{N} \approx 47$~K, primarily driven by 4d–4f Ru$^{5+}$–Dy$^{3+}$ exchange interactions, where both Dy and Ru moments start to order simultaneously. The ordered ground state is a collinear antiferromagnet with Ising character, carrying ordered moments of $\mu_{\mathrm{Ru}} = 1.6(1)~\mu_\mathrm{B}$ and $\mu_{\mathrm{Dy}} = 5.1(1)~\mu_\mathrm{B}$ at 1.5~K. Low-temperature INS reveals well-defined magnon excitations below 10~meV. SpinW modelling of the INS spectra evidences complex exchange interactions and the presence of magnetic anisotropy, which governs the Ising ground state and accounts for the observed magnon spectrum. Combined INS and Raman spectroscopy reveal crystal-electric-field (CEF) excitations of Dy$^{3+}$ at 46.5 and 71.8~meV in the paramagnetic region. The observed CEF levels are reproduced by point-charge calculations consistent with the $O_h$ symmetry of Dy$^{3+}$. A complementary machine-learning approach is used to analyse the phonon spectrum and compare with INS data. Together, these results clarify the origin of phonon and magnon excitations and their role in the ground-state magnetism of Ba$_2$DyRuO$_6$.