Papers

We study a non-Hermitian extension of the Creutz ladder with generic non-reciprocal hopping. By mapping the ladder onto two decoupled non-Hermitian Su–Schrieffer–Heeger (SSH) chains, we uncover a rich structure in parameter space under different boundary conditions. Under periodic boundary conditions, the spectrum admits a fine-tuned line in parameter space with entirely real eigenvalues, while deviations from this line induce a real–complex spectral transition without crossing exceptional points. In contrast, an exact analytical diagonalization under open boundary conditions reveals extended regions in parameter space with purely real or purely imaginary spectra, separated from complex spectral domains by exceptional lines. The intersections of these exceptional lines define triple-junction points where distinct spectral regimes meet, giving rise to a structured phase diagram that is absent under periodic boundary conditions. We further show that flat bands in this system can occur both as Hermitian diabolical points and as non-Hermitian exceptional points, known as exceptional flat bands, where the dynamics is more stringent than in the Hermitian case, leading to distinct spectral and dynamical signatures.

To compute approximate solutions for combinatorial optimization problems, we describe variational methods based on the product state (PS) and matrix product state (MPS) ansätze. We perform variational energy minimization with respect to a quantum annealing Hamiltonian and utilize randomness by embedding the approaches in the metaheuristic iterated local search (ILS). The resulting quantum-inspired ILS algorithms are benchmarked on maximum cut problems of up to 50000 variables. We show that they can outperform traditional (M)PS methods, classical ILS, the quantum approximate optimization algorithm and other variational quantum-inspired solvers.

Through their ability to achieve cryogenic levels of noise performance while operating at room temperature, optically-pumped, solid-state (OPSS) masers show great promise as quantum sensors, oscillators, and amplifiers. We here demonstrate maser oscillation in a microwave cavity containing a crystal of pentacene-doped para-terphenyl (ptc:ptp) pumped by a single, chip-scale LED. Here, unlike previous work, the size of the pump source does not dominate the size of the maser system as a whole. This miniaturization is achieved through invasive optical pumping in the form of a waveguide, the tip of which is embedded into the maser crystal. Using experimental measurements combined with microwave and optical simulations, we find that our approach offers at least a factor-of-2 enhancement in cooperativity over end-on optical excitation. We use our simulations to define a figure of merit for maser pumping efficiency, and conclude that there remains significant headroom to improve the performance of ptc:ptp masers through improved optical design.

Divalent atoms have emerged as powerful alternatives to alkalis in ultracold atom platforms, offering unique advantages arising from their two-electron structure. Among these species, ytterbium (Yb) is especially promising, yet its anionic properties and its Rydberg spectrum remain comparatively unexplored. In this work, we perform a first and comprehensive experimental and theoretical investigation of ultralong-range Rydberg molecules (ULRMs) of $^{174}$Yb in $6sns\,^1S_0$ Rydberg states across nearly two decades in principal quantum number $n$ and three orders of magnitude in molecular binding energy. Using the Coulomb Green's function formalism, we compute Born-Oppenheimer molecular potentials describing the Rydberg atom in the presence of a ground-state perturber and achieve quantitative agreement with high-resolution molecular spectra. This enables the extraction of low-energy electron-Yb scattering phase shifts, including the zero-energy $s$-wave scattering length and the positions of two spin-orbit split $p$-wave shape resonances. Our results provide strong evidence that the Yb$^{-}$ anion exists only as a metastable resonance.% We additionally show the sensitivity of ULRM spectra to the atomic quantum defects, using this to determine the quantum defect of the $6s23f\, ^1F_3$ state. Together, these findings establish Yb ULRMs as a powerful probe of electron-Yb interactions and lay essential groundwork for future Rydberg experiments with divalent atoms.

We propose a ground state entanglement probe for gapped, two-dimensional quantum many-body systems that involves taking powers of reduced density matrices in a particular geometric configuration. This quantity, which we denote by $\omega_{\alpha,\beta}$, is parameterized by two positive real numbers $\alpha, \beta$, and can be seen as a “Rényi-like" generalization of the modular commutator – another entanglement probe proposed as a way to compute the chiral central charge from a bulk wave function. We obtain analytic expressions for $\omega_{\alpha,\beta}$ for gapped ground states of non-interacting fermion Hamiltonians as well as ground states of string-net models. In both cases, we find that $\omega_{\alpha,\beta}$ takes a universal value related to the chiral central charge. For integer values of $\alpha$ and $\beta$, our quantity $\omega_{\alpha,\beta}$ can be expressed as an expectation value of permutation operators acting on an appropriate replica system, providing a natural route to measuring $\omega_{\alpha,\beta}$ in numerical simulations and potentially, experiments.

We investigate the dynamical phases that emerge in collective spin models subjected to a spatially non-uniform periodic drive. Taking the paradigmatic Lipkin-Meshkov-Glick (LMG) model as a concrete platform, we establish that a rich landscape of dynamical phases emerges when two regions of the system are driven with different field strengths, $h_1$ and $h_2$. Remarkably, despite the `all-to-all' nature of the interactions, the system can be driven into dynamical phases characterized by distinct kinds of discrete time crystal (DTC) orders in different parts of the system. Apart from these coexisting DTCs, tuning the driving field leads to the emergence of phases where DTCs coexist with Floquet-synchronized or oscillatory phases; the former has been dubbed a chimera DTC. Finally, we demonstrate that a tunable set of global DTC phases emerges when $h_1$ and $h_2$ are proximate. Crucially, these dynamical regimes can be observed both for experimentally relevant finite-size systems and in the thermodynamic limit. Our results establish spatially structured driving as a powerful route to realize non-equilibrium phase coexistence in collective spin systems.

The recently introduced random purification channel, which converts $n$ copies of an arbitrary mixed quantum state into $n$ copies of the same uniformly random purification, has emerged as a powerful tool in quantum information theory. Motivated by this development, we introduce a channel-level analogue, which we call the random Stinespring superchannel. This consists in a procedure to transform $n$ parallel queries of an arbitrary quantum channel into $n$ parallel queries of the same uniformly random Stinespring isometry, via universal encoding and decoding operations that are efficiently implementable. When the channel is promised to have Choi rank at most $r$, the procedure can be tailored to yield a Stinespring environment of dimension $r$. We present two applications of the random Stinespring superchannel, one in quantum Shannon theory and one in quantum learning theory. In quantum Shannon theory, we prove a channel-level analogue of Uhlmann's theorem for quantum divergences. In quantum learning theory, our construction shows that tomography of quantum channels reduces to tomography of isometries. This yields a simple channel learning algorithm, based on existing isometry learning protocols, that matches the performance of the two recently proposed channel tomography algorithms. Complementarily, whereas the optimality of these algorithms had previously been established only up to a logarithmic factor in the dimension, we close this gap by removing this logarithmic factor from the lower bound. Taken together, our results fully establish the optimality of these recently introduced channel learning algorithms, showing that the optimal query complexity of learning a quantum channel with input dimension $d_A$, output dimension $d_B$, and Choi rank $r$ is $\Theta(d_A d_B r)$.

The minimum accuracy heuristic evaluates quantum feature maps without requiring full quantum support vector machine (QSVM) training. However, the original formulation is computationally expensive, restricted to balanced datasets, and lacks theoretical backing. This work generalizes the metric to arbitrary binary datasets and formally proves it constitutes a certified lower bound on the optimal empirical accuracy of any linear classifier in the same feature space. Furthermore, we introduce Monte Carlo strategies to efficiently estimate this bound using a random subset of Pauli directions, accompanied by rigorous probabilistic guarantees. These contributions establish minimum accuracy as a scalable, theoretically sound tool for pre-screening feature maps on near-term quantum devices.

We show how representations of finite-dimensional quantum operators can be constructed using nondeterministic rewriting systems. In particular, we investigate Wolfram model multiway rewriting systems based on string substitutions. Multiway systems were proposed by S. Wolfram as generic model systems for multicomputational processes, emphasizing their significance as a foundation for modeling complexity, nondeterminism, and branching structures of measurement outcomes. Here, we investigate a specific class of multiway systems based on cyclic character strings with a neighborhood constraint - the latter called Leibnizian strings. We show that such strings exhibit a Fermi-Dirac distribution for expectation values of occupation numbers of character neighborhoods. A Leibnizian string serves as an abstraction of a $N$-fermion system. A multiway system of these strings encodes causal relations between rewriting events in a nondeterministic manner. The collection of character strings realizes a $\mathbb{Z}$-module with a symmetric $\mathbb{Z}$-bilinear form. For discrete spaces, this generalizes the notion of an inner product over a vector field. This admits a discrete analogue of the path integral and a $S$-matrix for multiway systems of Leibnizian strings. The elements of this $S$-matrix yield transition amplitudes between states of the multiway system based on an action defined over a sequence of Leibnizian strings. We then show that these $S$-matrices give explicit representations of quantum gates for qubits and qudits, and also circuits composed of such gates. We find that, as formal models of nondeterministic computation, rewriting systems of Leibnizian strings with causal structure encode representations of the CNOT, $\pi/8$, and Hadamard gates. Hence, using multiway systems one can represent quantum circuits for qubits.

Radial basis function (RBF) networks are expanded to incorporate quantum kernel functions enabling a new type of hybrid quantum-classical machine learning algorithm. Using this approach, synthetic examples are introduced which allow for proof of concept on interpolation and classification applications. Quantum kernels have primarily been applied to support vector machines (SVMs), however the quantum kernel RBF network offers potential benefit over quantum kernel based SVMs due to the RBF networks ability to perform multi-class classification natively compared to the standard implementation of the SVM.

The rapid expansion of quantum cloud services has led to long job queues due to single-tenant execution models that underutilize hardware resources. Quantum multi-programming (QMP) mitigates this by executing multiple circuits in parallel on a single device, but existing methods target superconducting systems with limited connectivity, high crosstalk, and lower gate fidelity. Trapped-ion architectures, with all-to-all connectivity, long coherence times, and high-fidelity mid-circuit measurement properties, presents itself as a more suitable platform for scalable QMP. We present CircPack, a hardware-aware circuit packing framework designed for modular trapped-ion devices based on the Quantum Charge-Coupled Device (QCCD) architecture. CircPack formulates static circuit scheduling as a two-dimensional packing problem with hardware-specific shuttling constraints. Compared to superconducting-based QMP approaches, CircPack achieves up to 70.72% better fidelity, 62.67% higher utilization, and 32.80% improved layer reduction. This framework is also capable of scalable, balanced scheduling across a cluster of independent QCCD modules, highlighting trapped-ion systems' potential in improving the throughput of quantum cloud computing in the near future.

Channel spectrum benchmarking (CSB) provides a robust framework for characterizing quantum gate fidelities while remaining insensitive to state preparation and measurement (SPAM) errors. Yet, current CSB implementations encounter fundamental challenges when reconstructing noisy eigenvalues, particularly in the presence of spectral degeneracies and off-diagonal noise components in the target gate's eigenbasis. These issues become especially pronounced in the strong noise regime for gates with fidelities around $90\%$. To address these limitations, we introduce an extended CSB model together with a fidelity estimate interval (FEI) – an interval-valued estimate of the target gate fidelity. Numerical simulation demonstrates that FEI remains sufficiently narrow, with its midpoint reliably approximating the true fidelity. We further validate the protocol on a trapped-ion quantum processor by benchmarking two implementations of the three-qubit Toffoli gate. The results reveal a clear advantage of the qutrit-based implementation over its qubit-based counterpart.

Quantum state preparation represents a critical bottleneck for a broad class of quantum algorithms. In this work, we introduce the Schmidt Spectrum Optimisation (SSO) algorithm as an efficient and scalable approach for preparing quantum states described by Matrix Product States (MPS). The SSO algorithm employs a preparation-by-disentangling strategy by optimising circuit layers of two-qubit gates to progressively remove entanglement from a target state. Each circuit layer is computed sequentially and efficiently on a classical computer using tensor network optimisation techniques. Once the target state has been successfully disentangled, a quantum state-preparation circuit is formed by reversing the sequence of optimised disentangling layers. Across benchmarks including random MPS and MPS approximations to the ground-states of local Hamiltonians, we find that the SSO algorithm significantly improves upon prior variational and disentangling-based approaches, highlighting its potential as a scalable framework for quantum state preparation.

Famously, the quantum Fisher information – the maximum Fisher information over all physical measurements – is additive for independent copies of a system and the optimal measurement acts locally. We are left to wonder: does the same hold when the set of accessible measurements is constrained? Such constraints are necessary to account for realistic experimental restrictions. Here, we consider a fully Gaussian scenario focusing on only Gaussian measurements. We prove that the optimal Gaussian measurement protocol remains local, if the information is encoded in either the displacement or the covariance matrix. However, when the information is imprinted on both, this no longer holds true: we construct a simple global Gaussian measurement where the Fisher information becomes super additive. These results can improve parameter estimation tasks via feasible tools. Namely, in quantum optical platforms our proposed global operation requires only passive global operations and single mode Gaussian measurements. We demonstrate this in two examples where we estimate squeezing and losses. While in the former case there is a significant gap between the Fisher information of the optimal Gaussian measurement and the quantum Fisher information for a single copy, this gap can be reduced with joint Gaussian measurements and closed in the asymptotic limit of many copies.

Quantum Tanner codes are a class of quantum low-density parity-check codes that provably display a linear minimum distance and a constant encoding rate in the asymptotic limit. When built from left–right Cayley complexes, they can be described through a lifting procedure and a base code, which we characterize. We also compute the dimension of quantum Tanner codes when the right degree of the complex is 2. Finally, we perform an extensive search over small groups and identify instances of quantum Tanner codes with parameters $[[144,12,11]]$, $[[432,20,\leq 22]]$ and $[[576,28,\leq 24]]$ for generators of weight 9.

We identify the transition from the oscillatory Rabi regime to the localized Zeno/Anti-Zeno regime in continuous measurement and feedback of a qubit as a quantum analogue of Motility-Induced Phase Separation (MIPS). A mapping between a biased monitored qubit and a classical “Run-and-Tumble" active particle is studied. We demonstrate that the competition between coherent Rabi driving (analogous to active motility) and measurement-induced feedback bias (analogous to persistence) mimics the behavior of biological swimmers. This framework provides a picture of measurement-induced phase transitions using the language of active matter and offering a novel pathway for designing dissipative noisy quantum systems.

We investigate the concept of macroscopically distinguishable superpositions within an infinite array of boson sites. Our approach is rigorous within the frame of Hilbert space theory. In this context, it is natural to differentiate between states – and corresponding dynamics – that involve only finitely many degrees of freedom, referred to as local, and those that are inherently nonlocal. Previous studies have shown that such systems can support nonlocal coherent states (NCS). In this work, we demonstrate that NCS can dynamically evolve into nonlocal cat states under the influence of a nonlocal Hamiltonian – specifically, the square of the total number operator. Crucially, the resulting dynamics cannot be decomposed into local factors. Furthermore, we explore broader mathematical implications of these phenomena within the framework of generalized bosons. Our findings highlight that the concepts of coherent states and nonlocal cat states are not inherently bound together; rather, their fusion is a distinctive feature of standard bosons. Finally, we propose that if the generalized boson framework can be physically realized in engineered quantum systems, the phenomena described here may hold significant relevance for both physics and materials science.

We introduce an end-to-end optimization strategy for quantum machine learning that directly targets performance under finite measurement resources, where learning objectives are defined directly at the level of task performance. The method is applied on a Bayesian quantum metrology task since it provides a natural testbed with known fundamental limits and scaling with system size. The sampling-aware hybrid algorithm achieves a single-shot risk within 1 dB of the -20 dB Bayesian limit using 32 qubits. We extend the Bayesian framework from parameter estimation to global function inference, where the task is to infer a target function of the sensor input drawn from an arbitrary prior, and we demonstrate a clear computational-sensing advantage for direct functional inference over indirect reconstruction. We relate the corresponding Bayesian risk to the Capacity metric and argue that the Resolvable Expressive Capacity provides a natural measure of the space of functions accessible in a single shot. The resulting eigentask analysis identifies noise-robust feature combinations that yield compact estimators with improved accuracy and reduced optimization cost in resource-limited or real-time on-device settings. Going beyond the irreducible statistical uncertainty associated with finite measurement records, we study implementation-induced distortions of the sensor response focusing on representative imperfections arising from readout errors and static coherent gate disorder. We show that when these imperfections are stationary across training and inference, end-to-end optimization can adapt the quantum circuit and classical estimator to the implemented hardware response, preserving high inference performance over a broad range of imperfection strengths.

Rapid advancements in quantum computing and machine learning threaten the long-term security of classical blockchain systems, whose protection mechanisms largely rely on computational difficulties. In this study, we propose a quantum blockchain protocol whose protection mechanism is directly derived from quantum mechanical principles. The protocol combines high-dimensional Bell states, time-entanglement, entanglement switching, and high-dimensional superdense coding. Encoding classical block information into time-delimited qudit states allows block identity and data verification to be implemented through the causal sequencing of quantum measurements instead of cryptographic hash functions. High-dimensional coding increases the information capacity per quantum carrier and improves noise resistance. Time-entanglement provides distributed authentication, non-repudiation, and tamper detection across the blockchain. Each block derives its own public-private key pair directly from the observed quantum correlations by performing high-dimensional Bell state measurements in successive time steps. Because these keys are dependent on the time ordering of measurements, attempts to alter block data or disrupt the protocol's timing structure inevitably affect the reconstructed correlations and are revealed during validation. Recent advances in the creation and detection of high-dimensional time-slice entanglement demonstrate that the necessary quantum resources are compatible with emerging quantum communication platforms. Taken together, these considerations suggest that the proposed framework can be evaluated as a viable and scalable candidate for quantum-secure blockchain architectures in future quantum network environments.

The rapid adoption of diffusion models (DMs) in the Earth Observation (EO) domain has unlocked new generative capabilities aimed at producing new samples, whose statistical properties closely match real imagery, for tasks such as synthesizing missing data, augmenting scarce labeled datasets, and improving image reconstruction. This is particularly relevant in EO, where labeled data are often costly to obtain and limited in availability. However, classical DMs still face significant computational limitations, requiring hundreds to thousands of inference steps, as well as difficulties in capturing the intricate spatial and spectral correlations characteristic of EO data. Recent research in Quantum Machine Learning (QML), including initial attempts of Quantum Generative Models, offers a fundamentally different approach to overcome these challenges. Motivated by these considerations, we introduce the Quanvolutional Conditioned U-Net (QCU-Net), a hybrid quantum–classical architecture that applies quantum operations within a conditioned diffusion framework using a novel quanvolutional feature-extraction approach, for generating synthetic labeled EO imagery. Extensive experiments on the EuroSAT RGB dataset demonstrate that our QCU-Net achieves superior results. Notably, it reduces the Fréchet Inception Distance by 64%, lowers the Kernel Inception Distance by 76%, and yields higher semantic accuracy. Ablation studies further reveal that strategically positioning quantum layers and employing entangling variational circuits enhance model performance and convergence. This work represents the first successful adaptation of class-conditioned quantum diffusion modeling in the EO domain, paving the way for quantum-enhanced remote sensing imagery synthesis.

In this work, we propose a hybrid quantum-inspired heuristic for automatically tuning the Lorenz-96 model – a simple proxy to describe atmospheric dynamics, yet exhibiting chaotic behavior. Building on the history matching framework by Lguensat et al. (2023), we fully automate the tuning process with a new convergence criterion and propose replacing classical Gaussian process emulators with quantum counterparts. We benchmark three quantum kernel architectures, distinguished by their quantum feature map circuits. A dimensionality argument implies, in principle, an increased expressivity of the quantum kernels over their classical competitors. For each kernel type, we perform an extensive hyperparameter optimization of our tuning algorithm. We confirm the validity of a quantum-inspired approach based on statevector simulation by numerically demonstrating the superiority of two studied quantum kernels over the canonical classical RBF kernel. Finally, we discuss the pathway towards real quantum hardware, mainly driven by a transition to shot-based simulations and evaluating quantum kernels via randomized measurements, which can mitigate the effect of gate errors. The very low qubit requirements and moderate circuit depths, together with a minimal number of trainable circuit parameters, make our method particularly NISQ-friendly.

We present a footprint study for the scaling of modular quantum error correction (QEC) protocols designed for triangular color codes, including a lattice-surgery-based logical teleportation gadget, and compare the performance of various possible architectures based on trapped ions. The differences in these architectures arise from the technology that enables the connectivity between physical qubits and the modularity required for the QEC gadgets, which is either based on laser-beam deflectors focused to independent modules hosting mid-size ion crystals, or integrated photonics guided to segmented modules of the trap and allowing for the manipulation of smaller ion crystals. Our approach integrates the transpilation of the QEC gadgets into native trapped-ion primitives and a detailed account of the specific laser addressing and ion transport leading to different amounts of crosstalk errors, motional excitation and idle qubit errors. Combining a microscopically-informed noise model with an efficient Pauli-frame simulator and different scalable decoders, we assess the near-term performance of the color-code memory and teleportation protocols on these architectures. Our analysis demonstrates that modular color-code teleportation is achievable in these near-term trapped-ion architectures, and identifies the integrated-photonics connectivity as the most promising route for longer-term scaling.

The aim of this article is to provide an introduction to the use of quantum information methods for investigating the interface between quantum theory and gravity. To this end, we discuss the basic principles of two current research streams that use this approach. The first one explores a phenomenon known as gravitationally induced entanglement, which aims to infer whether the gravitational field responsible for the interaction between two massive bodies must be quantized or not. The second stream investigates causal structures, thereby providing indirect evidence that spacetime may exhibit non-classical behavior. Before presenting these topics, we briefly review some fundamental concepts and experiments from quantum information theory, such as the Mach-Zehnder interferometer, the Stern-Gerlach experiment, Bell inequalities and entanglement, and the language of quantum circuits.

Quantum metrology surpasses the classical precision limit by encoding signals in a probe state such that signal contributions are indistinguishable and their phases accumulate coherently as a collective response. In realistic settings, scalable quantum metrology requires quantum error correction to protect the probe against noise. However, quantum error correction relies on syndrome information that distinguishes errors for identification and correction. Because signals and errors act on the same physical degrees of freedom, there is a structural incompatibility between signal-sensitivity and noise-protection in quantum-error-corrected metrology. We quantify this incompatibility by establishing trade-offs between code distance and the quantum Fisher information of code states for non-degenerate codes, quantum low-density parity-check codes, and generalized Shor codes. We bypass this limitation with asymmetric quantum error correction, in which protection is relaxed along the signal direction while being maintained in complementary directions. We construct such codes for local sensing Hamiltonians, restoring Heisenberg-limited precision while retaining a growing distance and hence protection against local perturbations in complementary directions. Strongly asymmetric quantum low-density parity-check and concatenated asymmetric constructions make the framework sparse, scalable, and continuously tunable. The associated probe states can be prepared by constant-depth adaptive circuits with optimal resource scaling.

The rigorous description of Conical Intersections (CIs) remains the central challenge of non-adiabatic quantum chemistry. While the “Yarkony Seam” – the $(3N-8)$-dimensional manifold of degeneracy – is well-understood geometrically, its accurate characterization by high-level electronic structure methods is plagued by numerical instabilities. Specifically, standard Coupled Cluster (CC) theory suffers from root bifurcations near Ground State CIs, rendering the “Gold Standard” of chemistry inapplicable where it is needed most. Here, we present QuMorpheus, an open-source computational package that resolves these singularities by implementing a topological framework based on Dissipative Mixed Hodge Modules (DMHM) [P. Saurabh, arXiv:2512.19487 (2025)]. By algorithmically mapping the CC polynomial equations to a spectral sheaf, we compute the exact Monodromy ($\mu$) invariants of the intersection. We demonstrate that this automated algebraic geometry approach correctly identifies the physical ground state topology in the Köhn-Tajti model and resolves the intersection seams of realistic chemical systems, including Ethylene and the Chloronium ion ($\mathrm{H_2Cl^+}$). Furthermore, we apply QuMorpheus to the photoisomerization of Previtamin D, proving that the experimentally observed Woodward-Hoffmann selection rules are a direct consequence of a topological “Monodromy Wall” ($\mu=1, \gamma=\pi$) rather than purely energetic barriers. This establishes a general software solution to the “Yarkony Problem,” enabling the robust, automated mapping of global intersection seams in complex molecular systems. The topological stability of these intersections allows for the control protocols discussed in Ref.[P. Saurabh, Submitted to Phys. Rev. X (2025)].

We show how combining a discrete symmetry with topological Hilbert space fragmentation can give rise to exponentially many topologically stable qubits protected by a single discrete symmetry. We illustrate this explicitly with the example of the $\mathsf{CZ}_p$ model, where the encoded qubits are stable to arbitrary symmetry-respecting perturbations for parametrically long times, substantially enhancing the robustness of a recently proposed construction based on nontopological fragmentation. In this model, the encoded qubits naturally come in pairs for which a universal set of transversal logical gates can be performed, ruling out (by the Eastin-Knill theorem) the possibility of using them for quantum error correction. We also comment on the combination of symmetry enrichment and topological fragmentation more generally, and the implications for use of systems exhibiting Hilbert space fragmentation as quantum memories.

Optical skyrmions are topological structures of light whose defining property, the skyrmion number, is robust against perturbations. This makes them attractive for applications in quantum information storage, where resilience to decoherence is paramount. However, their preservation during coherent storage remains unexplored. We report the first experimental demonstration of storing and retrieving optical skyrmions in a cold $^{87}$Rb vapor using a dual-path electromagnetically induced transparency memory. Crucially, we show that the skyrmion number remains invariant for storage times up to several microseconds, even when subjected to imbalanced loss between the two paths and substantial perturbations in control beam power. Our work demonstrates the survival of a non-trivial topological invariant in a quantum memory, marking a significant step towards topologically protected photonic technologies.

We have combined a cryogenic BiCMOS integrated circuit with a superconducting Josephson junction array. The BiCMOS circuit serves as an on-chip pulse generator delivering return-to-zero pulses with pulse frequencies of up to 15 GHz. With this microwave drive, we observe wide and flat Shapiro steps in the voltage-versus-current characteristics of the Josephson junction array. To the best of our knowledge, this is the first integration of a Josephson junction array with a cryogenic BiCMOS chip. Our results pave the way to a hybrid and fully integrated Josephson arbitrary waveform synthesizer with possible applications in quantum electronics and quantum voltage metrology.

Krylov representations of operator dynamics encode two inequivalent motions: probability transport along the discrete Krylov chain and motion of the normalized amplitude vector on the associated sphere. We lift Hall's exact uncertainty relation to Liouville space and show that, for the fixed Krylov-basis measurement, its classical Fisher information locally attains the quantum Fisher information. The amplitude vector therefore follows an exact constant-speed spherical trajectory. We construct its moving frame, identifying the first Lanczos coefficient with the speed and the higher coefficients with successive bending. Geodesic curvature controls the leading departure from Mandelstam-Tamm saturation. Separately, we compare cumulative and pointwise bounds on Krylov-index transport, which depends on the full Lanczos sequence.

The evolution of a quantum system under time-dependent driving exhibits phenomena that are absent in its stationary counterpart. However, the high dimensionality and non-commutative nature of quantum dynamics make this a challenging problem. The Magnus expansion provides an analytic framework to approximate the effective dynamics on short time-scales, but computing high-order terms with existing methods is computationally expensive. We introduce a scalable approach that reduces the computational effort to depend only on the degrees of freedom defining the time-dependent control function. We focus specifically on Hamiltonians consisting of a constant drift term and a controllable term. Our method provides a polynomial expression for the Magnus expansion which can be evaluated several orders of magnitude faster than previous techniques, enabling broad applications in the realms of quantum simulation and quantum optimal control. We showcase an application of the method by designing control pulses for the 5-qubit phase gate on a neutral-atom platform utilizing Rydberg atoms.