Papers

Learning general-purpose robot policies requires large-scale real-world interaction data, yet collecting robot demonstrations remains expensive and difficult to scale. Egocentric videos offer abundant human interaction experience with task-relevant semantics for robotic manipulation, but direct transfer is challenging for two reasons: latent actions inferred from frame reconstruction can be dominated by nuisance variation such as ego-camera motion, and human and robot behaviors often exhibit different temporal dynamics. We propose WING (World Action Learning via INteraction-Centric Spectral Latent Guidance), a framework for transferring interaction knowledge from egocentric videos to robot policies. WING first separates observer-induced motion from hand-object interaction and distills the interaction-centric component into latent actions. It then exploits the observation that cross-embodiment task semantics are concentrated in slowly varying temporal structures, identifying shared low-frequency components between egocentric latent actions and robot behaviors in the spectral domain and using them to guide action generation. WING achieves average success rates of 99.20% on LIBERO, 93.80% on RoboTwin 2.0, and 57.7% on RoboCasa-GR1, and also performs strongly across four real-world manipulation tasks under diverse generalization settings. These results show that interaction-centric spectral guidance provides an effective and scalable way to transfer physical interaction knowledge from human egocentric video to robot control. Project page: https://mikuz12.github.io/wing/

We study extremal and next-to-extremal four-point correlators involving general quarter-BPS operators in $\mathcal{N}$=4 Super Yang-Mills. Using a combination of $R$-symmetry considerations, operator product expansion content, and analytic superspace techniques, we show that such correlators get contributions only from operators belonging to short and semi-short multiplets. This result together with the non-renormalizability of the relevant three-point functions guarantees that all such four-point correlators are protected from quantum corrections.

Non-Clifford gates are essential for avoiding classical simulability under the Gottesman-Knill theorem. An error-corrected circuit with non-Clifford gates will therefore be an important element for realizing useful fault-tolerant quantum algorithms. However, accurately understanding the fault-tolerant performance of such circuits faces challenges due to the classical hardness of simulating these circuits. We avoid simulating logical measurements and develop exact and efficient classical methods for benchmarking circuits composed of X, CNOT, and diagonal gates in the Clifford hierarchy, including state and gate teleportation gadgets with feedforward. For circuits with third-level diagonal gates, our benchmarking algorithm efficiently samples syndrome statistics and estimates the output logical fidelity and expectation values of certain Clifford observables, including all Pauli observables. The evaluation of syndrome expectation values also extends to circuits with fourth-level diagonal gates. Our algorithm scales polynomially in the number of physical qubits n and circuit depth T, independent of the number of logical qubits. The benchmarking applications include IQP sampling and magic state preparation/cultivation. We demonstrate the practical utility of our simulation algorithms by using them to optimize high-rate magic state distillation factories based on three copies of a [[27,3,3]] tricycle code.

Temporal abstractions, often instantiated as options, have long been regarded as a mechanism for accelerating credit assignment, facilitating exploration, and enabling generalisation in reinforcement learning (RL). However, developing general option discovery methods that are effective in large-scale, high-dimensional domains remains a fundamental challenge. Existing option discovery methods are either confined to relatively simple domains, depend on handcrafted or quasi-symbolic representations, or offer little improvement over learning without options. We present Wayfarer, a general, domain-agnostic, online deep RL agent that discovers options through Laplacian representation learning from high-dimensional observations and leverages them for control. We show that the resulting options simultaneously improve exploration, accelerate credit assignment, and generalise effectively to unseen settings, enabling substantially faster learning of complex policies. Wayfarer achieves state-of-the-art performance among single-stream agents on the most challenging Atari 2600 games, with the largest gains in games that require long-horizon exploration and strategic behaviour, such as Montezuma's Revenge and Private Eye.

We present a phenomenology-driven overview of opportunities and outstanding challenges in baryon electroweak transitions, focusing on hyperon and charmed-baryon processes for which lattice-QCD results are available, including semileptonic decays and selected radiative, dileptonic, and neutrino-induced channels. We identify semileptonic decays of strange and charmed baryons as a particularly promising domain for synergy between phenomenology, experiment, and lattice QCD. Particular emphasis is placed on the determination of vector and axial form factors, the precision and model-independent extraction of $|V_{us}|$ from hyperon semileptonic decays including radiative corrections, and on searches for non-standard interactions through lepton-flavor- and CP-violating observables. We examine the momentum dependence of form factors in ground-state transitions, highlight the emerging $\Xi_c \to \Xi$ semileptonic puzzle stemming from tensions between lattice-QCD predictions and experimental measurements, discuss inclusive decay rates, and outline strategies for extending these studies to transitions involving excited baryon states. For completeness, we review also results involving beauty-baryon decays.

Spatial semantic segmentation of sound scenes (S5) involves the detection and extraction of target sound events in audio files. However, in typical detection-extraction pipelines, errors in the detection module propagate to the extraction module, degrading overall performance. In this work, we develop a multichannel detection-extraction model and evaluate inference-time algorithms to improve the class detection and target sound extraction in a multi-stage setup. We evaluate two fitness functions: binary cross entropy and mixture consistency; two relabeling strategies: naive and conditional confusion matrix relabeling; and three source estimate evaluation models: a multi-label classifier, a fine-tuned single-source classifier, and an off-the-shelf audio judge. We thoroughly evaluate the impact of these design choices on the DCASE 2025 Task 4 dataset, and validate entropy-based gating of inference-time updates on the held-out evaluation set, laying the groundwork for inference-time updates of S5 systems in real-world scenarios.

The recent discovery of high-T$_c$ superconductivity in bilayer nickelates has highlighted the crucial role of interlayer coupling and motivated proposals for dominant interlayer pairing. Whether such pairing can support topological superconductivity, however, remains unexplored. Here, we demonstrate that substrate-supported bilayer nickelate thin films can host an intrinsic time-reversal-invariant topological superconducting phase protected by diagonal mirror symmetry. Using a two-orbital model derived from first-principles calculations, we show that a modest layer-asymmetric potential and layer-staggered Rashba spin-orbit coupling drive the system into this topological phase over a broad parameter range with a dominant interlayer pairing. The nontrivial topology arises from a reversal of the pairing sign on one of the spin-split bonding Fermi surfaces and is characterized by a nonzero mirror winding number along the diagonal direction, as well as a Majorana Kramers pair at the [11] edge. The phase also features bulk gap nodes located slightly away from the diagonal directions, featuring chiral charge and zero-energy flat bands. We discuss experimental routes for realizing and tuning this phase. Our results establish high-T$_c$ bilayer nickelates as a promising platform for topological superconductivity, where tunable topological transitions and Majorana boundary modes can provide probes of unconventional pairing.

This paper proposes a learning-based beam adaptation framework for active/passive-aware monopulse integrated sensing and communication (ISAC) with spatial leakage suppression. A single gNB uses a shared array and orthogonal frequency division multiplexing dual-functional radar-communication signaling to jointly support downlink transmission and monopulse sensing. Radar detections and uplink spatial evidence are fused to distinguish cooperative active directions from passive directions, while a protected angular zone limits unintended illumination. Soft Actor-Critic deep reinforcement learning adapts the transmit beam using communication, sensing, leakage, and previous-action feedback. Numerical results show accurate active/passive spatial classification and robust leakage control as the number of passive targets increases from one to twelve. The proposed SAC controller maintains aggregate passive leakage below the prescribed budget across the full sweep and, from two passive targets onward, achieves the highest leakage-compliant sum rate among the considered baselines.

High-fidelity 3D head avatars have reached near-photorealistic quality. While recent methods enable text-driven manipulation, they struggle to provide fine-grained localized control, often entangling features or lacking geometric consistency. Modifying geometry through natural language currently requires slow per-prompt optimization or compromises identity and rigging. We present ManifoldSplat, the first end-toend framework for language-guided semantic shape editing of animatable 3D Gaussian Splatting avatars reconstructed from monocular videos. By performing edits within the structured FLAME manifold rather than directly optimizing an unstructured Gaussian cloud, we strictly preserve identity and animation. We introduce DeltaRegion, a per-region disentangled Conditional Variational Autoencoder (CVAE) delivering feedforward shape deltas, alongside a refining stage to recover view-consistent details. ManifoldSplat reconstructs and edits an avatar in ~90 seconds on a consumer GPU, rendering at ~800 FPS. Extensive evaluations demonstrate our approach sets a new state-of-the-art in localized prompt alignment, geometric coherence, and identity preservation. Project page and code: https://a-canela.github.io/manifoldsplat/

Reinforcement learning (RL) is increasingly used for financial optimal-control problems when complex dynamics make analytical strategies difficult to obtain. There are financial mathematics literactures which provides many solved models whose equations and controls could evaluate and guide learning; we ask whether RL can exploit these results. We place a proximal policy optimisation (PPO) agent in an analytically solved continuous-time broker–trader game. PPO replaces the broker and chooses its trading speed while interacting with an informed trader and stochastic uninformed order flow. We derive a finite-step reward from the broker's continuous-time payoff and verify its discrete implementation through grid refinement and an exact one-step identity. With zero uninformed flow, a validation-selected PPO–FFNN approaches the reference action. With stochastic uninformed flow, the tested PPO–FFNN and PPO–LSTM remain inaccurate, although supervised learning confirms that their actors can represent the action. Monte Carlo diagnostics show that their critics do not reliably rank nearby actions; potential-based reward shaping also gives no reliable improvement. Under partial information, a causal certainty-equivalent controller based on the broker's observable history remains close to the reference, while PPO has larger errors and lower payoffs. Finally, we freeze the analytical policy and train PPO to adjust it after the execution cost changes. Halving the cost yields a repeatable improvement that closes \(2.22\%\) of the gap to the changed-cost reference. The analytical solution therefore provides both a benchmark for diagnosing RL and a useful starting policy for adaptation.

Federated learning lets many clients train a shared model together without ever sending their private data to a central server. Each client shares only a model update, and this update should reveal far less about the client than its raw training examples would. This premise is what protects the privacy of the clients. Gradient inversion attacks challenge it directly by trying to reconstruct a client's private input images from the single update it shared. Under FedAvg, a client's update accumulates several local training steps, so the server sees only the two endpoints of a hidden weight trajectory. Recent gradient inversion attacks fit a surrogate model along the path between these two endpoints but they still read its gradient at a single point. We propose the Path-Integral Surrogate Model Extension (PI-SME) which treats the accumulated update as a path integral of the gradient field and approximates it by Gauss–Legendre quadrature over several nodes along a learnable Bézier path. On CIFAR-100 and FEMNIST images across a range of trajectory lengths and class-restricted batches PI-SME reconstructs the private inputs more faithfully than the strongest surrogate baseline on several inversion metrics and the matching loss.

Larval dispersal and settlement govern the replenishment of sessile marine populations and the assembly of benthic communities, yet how larval traits interact with near-surface flow structures to direct settlement remains unclear. We used coupled hydrodynamic and larval-scale simulations to resolve how swimming speed and body shape, from circular to elongated, influence settlement in oscillatory flow over ridged substrates. Settlement success differed by up to an order of magnitude across trait combinations. Near-surface flow acted as a trait filter by differentially regulating transport to, retention near, and encounters with the substrate. The trait that mattered most depended on the local flow structure. Where rapid flow restricted access to settlement surfaces, swimming speed was most important. Where flow recirculated between substrate ridges, shape-dependent alignment controlled transport and retention. These results link larval traits to flow-mediated settlement mechanisms and provide a physical framework for understanding how recruitment varies across complex benthic habitats.

The minimal sampling overhead of the quadratic collective phase $e^{-i\gamma K^2}$ over one layer of single-qubit rotations is decided by the continued fraction of $\gamma/\pi$. Here $K$ is a collective observable with spectrum $\{0,\dots,n\}$, such as the permutation-symmetric Hamming weight. This gate is the cardinality-penalty layer of constrained optimization, the one-axis-twisting gate of spin squeezing and the Kerr phase of a bosonic mode. Instead of compiling it to two-qubit gates, we sample it as an LCU over such layers at overhead $\Gamma$. Our results give an optimality theory for this overhead. Ancilla-free sampling reproduces the target's outcome probabilities up to the minimal $\Gamma$, and no smaller factor works for every input; for permutation-symmetric $K$, independent per-qubit angles or one layer of arbitrary single-qubit gates give no further reduction. Rational angles $\pi p/q$ in lowest terms cost exactly $q$ once $n\ge2q-2$, attained uniquely by a uniform $q$-point sampler; the cost is $\Theta(n)$ if and only if $\gamma/\pi$ is badly approximable, and bounded in $n$ if and only if it is rational. A second result shows what the symmetry buys: without it, the squaring phase of Fourier arithmetic on $m$ qubits costs at least $2^{0.557m-O(1)}$ over single-qubit gates, beyond the $2^{m/2}$ of every cut bound, by a new certificate-lifting argument. For constructions known only through upper bounds, it gives the optimum: the Fourier-based LCU of Carrera Vazquez, Egger and Woerner is, at fixed $n$, optimal up to a constant at typical angles and beaten by $(n+1)/q$ at rational ones with an $n$-independent sampler; the Kerr decomposition of Upreti, Quesada and Chabaud is the unique optimum over phase shifters at rational parameters without photon-number cutoff; and it identifies the rational couplings where one-axis twisting admits optimal cat decompositions.

For quantum low-density parity check (qLDPC) codes, the ability to manipulate individual logical units of information, i.e. the use of addressable gates, enables maximal utility of their efficient encoding. We introduce explicit low-depth unitary circuits that realize fully addressable and fault-tolerant two-qubit Clifford gates for a subset of two-dimensional translationally invariant qLDPC codes. Our transversal unitaries are created by applying a geometrically structured sparsification procedure to round-robin circuits. We verify the general applicability of our protocol by proposing and numerically simulating a range of addressable CZs between toric, cyclic hypergraph-product, color, gross, and directional codes, demonstrating fault-tolerant memory-like logical error rate scaling.

Quantum fire is a recently introduced cryptographic primitive consisting of efficiently preparable quantum states, called flames, that admit efficient cloning but resist efficient telegraphing, namely reconstruction via classical communication without preshared entanglement. In all prior constructions of quantum fire, cloning is a public operation that requires no separate key and every holder of a flame state can clone it. For applications to access control, however, an issuer may wish to delegate cloning to designated quantum servers while withholding this capability from other flame holders. To address this, we introduce delegatable quantum fire, in which cloning requires a separate key. We give two constructions in the classical-oracle model. Our first construction uses a classical secret key which enables cloning, and any user with the entire key may clone successfully. Our second construction, which we call torch-fire, uses quantum cloning keys, called torches, which enable cloning while remaining unaffected in the process but cannot otherwise be split or delegated to enable additional cloning. An efficient adversary given $m$ torches cannot, except with negligible probability, enable more than $m$ noncommunicating parties to each clone a fresh, independently issued challenge flame. The adversary may jointly process its resources before separating the parties and distribute arbitrarily entangled registers among them. Both constructions are in the oracle model, relying on public classical oracles that allow queries in quantum superposition.

For noncompact smooth Kähler-Ricci shrinkers, we prove a Matsushima theorem identifying the centralizer of the soliton field with the complexification of its Killing centralizer, uniqueness up to biholomorphism on a fixed complex manifold, and K-polystability of the associated polarized Fano fibration.

Understanding and assessing natural hazards is essential for disaster preparedness and risk reduction. Recent advances in large language models have spurred growing interest in AI agents for hazard analysis, particularly their ability to integrate scientific data, models, and tools into automated workflows. However, effective automation requires agents to determine which scientific methods are appropriate for a given event and executable with the available data and tools. As new evidence and execution results become available, these conditions can change, requiring agents to reconsider their choices. We formulate this problem as state-dependent scientific route selection and introduce HazardWeaver. Specifically, HazardWeaver first leverages the Hazard Knowledge Compiler to extract evidence-linked conditions governing scientific applicability, then its Hazard Capability Graph represents executable scientific capabilities and checks compatibility between their inputs and outputs. Using these complementary representations, the Hazard Weaver Agent component selects applicable and executable routes, carries out their workflows, and revises its decisions as the analysis state changes. To evaluate both the scientific outputs and the decisions that produce them, we introduce the Hazard Weaver Benchmark, comprising 141 instances across seven single-hazard domains and four multi-hazard interaction classes. The benchmark accommodates multiple valid scientific routes and evaluates output correctness, route validity, and justified abstention. Extensive experiments on this benchmark show that HazardWeaver outperforms existing agent systems, with the largest gains on tasks with multiple eligible scientific routes. Our code is publicly available at https://github.com/LabRAI/HazardWeaver.

We present a unified framework for upgrading a broad class of cryptographic primitives to support constant-rate certified deletion. Previous constructions require a linear number of qubits per encrypted bit of certified-deletable plaintext. In contrast, we obtain the first constant-rate constructions in the plain model that achieve certified deletion while preserving everlasting security. Our approach applies to a wide range of "all-or-nothing"-type primitives based on BB84-style encodings, including commitment schemes, public-key encryption, attribute-based encryption, and fully homomorphic encryption. Beyond this class, we also obtain constant-rate certified deletion for primitives built from subspace coset states, such as blind delegation, secure software leasing, functional encryption, and differing-inputs iO, and CCA-PKE. Importantly, our framework does not introduce any additional assumptions beyond those required by the underlying certified deletion primitives. Finally, under the hardness of SIS, we show that public verifiability can be incorporated into BB84- and coset-based certified deletion. In combination with our constant-rate constructions, this yields publicly verifiable certified deletion schemes with constant rate.

Post-training text-to-music generation requires reward signals that capture multiple aspects of musical quality beyond what any single automatic metric can measure. We study structured, rubric-based rewards from pretrained audio-language models (ALMs) as training signals for both autoregressive and diffusion-based music generators. An ALM scores each generated clip against the rubric; we rank candidates generated for the same text prompt by their scores and convert these rankings into preference pairs for DPO on both MusicGen-small and ACE-Step v1, and additionally use the rubric scores directly as scalar rewards for DiffusionNFT on ACE-Step v1. On MusicCaps, rubric-based optimization improves CLAP, SongEval, and Audiobox-Aesthetics simultaneously, with the strongest gains obtained by DiffusionNFT on ACE-Step. By contrast, on MusicGen-small, building preferences from any one of these automatic evaluators produces clear cross-metric trade-offs: the targeted evaluator improves while other independent evaluators deteriorate. We further study tempo, key, and instrumentation, where precise objective rewards are available. Directly optimizing these specialized rewards reliably improves the target attributes, whereas ALM rubrics provide only partial transfer for tempo and instrumentation and no measurable improvement for key. Together, these results suggest a practical division of labor: ALM rubrics are effective for broad perceptual qualities that are difficult to formalize, while specialized objective rewards remain preferable when reliable measurements are available.

We give a sublinear-time algorithm for estimating the size of a maximal independent set in a graph using adjacency-query access with expected running time $\tilde{O}(n^{1+1/3})$, improving over the previous $\tilde{O}(n^{1+1/2})$ bound of Mahadabi et al. [MRTV26]. As a consequence of a reduction of [MRTV26], this also improves the running time for sublinear metric Steiner forest. We further show that a bi-criteria estimate of the $k$-center objective in general metrics can be obtained via a reduction to maximal independent set size estimation.

Joint embedding predictive architectures (JEPAs) predict future latent representations without reconstructing observations, enabling world models to focus on high-level semantic dynamics. However, a JEPA can preserve high dimensional visual information while discarding information about the physical consequences of actions. We call this failure mode causal dynamics information collapse and propose action-grounded vision-invariance latent (AVL) to prevent this collapse. We first use the executed action as an auxiliary dynamics anchor that encourages the model to preserve dynamics information, and then use a vision-invariance pathway which aligns perturbed and clean latent predictions without discarding dynamics information, forcing the model to fully understand and utilize causal dynamics information. We validate AVL on four robotic control tasks (TwoRoom, PushT, OGBench Cube, and Reacher), showing that it substantially improves success rates under visual perturbations while preserving clean-environment performance. We further evaluate physical consequence alignment, clean-noisy dynamics consistency, and the causal effect of targeted transition subspace erasure. Collectively, these results indicate that dynamic information causally relevant to planning is preserved from collapse under AVL.

Randomized benchmarking comprises a suite of standard techniques for assessing the operational fidelity of quantum processors. These techniques can be reliably applied to groups with process matrix representations that are free of multiplicity. However, many groups that are naturally formed from native gates do have multiplicity, and it is difficult to draw robust conclusions from the resulting data. In this work, we present a new and intrinsic solution to the problem of multiplicity that completely eliminates the need to fit multi-exponential decays while still remaining robust to errors in state preparation and measurement. Our procedure, which we call lifted randomized benchmarking, generalizes key elements of both character and synthetic randomized benchmarking to benchmark a target group of quantum gates with respect to an enlarged group. We illustrate in numerical examples that our method can efficiently and reliably estimate the fidelity of two-qubit gates relevant to experimental trapped-ion systems. These techniques may find applications beyond randomized benchmarking to quantum tomography and learning, as well as the characterization of error-correcting codes.

Security benchmarks for LLM-based agents often report the attack success rate (ASR) as a measure of model robustness and use these scores to compare different models and defense mechanisms, assuming that they describe the security of the agent. In this paper, we explore whether it also influences the benchmark's measurement. To measure the effect of the benchmark representation, we introduce threat-preserving representation sensitivity (TPRS), which measures how much the ASR changes when we change the agent-visible representation while holding the underlying task, harmful action, security policy, ground truth, environment, and the evaluation criteria fixed. On Agent Security Bench (ASB), replacing threat-related tool names with threat-neutral names raises the committed attack success rate by 11.67 percentage points on GPT-5-mini and by 13.21 points on Claude Haiku 4.5. On MCPTox, replacing the original neutral tool name with an explicit threat-related name lowers the ASR by 11.00 percentage points on GPT-5-mini and 4.11 points on Claude Haiku 4.5. On AgentDojo, adding threat-related wording to the attack-relevant tool changes ASR by only 0.50 percentage points on GPT-4o-mini, yet the benign utility falls by 5.36 points on tasks requiring that tool. We ran an experiment on MCPTox where we observed that a threat-neutral name matched on token count, length, and casing reproduces most of the shift produced by the threat-explicit name (8.54 of 11.00 points on GPT-5-mini). The results show that a security score measured under one representation may fail to generalize across threat-preserving representations of the same security problem. Robustness claims should therefore be supported by performance across a controlled set of threat-preserving representations rather than relying on a single representation-dependent score.

The computational complexity of simplicial homology has been studied since the question was raised by Kaibel and Pfetsch, and clique homology was later shown to be $\mathsf{QMA}_1$-hard by Crichigno and Kohler. King and Kohler subsequently introduced the weighted, spectrally gapped version considered here and developed a reduction intended to establish the same hardness result in this setting. We give a complete proof of the hard direction. The earlier King-Kohler argument contains a gap in the analysis of the nontrivially folded local gadgets, so the required topological and spectral properties have to be re-established on the clique complexes actually produced by the reduction. This is not a local repair of the published proof: the argument requires a new analysis of the local topology, the filtered cochain complexes, and the interaction of many overlapping gadgets. Our proof uses exact finite certificates for the local combinatorial data and relative homology to determine the effect of each gadget on the encoded qubit space. We then prove the finite-dimensional filtered-Hodge statement needed to recover the corresponding rank-one low-energy penalty and derive a quantitative global estimate that transfers the source-Hamiltonian promise gap to the final weighted Hodge Laplacian. Consequently, for fixed efficiently computable $k(n)$ and inverse-polynomial $\gamma(n)$, weighted gapped clique homology is $\mathsf{QMA}_1(\mathcal G)$-hard. The previously known $\mathsf{QMA}$-containment argument is logically independent of the gap and remains unaffected.

We present a state-specific second-order perturbation theory based on a configuration interaction singles (CIS) reference and its generalized Fock operator. Starting from a fully internally contracted construction, we retain the complete doubles space and internally contracted triples in the first-order wave function. We consider two partitions, Canonical and Block-diagonal, with reference excitation energies given by the Fock excitation gap $\omega^{(0)}$ and the CIS excitation energy $\omega_{\rm CIS}$, respectively. Our analysis establishes that strict size-intensivity is preserved when the contracted-triples denominators use bare Fock gaps and the occupied–virtual Fock block is projected to remove residual spectator coupling. Based on this observation, combining Canonical triples with Block-diagonal doubles yields a size-intensive Hybrid partition. These properties are verified for water with non-interacting helium atoms. Our formulation enables $O(o^3v^2)$ cost per matrix–vector product in a semicanonical basis. On the QUEST\#1 benchmark, Canonical and Block-diagonal show opposite systematic biases, whereas Hybrid gives the best overall accuracy among the three partitions. Its mean absolute errors for singlets and triplets are 0.24 and 0.15~eV, compared with 0.28 and 0.22~eV for CIS(D). The improvement is largest for Rydberg excitations, although CIS(D) remains more accurate for valence singlets.

We initiate the study of weak Schur sampling (WSS) under noisy inputs. Many optimal quantum learning algorithms rely on this measurement, for instance in quantum spectrum estimation (QSE) and quantum state tomography (QST). The standard analysis of WSS, QSE and QST assumes that the $n$ input copies of the target state $\rho$ are identical, i.e. $\rho^{\otimes n}$. We study what happens when they are not, a more realistic noisy scenario that breaks the very permutation symmetry on which WSS is built. In the simplest model the input is a noisy product state: the copies are independent but not necessarily identical and each is $\epsilon$-close in trace distance to the $d$-dimensional target state $\rho$. A naive argument via the data-processing inequality allows the per-copy errors to accumulate to $n\epsilon$ on the measurement outcome. We show that for QSE via WSS this does not happen: the expected estimation error in total variation is at most $\epsilon+\eta(n,d)$, where $\eta(n,d)=O(d/\sqrt n)$ is the noiseless error, and the additive noise term $\epsilon$ is optimal. The output error does not grow with $n$ even though the input error does; in this sense WSS is robust. Beyond noisy product states, for arbitrary input $\omega$ we show that the error is at most $\eta(n,d)+\frac{1}{n}\|\omega-\rho^{\otimes n}\|_{W_1}$, where $W_1$ is the quantum Wasserstein distance of De Palma et al. In particular, our results imply, for the first time, noise-robustness of Keyl and Werner's seminal algorithm for QSE, more than two decades after its introduction. Finally, we show that the noise cannot be too bad: within our model of robustness the promise on the input cannot be weakened to closeness of single-copy marginals or to a global trace-distance budget alone, as in both cases some inputs defeat every measurement and estimator.

A quantum orthogonal polynomial transform (QOPT) is an algorithmic primitive that maps a superposition of standard basis states $\sum_k \alpha_{k} \ket{k}$ coherently to a basis of normalized univariate polynomials orthogonal with respect to a probability measure $\mu(x)$. We provide new discrete and continuous QOPTs for polynomial families in the Askey scheme extending the results for the quantum Hermite transform (Jain et al., STOC'26). Our efficient QOPT algorithms require time $O(\text{polylog}(N, 1/\epsilon))$, where $N$ is the grid size and $\epsilon$ is the error, for the discrete Charlier, Meixner and Krawtchouk transforms and for the integer-order Laguerre transform in the continuous setting. The efficient QOPTs are obtained by uncovering the links between Askey scheme polynomials and Gaussian quantum optical gates and developing a compilation framework for $SU(2)$ and $SU(1,1)$ optical gates on Cartesian grids extending the framework developed by Iyer et al. (arXiv:2602.15180). Further, we reduce the continuous Jacobi transform to the discrete Hahn transform and provide an $O\!\left(N\operatorname{polylog}((N+\alpha+\beta+1)/\epsilon)\right)$-time Hahn transform, a quadratic speedup over the naive implementation. This is based on a more efficient compilation of the Clebsch–Gordan transform for coupling $\mathrm{SU}(2)$ representations with spins $(j_{1}, j_{2})$. Finally, we develop a new framework for Laguerre transforms for all orders $\nu>0$ by fast-forwarding the corresponding radial oscillator using a 3-term chirp decomposition and an efficient algorithm for the Quantum Hankel Transform on a logarithmic grid.

For classical–quantum wiretap channels with a transitive covariant input action, both output ensembles admit a description as unitary group orbits of fixed seed states. We use this structure to construct finite-block preprocessing schemes whose private information is an entropy difference evaluated at two distributions related by group convolution. Applying the construction to product groups allows correlations across any fixed number of channel uses. We give a sufficient condition for the associated uniform-input bound to equal the single-use private information. Constant-composition channel codes and universal$_2$ hashing achieve the resulting rates, with trace-distance leakage controlled by sandwiched Rényi information. For uniform outer randomization, the representation structure reduces the comparison-state optimization to Eve's invariant states. For the hybrid binary channel considered by Tikku, Berta and Renes, numerical optimization at three and four uses gives rates above our numerical estimate of the optimized noisy-repetition benchmark wherever that estimate is positive on the tested grid. The improvement comes from noise distributions beyond the family of independent physical flips and a symmetric logical flip. We also prove nonadditivity at an explicit channel parameter using a two-use encoder, an analytic single-use converse, and certified entropy bounds. Finally, we relate the hybrid model to binary phase-shift keying with a fixed receiver measurement.

We study the average sizes of ideals and antichains in several families of posets arising from rooted unlabeled trees. For ideals, we encode order ideals by coloring vertices red, with the condition that every descendant of a red vertex is also red. Using generating functions and singularity analysis, we show that for every family governed by a quadratic root decomposition, the average number of red vertices in a tree of size $n$ is asymptotic to $n/3$. This includes binary plane trees, plane 1-2 trees, plane 2-trees, and 0-1-trees, while unrestricted rooted plane trees instead have average ideal size asymptotic to $2n/5$. For antichains, represented by pairwise incomparable blue vertices, the corresponding asymptotic constants depend on the particular branching function; for example, binary plane trees have average antichain size asymptotic to $n/6$. We also consider plane trees in which every vertex has at most $k$ children and prove that the asymptotic proportion of red vertices increases strictly with $k$, from $1/3$ when $k=2$ to the limiting value $2/5$ for unrestricted rooted plane trees. The asymptotic proportion of blue vertices also increases strictly with $k$, tending to $3/10$. The proofs are based on bivariate generating functions together with the analytic implicit-function and smooth implicit-function methods of analytic combinatorics.

Classical Dobrushin–Shlosman theory uses heat-bath block updates to identify sharp temperature thresholds for establishing the rapid mixing of Gibbs samplers. In particular, these mixing guarantees often hold even when stricter single-site conditions fail. We extend this approach to noncommuting quantum lattice systems through a quantum Dobrushin–Shlosman condition for finite-block dynamics, which we call smoothed heat-bath dynamics. We establish this condition in two regimes. For finite-range quantum spin chains at every fixed finite temperature, we prove logarithmic trace-norm mixing in system size, with normalized bounds uniform in on-site fields and single exponential in inverse temperature. We also prove stability under small local perturbations of interacting, possibly noncommuting reference Hamiltonians on graphs of polynomial volume growth. For classical references with bounded local interactions, uniform strong spatial mixing implies our quantum condition. With bounded local terms and fixed physical, geometric and block parameters, the resulting samplers prepare Gibbs states to trace-norm error $\varepsilon$ using $N\operatorname{polylog}(N/\varepsilon)$ gates and classical operations. Our block updates combine a local Gibbs reset with quantum belief propagation to incorporate interactions across the block boundary, yielding exactly Gibbs-preserving, KMS-reversible channels. Two independently tunable parameters control contraction: an internal evolution time suppresses the influence of sites inside a block, while the block size allows interior contraction to dominate boundary influence. This finite-time relaxation has no counterpart in a classical heat-bath block update.