Papers

We study integrability breaking in translationally invariant spin-$1/2$ chains with genuine three-site interactions. Using a two-qubit composite representation, we prove that the deformed Fredkin spin chain is nonintegrable for any nonzero deformation parameter, although its Hamiltonian decomposes into coupled integrable building blocks. We then extract the minimal injective models, defined as the simplest models needed for a rigorous nonintegrability test, from the Hamiltonian density of the deformed Fredkin spin chain. Among the sixteen such models, six satisfy the Reshetikhin condition and are integrable, while two satisfy Hokkyo's criterion and are nonintegrable away from special coefficient values. Returning to one-site translation-invariant spin-$1/2$ chains leaves four genuine three-site models: two integrable models and two generically nonintegrable models. These results give a compact classification of minimal three-site models obtained from the deformed Fredkin spin chain and identify a local mechanism by which coupling individually integrable structures can destroy integrability beyond nearest-neighbor interactions.

We present a microscopic calculation of spontaneous photon emission by twisted (paraxial) electrons propagating through inhomogeneous, axisymmetric magnetic fields. We construct exact electron states that incorporate transverse mode structure and wavefront curvature by combining the Foldy-Wouthuysen transformation with a geometric framework based on Lewis-Ermakov invariants and metaplectic transformations. We show that the evolution of such structured states corresponds to an open path in the space of quadratic forms, giving rise to a geometric contribution to the emission amplitude that cannot be eliminated by gauge choice or adiabatic arguments. The inverse radius of curvature of the electron wavefront controls a finite-window boundary contribution to the emission amplitude in regions where the external magnetic field vanishes locally, this contribution vanishes when the observation window is extended to infinity. Presented mechanism generalizes Landau-level radiation to nonasymptotic, structured electron states and establishes a direct connection between noncyclic geometric evolution and photon emission.

Certifying high-dimensional quantum channels is essential for ensuring the reliability of quantum communication protocols. Existing certification schemes often rely on fully trusted internal devices, which is difficult to achieve in realistic scenarios. Here, we propose a semi-device-independent framework for certifying channel properties directly from observed statistics, assuming only that the system dimension is known. By explicitly incorporating the full set of structural constraints inherent to Choi states, our approach exploits the Choi-Jamiołkowski isomorphism for rigorous certification of quantum channels. The entanglement dimensionality of quantum channels is first certified by introducing a witness and numerically determining its Schmidt-number-dependent bounds. This certification method reproduces known analytical benchmarks and is applied to dephasing and depolarizing noise channels, thereby confirming its validity. To provide a more complete assessment of channel performance, the entanglement fidelity of quantum channels is also certified using a hierarchy of semidefinite programming relaxations based on localizing matrices. Lower bounds on the entanglement fidelity are obtained that are compatible with either the full set of observed statistics or a single witness value.

When the photonic mode in the Jaynes-Cummings model is driven by an external classical field, the system can undergo the photon-blockade breakdown phase transition at a critical point. Such a phase transition has been detailedly investigated, but the critical properties of the eigenstates remain largely unexplored so far. We here study the geometric criticality associated with these eigenstates. The amplitude and phase of the drive serve as the control parameter of the governing Hamiltonian. We find the quantum metric and Berry curvature tensors for each eigenstate display divergent behaviors in the critical region. More importantly, the divergence associated with bright eigenstates is much more pronounced than that for the unique dark state. Our theoretical results can be experimentally confirmed in circuit quantum electrodynamics systems, where the driven Jaynes-Cummings model has been realized.

We present a comprehensive phase diagram of quantum correlations in a three-mode Gaussian state generated by a tritter, driven by a two-mode squeezed vacuum and a coherent state. The coherent amplitude does not affect the correlation structure, which is solely governed by the initial squeezing. By systematically analyzing five physically relevant asymmetric loss configurations, we map out the exact resilience thresholds for entanglement and Einstein-Podolsky-Rosen (EPR) steering under all bipartite partitions. We reveal that EPR steering exhibits a pronounced directional asymmetry under loss, and its survival can be maintained over a much wider range of loss by strategically protecting a single channel. This tunable fragility provides practical guidance for one-sided device-independent quantum protocols in noisy asymmetric networks. We further confirm the limitations of Rényi-2 entropy in the quantification of entanglement and steering. Our results transform the abstract correlation hierarchy into a calculable, experimentally relevant guide for engineering robust quantum resources.

We establish an operational rigidity result for a broad class of probability rules in infinite-dimensional settings, applicable under normality and steering assumptions. Starting from a topological generalization of generalized probabilistic theories, we consider probability assignments defined as functions of an operational transition probability between pure states. We show that under three operationally motivated requirements: no superluminal signaling, availability of normal steering via purification in a sigma additive sense, and sigma affinity of probabilities under countable preparation mixtures, any admissible rule within this class must reduce to the identity. In particular, nonlinear deviations generically enable operational signaling distinctions in steering scenarios, while continuity combined with sigma affinity excludes non affine alternatives. This identifies a unique causal fixed point. Within this class of probability rules, the Born rule emerges as the only assignment compatible with no signaling in operational theories admitting normal steering. We connect the operational result to standard infinite-dimensional quantum mechanics through the normal state space of von Neumann algebras and the GNS representation, recovering the conventional Born rule for projective and generalized measurements. We discuss the scope of the assumptions and implications for proposed post quantum modifications in continuous variable and quantum field theoretic regimes.

Relative-entropy revivals and negative entropy-production rates are established signatures of memory effects in non-Markovian dynamics. The present paper addresses a more specific question: what minimal dynamical mechanism produces entropy overshoot in classical stochastic relaxation? We define entropy overshoot as a transient increase of the Kullback–Leibler divergence from a stationary distribution during a relaxation process that ultimately returns to equilibrium. Starting from finite-state generalized master equations with memory kernels, we analyze the effective time-local generator governing the observed dynamics. The standard monotonic decay of relative entropy is recalled as a reference property of reversible Markov dynamics. We then show that memory can destroy stochastic divisibility by producing transiently negative effective rates. Once the evolution ceases to be divisible into intermediate Markov steps, the usual relative-entropy contraction argument no longer applies, and entropy overshoot can occur. The contribution of the paper is therefore not the introduction of another witness of non-Markovianity, but the identification of a minimal structural mechanism and its phase structure. The mechanism is illustrated with two- and three-state stochastic models, where the competition between the intrinsic relaxation time and the memory time separates monotonic relaxation from overshoot. Numerical phase diagrams show that the overshoot region expands when memory persists on the relaxation timescale. These results clarify the relation between classical information backflow, negative entropy-rate behavior, and memory-induced loss of divisibility. They also distinguish the present mechanism-based interpretation from previous work that used relative-entropy revivals or entropy-production rates primarily as indicators of non-Markovianity.

A linear radio-frequency Paul trap is traditionally driven with one diagonal pair of electrodes grounded and the other connected to a high-voltage radio-frequency source. This method simplifies impedance matching of the voltage source to the trap. However, for several architectures it leads to increasing the axial micromotion amplitude, for example, when the capacitance between radio-frequency and end-cap electrodes is not negligible. Here, we present a technique to generate two high-voltage radio-frequency signals \SI{180}{\degree} out of phase to drive a linear Paul trap with opposite voltages between neighbouring electrodes. Using this, we have successfully trapped and cooled a chain of Ytterbium ions in a linear radio-frequency Paul trap.

The transition probability of a spin driven by a rotating magnetic field is reformulated. This work shows that, once projection onto the measurement basis is properly accounted for, the laboratory measured probability is governed by both intrinsic spin dynamics and the time dependence of the measurement basis. For the rotating-field eigenbasis, this yields an additional kinematic modulation, leading to measurable deviations under strong driving. A unified probability expression is derived that subsumes the classic 1937 and 1954 formulations as limiting cases, while correcting the conventional treatment of magnetic resonance transitions.

We formulate a model of gravitationally induced decoherence for photons starting from Maxwell theory coupled to linearised gravity, expressed in terms of Ashtekar-Barbero variables and treated as an open quantum field theoretic system. In contrast to quantum mechanical models, the interaction between the system (Maxwell field) and the environment (gravitational field) is not postulated phenomenologically, but is instead dictated by the underlying action in a post-Minkowskian approximation. This framework extends earlier models for a scalar field and enables a more detailed analysis of the role of dynamical reference fields (clocks) within the relational formalism. We show that, for a suitable choice of geometrical clocks together with a U(1)-Gauss clock, and by employing an appropriate combination of the observable map and its dual, the resulting Dirac observables are given directly by the transverse components of the photon field as well as the symmetric-transverse-traceless degrees of freedom of gravitational waves on the linearised phase space of the coupled system. In addition we also compare different choices of Dirac observables and their dynamics. Upon applying a Fock quantisation to the reduced system, we derive the time convolutionless (TCL) master equation, truncated at second order, and analyse its structural properties. These results provide a foundation for further investigations of the decoherence model, including its renormalisation and a detailed study of its one-particle sector, and are found to be structurally consistent with former master equations for photons derived using ADM variables and a specific gauge fixing.

Quantum computing is increasingly practised through programming, yet most educational offerings emphasize algorithmic or framework-level use rather than software engineering concerns such as testing, abstraction, tooling, and lifecycle management. This paper reports on the design and first offering of a cross-listed undergraduate–graduate course that frames quantum computing through a software engineering lens, focusing on early-stage competence relevant to software engineering practice. The course integrates foundational quantum concepts with software engineering perspectives, emphasizing executable artifacts, empirical reasoning, and trade-offs arising from probabilistic behaviour, noise, and evolving toolchains. Evidence is drawn from instructor observations, supplemented by anonymous student feedback, a background survey, and inspection of student work. Instructor observations and inspected work artifacts indicated that students with little prior exposure could engage with quantum software engineering topics after foundational quantum concepts had been introduced using executable artifacts. The contribution is the systematic software engineering framing and sequencing of the course, its mixed-level assessment design, and practice-grounded lessons from an actual offering; the report does not estimate causal learning effects.

Elemental good metals, including noble metals (Cu, Ag, Au) and several $s$-block elements, do not exhibit superconductivity in bulk at ambient pressure, mainly due to weak electron-phonon coupling that cannot overcome Coulomb repulsion. Quantum confinement in ultra-thin films reshapes the electronic spectrum and the density of states near the Fermi level, producing strong, often non-monotonic, thickness dependencies of the critical temperature in established superconductors. Here, we examine whether confinement alone, or combined with proximity effects, can induce superconductivity in metals that are non-superconducting in bulk form. We review recent theoretical progress and introduce a unified framework based on a confinement-generalized, isotropic one-band Eliashberg theory, where the normal density of states becomes energy dependent and key parameters ($E_F$, $\lambda$, $\mu^$) acquire explicit thickness dependence. By numerically solving the Eliashberg equations using ab initio or experimentally determined electron-phonon spectral functions $\alpha^2F(\Omega)$ and Coulomb pseudopotentials $\mu^$, and without adjustable parameters, we compute the critical temperature $T_c$ as a function of film thickness for representative noble, alkali, and alkaline-earth metals. The results predict that superconductivity emerges only in selected cases and within extremely narrow thickness windows, typically at sub-nanometer scales ($L \sim 0.4-0.6$ nm), indicating strong fine-tuning requirements for confinement-induced superconductivity in good metals. We also consider layered superconductor/normal-metal systems where confinement and proximity effects coexist. In these heterostructures, a substantial enhancement of the critical temperature is predicted, even when the constituent materials are non-superconducting or weak superconductors in bulk form.

Erasure qubits reduce overhead in fault-tolerant quantum error correction (QEC) by converting dominant faults into detectable errors known as erasures. They have demonstrated notable improvements in thresholds and scaling in surface and Floquet code memories. In this work, we use erasure qubits on Bivariate Bicycle (BB) codes from the quantum low-density parity-check (QLDPC) regime. Owing to their sparse structure and favorable rate-distance trade-offs, BB codes are practical candidates for QEC. We introduce BiBiEQ, a novel framework that compiles a given BB code into an erasure-aware memory circuit C_E. This erasure circuit C_E comprises erasure checks (ECs), resets, and erasures spread over a user-specified erasure check schedule (2EC, 4EC). BiBiEQ converts this erasure circuit C_E into the stabilizer circuit C for general-purpose decoding. BiBiEQ provides two engines for this conversion, BiBiEQ-Exact and BiBiEQ-Approx. BiBiEQ-Exact preserves the joint-erasure correlations and serves as our accuracy benchmark, while BiBiEQ-Approx uses an independence approximation to accelerate large sweeps and expose accuracy-throughput trade-offs. Using BiBiEQ, we decode the stabilizer circuits to get a per-round logical error rate (LER) for the BB codes and quantify the effect of the EC schedules on the correctable operating region below the pseudo-threshold. The 4EC schedule keeps the accuracy of both engines close to one another, making BiBiEQ-Approx a reliable proxy for BiBiEQ-Exact for faster sweeps. Below the pseudo-threshold, the code distance (d) hop from distance (d) 6 to 10 yields a drop in LER by 10-17x larger than distance (d) 10 to 12, showing that most gains are realized by d=10.

Optical fibers are crucial for guiding light in various sensing applications. Especially for quantum sensors such as the nitrogen-vacancy (NV) center in diamond, they enable light control and device miniaturization. However, fluorescence and scattering within the fiber, often referred to as fiber background, autofluorescence, or autoluminescence, can overlap spectrally with the NV centers' fluorescence, degrading the signal-to-noise ratio and thus limiting sensor sensitivity. Here, we investigate the optical spectra of standard optical fibers, considering material dependencies, physical influences, and their fluorescence scaling with excitation power and wavelength. Our results identify spectral components and fiber types with minimal unwanted background signals, guiding the selection of optimal fibers for NV-based quantum sensing.

Cooling the center-of-mass (CM) motion of a macroscopic oscillator to its quantum ground state is a fundamental prerequisite for testing quantum mechanics at macroscopic scales. However, achieving this goal is currently hindered by the stringent requirement for an ultrahigh mechanical quality factor ($Q_c$). Here, we propose a dual-channel cooling scheme based on squeezing-enhanced quantum interference within a hybrid levitated cavity-magnomechanical system to overcome this limitation. By synergizing squeezing effects with quantum interference between the magnon-CM and cavity-CM channels, our scheme simultaneously suppresses Stokes (heating) scattering while enhancing anti-Stokes (cooling) scattering.~We demonstrate that this cooling mechanism reduces the critical $Q_c$ required for ground-state cooling by three orders of magnitude, making it achievable in the experimentally accessible regime of $Q_c \sim 10^4$. Furthermore, the net cooling rate is enhanced by nearly 180-fold compared to that of conventional single-channel cooling. This improvement is accompanied by a two orders of magnitude reduction in both the steady-state CM occupancy and the cooling time. Importantly, this enhanced performance remains robust even deep within the unresolved-sideband regime. Our results provide a feasible path toward preparing macroscopic quantum states by actively controlling the cooling dynamics, thereby relaxing the constraints on intrinsic material properties.

The temporal stability and reproducibility of qubit parameters are critical for the long-term operation and maintenance of superconducting quantum processors. In this work, we present a comprehensive longitudinal characterization of 27 frequency-tunable transmon qubits spanning over one year across four thermal cycles. Our results establish a distinct hierarchy of stability for superconducting hardware. We find that the intrinsic device parameters determining the qubit frequency and the baseline energy relaxation times ($T_1$) exhibit high robustness against thermal stress, characterized by frequency deviations typically confined within 0.5% and non-degraded coherence baselines. In stark contrast, the environmental variables, specifically the background magnetic flux offsets and the microscopic landscape of two-level system (TLS) defects, undergo a significant stochastic reconfiguration after each cycle. By employing frequency-dependent relaxation spectroscopy and a quantitative metric, the $T_1$ Spectral Topography Fidelity, we demonstrate that thermal cycling acts as a “hard reset” for the local defect environment. This process introduces a level of spectral randomization equivalent to thousands of hours of continuous low-temperature evolution. These findings confirm that while the fabrication quality is preserved, the specific noise realization is statistically distinct for each thermal cycle, necessitating automated recalibration strategies for large-scale quantum systems.

Discrete radio resource management problems in dense wireless networks are naturally cast as quadratic unconstrained binary optimization (QUBO) programs but are difficult to solve at scale. We investigate a quantum-classical approach based on the Recursive Quantum Approximate Optimization Algorithm (RQAOA), which interleaves shallow QAOA layers with variable elimination guided by measured single- and two-qubit correlators. For interference-aware channel assignment, we give a compact QUBO/Ising formulation in which pairwise interference induces same-channel couplings and one-hot constraints are enforced via quadratic penalties (or, optionally, constraint-preserving mixers). Within RQAOA, fixing high-confidence variables or relations reduces the problem dimension, stabilizes training, and concentrates measurement effort on a shrinking instance that is solved exactly once below a cutoff. On simulated instances of modest size, including a four-user, four-channel example, the method consistently returns feasible assignments and, for the demonstrated case, attains the global optimum. These results indicate that recursion can mitigate parameter growth and feasibility issues that affect plain QAOA, and suggest a viable pathway for near-term quantum heuristics in wireless resource allocation.

We propose a scheme for enhanced sensing of weak anharmonicities based on a three-mode anti-parity-time (anti-PT) symmetric cavity-magnon-waveguide system. By tuning the optical gain to the active cavity mode, the linewidth suppression point for the anti-PT symmetric Hamiltonian can be flexibly controlled even when the two dissipative magnonic modes experience strong intrinsic decay. This essential characteristic is utilized for detecting weak nonlinearities in both the cavity and magnonic modes, with both demonstrating similar high levels of sensitivity. Moreover, the sensitivity can be greatly improved with a detuned laser drive. Based on the integrated passive-active three-mode anti-PT symmetric system, the sensing scheme can be generalized to various physical systems with anharmonicities.

We study the dynamics of a dressed qubit implemented by a spinless fermion hopping between two lattice sites with each site strongly coupled to a bath of phonons. We employ Lang-Firsov transformation to make the problem tractable perturbatively. Applying time-convolutionless master equation within the polaron frame, we investigate decoherence dynamics of the dressed qubit within the singlet-triplet basis of the system for a wide range of bath spectral densities. It is shown that the coherence persists for longer time scales for large coupling values and shows non-monotonic behaviour reflecting the presence of non-Markovianity in the dynamics. Non-Markovianity, characterized by coherence revivals and non-monotonic decay patterns, emerges distinctly depending on the bath spectrum and coupling strengths. Systems coupled to sub-Ohmic baths, whether both or in combination with another type, display pronounced memory effects at relatively small values of couplings. In contrast, combinations involving Ohmic and super-Ohmic baths exhibit noticeable non-Markovianity only at higher couplings.

Localized electron states induced by various disorders, including defects and impurities, usually exist in solids. Their electrical properties have been extensively investigated and well documented, while their optical properties such as localized-state ensemble (LSE) luminescence remain poorly understood. In particular, a microscopic quantum many-body (MB) theory has not yet been established for LSE luminescence so far. In this Letter, we attempt to fill this void via developing a quantum MB luminescence theory taking into account both electron-phonon (e-p) and electron-electron (e-e) interactions. Abnormal thermal behaviors such as redshift and subsequent blueshift of peak position, narrowing and succeeding broadening of linewidth, decline in intensity, and variation in lifetime can be quantitatively interpreted. Within the framework of the MB-LSE theory, moreover, Varshni's empirical formula for bandgap temperature dependence and Huang-Rhys factor for e-p coupling, and other key formulas are further derived and discussed.

In 1964, Aharonov, Bergmann, and Lebowitz introduced their well-known ABL rule with the intention of providing a time-symmetric formalism for computing novel kinds of conditional probabilities in quantum theory. Later papers attached additional significance to the ABL rule, including assertions that it supported violations of the uncertainty principle. The present work challenges these claims, as well as subsequent attempts to salvage the original interpretation of the ABL rule. Taking a broader view, this paper identifies a subtle category error at the heart of the ABL rule that consists of confusing observables that belong to a single system with emergent observables that arise only for physical ensembles. Along the way, this paper points out other problems and fallacious reasoning in the research literature surrounding the ABL rule, including the misuse of post-selection, a reliance on pattern matching to classical formulas, and a posture of measurementism that takes experimental data as providing answers to interpretational questions.

Non-Hermitian physics exhibits unique physical properties beyond those of traditional Hermitian systems, such as symmetry breaking, the emergence of exceptional points, topological phase transitions, and more. These phenomena have been extensively studied across various platforms, including quantum optics, cold atom systems, superconducting circuits, and condensed matter physics. Rydberg atoms, with their long-range interactions and flexible controllability, provide a promising platform for the experimental realization of non-Hermitian physics. This review primarily summarizes the key experimental and theoretical achievements in the field of non-Hermitian physics within Rydberg atomic systems in recent years. It outlines the fundamental construction of non-Hermitian Hamiltonians, reveals the effective dissipation mechanisms induced by Rydberg atomic interactions, and discusses their impact on spectral properties and symmetry breaking. These studies not only deepen the understanding of quantum phase transitions in non-Hermitian many-body systems but also highlight the unique value of Rydberg atomic platforms in realizing and controlling topological states.

Combinatorial optimization problems are typically formulated using Quadratic Unconstrained Binary Optimization (QUBO), where constraints are enforced through penalty terms that introduce auxiliary variables and rapidly increase Hamiltonian complexity, limiting scalability on near term quantum devices. In this work, we systematically study Quadratic Unconstrained D-ary Optimization (QUDO) as an alternative formulation in which decision variables are encoded directly in higher dimensional Hilbert spaces. We demonstrate that QUDO naturally captures structural constraints across a range of problem classes, including the Traveling Salesman Problem, two variants of the Vehicle Routing Problem, graph coloring, job scheduling, and Max-K-Cut, without the need for extensive penalty constructions. Using a qudit-level implementation of the Quantum Approximate Optimization Algorithm (qudit QAOA), we benchmark these formulations against their binary QUBO counterparts and exact classical solutions. Our study show consistently improved approximation ratios and substantially reduced computational overhead at comparable circuit depths, highlighting QUDO as a scalable and expressive representation for quantum combinatorial optimization.

Singular value decomposition (SVD) provides a convenient way to construct Hermitian-like diagnostics for non-Hermitian many-body systems, but its reliability for locating many-body localization (MBL) transitions remains unclear, particularly in systems preserving time-reversal symmetry (TRS). We benchmark SVD-based diagnostics against exact diagonalization (ED) in TRS-preserving non-Hermitian hard-core-boson chains with nonreciprocal hopping, considering quasiperiodic, random-disorder, and Stark potentials. We compare level statistics, half-chain entanglement entropy, inverse participation ratio, and spectral form factors. For the quasiperiodic and random-disorder models, ED-based entanglement and IPR yield mutually consistent finite-size transition estimates, whereas the corresponding SVD-based estimates are systematically shifted to larger disorder strengths and can lead to different phase assignments. The discrepancy is also reflected in the spectral form factors, where the ED-based dissipative spectral form factor and the SVD-based singular form factor can indicate different spectral regimes at the same parameters. In contrast, for the clean Stark model, ED and SVD give consistent transition estimates. We identify the origin of this model dependence as the fact that SVD probes the auxiliary Hermitian operator $\hat H^\dagger\hat H$, rather than the intrinsic right-eigenstate structure of $\hat H$; consequently, SVD can be quantitatively reliable only when the corresponding bulk-state structures remain aligned. Our results show that SVD-based diagnostics can capture qualitative RMT-to-Poisson trends, but are not generically reliable quantitative probes of MBL transitions in TRS-preserving non-Hermitian many-body systems.

We investigate a microwave-cavity-based displacement readout employing a split-post geometry to measure the motion of a dielectric membrane. Due to symmetry, the cavity response to membrane displacement is inherently quadratic when the membrane is positioned at the centre of the posts. We characterise this behaviour by driving the membrane with a piezoelectric actuator at both central and off-centre positions and we estimate the drive-to-displacement transfer function using the independently calibrated frequency-to-voltage response of the interferometric readout. When the membrane is located at the centre of the cavity and driven, the system exhibits the largest quadratic output, measured at the second harmonic of the membrane acoustic frequency. As the membrane is moved away from the centre, the response transitions from predominantly quadratic to predominantly a linear response at the membrane acoustic frequency. Quadratic optomechanical coupling is a key requirement for displacement - squared readout and, in the quantum regime, for measurements sensitive to mechanical energy or phonon number. The present work therefore establishes the split-post geometry as a promising platform for microwave-mechanical transduction, providing a practical route toward future experiments aimed at probing quantised mechanical motion and energy-sensitive readout schemes.

On the contrary to the common intuition, which suggests that a steep expulsive potential makes quantum states widely delocalized, we demonstrate that one- and two-dimensional (1D and 2D) Schroedinger equations, which include expulsive potentials that are steeper than the quadratic ones, give rise to normalizable eigenstates, which may be considered as a manifestation of effective self-trapping in the linear system. These states constitute full continuous spectra in both the 1D and 2D cases. In 1D, they are spatially even and odd eigenstates. The 2D states may carry any value of the vorticity (alias magnetic quantum number). Asymptotic expressions for wave functions of the 1D and 2D eigenstates, valid far from the center, are derived analytically, demonstrating excellent agreement with full numerical solutions. Special exact solutions for vortex states are obtained in the 2D case. These findings suggest an extension of the concept of bound states in the continuum, in quantum mechanics and paraxial photonics. Gross-Pitaevskii equations are briefly considered as the nonlinear extension of the 1D and 2D settings. In 1D, the cubic nonlinearity slightly deforms the eigenstates, maintaining their stability

HyperFrog is an experimental post-quantum Key Encapsulation Mechanism that explores a variant of the Learning With Errors (LWE) design space in which the secret is not sampled from an independent product distribution, but is deterministically derived from discrete topological structure. The scheme embeds a voxel grid in three dimensions and uses a topology mining procedure to search for connected subgraphs with prescribed complexity, measured by cyclomatic number (high genus). The resulting structure is encoded as a sparse binary secret vector, inducing strong geometric constraints on the secret distribution while retaining a large combinatorial search space. Encapsulation produces noisy linear relations over public parameters and derives the shared key via hashing; a Fujisaki-Okamoto style transform is used to target IND-CCA security in the random oracle model. We present the construction, parameterization, and serialization format, together with a reference implementation featuring self-tests and benchmarking on commodity CPUs. We also discuss how topology-derived secrets interact with known lattice and decoding attacks, and we outline open problems required for conservative parameter selection and for a full security analysis. HyperFrog is intended as a research vehicle rather than a production-ready KEM.

Answering a question of Claudet, we prove that the uniformly random graph $G\sim \mathbb G(n, 1/2)$ is $\Omega(\sqrt n)$-vertex-minor universal with high probability. That is, for some constant $\alpha\approx 0.911$, any graph on any $\alpha\sqrt n$ specified vertices of $G$ can be obtained as a vertex-minor of $G$. This has direct implications for quantum communications networks: an $n$-vertex $k$-vertex-minor universal graph corresponds to an $n$-qubit $k$-stabilizer universal graph state, which has the property that one can induce any stabilizer state on any $k$ qubits using only local operations and classical communications. We further employ our methods in two other contexts. We obtain a bipartite pivot-minor version of our main result, and we use it to derive a universality statement for minors in random binary matroids. We also introduce the vertex-minor Ramsey number $R_{\mathrm{vm}}(k)$ to be the smallest value $n$ such that every $n$-vertex graph contains an independent set of size $k$ as a vertex-minor. Supported by our main result, we conjecture that $R_{\mathrm{vm}}(k)$ is polynomial in $k$. We prove $\Omega(k^2) \leq R_{\mathrm{vm}}(k) \leq 2^k - 1$.

Optimizing carbon credit portfolios is a critical challenge for climate mitigation, particularly in high-biodiversity biomes such as the Brazilian Cerrado. This study explores the practical application of the Quantum Approximate Optimization Algorithm (QAOA) combined with Zero Noise Extrapolation (ZNE) to address a multi-objective territorial planning problem. We model an 88-variable portfolio optimization involving carbon sequestration, biodiversity connectivity, and social impact metrics, executed on intermediate-scale IBM Quantum hardware (ibm_torino and ibm_fez). The results of seven independent hardware runs demonstrate that the QAOA+ZNE workflow consistently outperforms a classical greedy baseline. The quantum method achieves a mean portfolio score of 58.47 +/- 6.98, corresponding to a 31.6% improvement over the classical heuristic (44.42), with high statistical significance (p = 0.0009) and a large effect size (Cohen's d = 2.01), where ZNE yields extrapolated expectation values of the portfolio objective rather than a discrete portfolio solution without noise. A validation run conducted after a 13-day interval confirms the temporal stability of the methodology against hardware calibration drifts. These findings establish empirical quantum utility in an environmental science context, showing that current NISQ-era devices, when coupled with rigorous error mitigation, can identify complex territorial synergies that myopic classical approaches overlook. The proposed workflow provides a scalable methodological template for high-precision environmental conservation policies.

Multi-plane light converters (MPLCs) are an emerging beam shaping technology capable of deterministically mapping a basis of input spatial light modes to a different basis of output modes. The ability to perform such multi-modal spatial reformatting operations has many future applications in both classical and quantum photonics, spanning from optical communications to photonic computing and advanced imaging. In this work we fabricate miniaturised transmissive MPLCs fully-encapsulated within a fused silica glass chip using single-step 3D direct laser writing. Our approach relies on the formation of femto-second laser induced birefringent nanogratings with a spatially controllable slow-axis orientation. Multiple layers of these nanogratings are laser-written throughout the volume of the glass to create a sequence of axially separated geometric phase holograms which imprint controllable phase patterns onto circularly polarised read-out light propagating through them. We construct and test a range of proof-of-concept laser-written MPLCs operating in the visible (lambda = 633nm). These miniature beam multiplexers are formed from up to 5 separate phase masks of width ~260um, cascaded along a total length of ~2.7mm, thus occupying a compact volume of ~0.15 mm3. We first demonstrate Hermite-Gaussian (HG) mode sorters capable of diverting the energy carried by up to 28 overlapping HG modes into spatially separated output channels. We next create a 7-mode orthogonal speckle sorter, highlighting the universal nature of the spatial transformations it is possible to encode. Finally, we show analogue optical matrix multiplications achieved by passively scattering light through these 3D structured glass elements. Our work begins to merge the concepts of free-space optics with 3D integrated photonics in glass and plots a path towards the rapid prototyping of robust monolithic MPLC technology.