Papers

For positive integers $t$ and $q$ let $b_q(t)$ be the smallest integer $n$ so that any coloring of the edges of the complete bipartite graph $K_{n,n}$ with $q$ colors yields a monochromatic copy of $K_{t,t}$. We give an independent proof that $b_2(t)\le 128\cdot 2^t$ for every positive integer $t$. More generally, for $0< p\le 1/2$, every bipartite graph of edge density at least $p$, with both classes of size at least $128\cdot p^{-t}$, contains $K_{t,t}$. This gives $b_q(t)\le 128\cdot q^t$ for every integer $q\ge 2$ and a uniform consequence for Zarankiewicz numbers.

Physics-constrained generative models aim to generate physical fields that match a target distribution and satisfy prescribed constraints. However, enforcing these constraints often increases sampling costs through iterative corrections or training costs through residual optimization and trajectory unrolling. To address this issue, we introduce Preconditioned Manifold one-step Flow Matching (PMosFM), a preconditioned manifold matching framework for one-step physics-constrained generation. By encoding constraints in a manifold decoder, PMosFM learns transport in intrinsic coordinates without separate residual losses or terminal residual unrolling. A geometric preconditioner rescales coordinates using the decoder-induced metric, while a regularized covariance transform approximately whitens the interpolation-state inputs. A finite-interval objective couples velocity supervision with consistency between decoded endpoints in physical space. We show that exact parameterization removes residual-induced Gauss–Newton curvature, that geometric and covariance effects separate in a local conditioning bound, and that physical flow-map error bounds endpoint distributional error. Controlled ablations examine conditioning, and experiments evaluate optimizer-update time and memory footprint. At inference, PMosFM uses one neural transport evaluation followed by physical decoding. Experiments across benchmarks show lower training and sampling time than the multi-step baselines at comparable physical and distributional fidelity. Code and datasets will be released publicly.

Unlearning a fact in one language does not guarantee its removal in others as changing the query or even the requested answer language can reopen seemingly forgotten knowledge – a cross-lingual loophole. The most straightforward solution to this challenge – unlearning in all languages – is neither scalable nor desirable as it amplifies damage to unrelated model capabilities. We introduce the task of language budgeted multilingual unlearning where the goal is to select a subset of languages that maximizes cross-lingual erasure. To study this task we introduce the Cross-Lingual Unlearning Tensor, an unlearning benchmark that spans 174 language–script pairs and 25 atomic paraphrase types to examine when forgetting generalizes across linguistic expressions of the same knowledge. We further propose COVER, which selects source languages to maximize predicted COVERage of languages receiving no forget supervision, enabling unlearning on a language budget. Surprisingly, we find naively selecting strong individual sources does not reliably compose into strong source sets motivating our development of COVER. At deployment COVER only requires benign calibration data and access to the frozen model. Across three model families and two disjoint forget sets, COVER reduces mean held-out residual access by 7.8–27.3% relative to uniform source selection. We find these gains extend beyond synthetic benchmarks to real news documents in low-resource language settings using human translated data from the Low Resource Languages for Emergent Incidents (LORELEI) corpus.

On-policy distillation (OPD) is a promising approach for training language agents, providing dense teacher supervision on student-generated trajectories. However, in multi-turn interaction, an incorrect action changes the states the student encounters later, so errors compound across turns. In preliminary experiments across three Qwen3 models (8B to 235B), we find that more than half of the failed rollouts contain a pivotal mistake, an action that moves the agent farther from completing the task, and this mistake typically occurs early. These pivotal mistakes often remain recoverable: guiding the model for only a few turns after the pivotal turn can restore task success. We therefore propose PivotOPD, an on-policy distillation framework that jointly trains the student to prevent pivotal mistakes and to recover from the states they create. At each pivotal mistake, a teacher model provides a gold action and then names a recovery action at each of the next few turns. Preventive distillation uses the gold action with reverse KL to steer the student away from the pivotal mistake, while recovery distillation uses the recovery actions with forward KL to transfer recovery behaviors that the student rarely samples. Against 13 baselines on ALFWorld, WebShop, and Search-based QA, PivotOPD achieves the strongest average performance for both Qwen3-1.7B and Qwen3-8B students, improving over the strongest baseline on ALFWorld by +5.5% with the 1.7B student. The gains also transfer to another model family on the software engineering domain, where PivotOPD raises the resolve rate of a Nemotron-3.5 student on SWE-Bench Verified by +3.2%. Project page: https://research.nvidia.com/labs/lpr/pivotopd/

Computer use agents (CUAs), which use graphical user interfaces (GUIs) to complete tasks on a computer, have recently surpassed human performance on many standard benchmarks, including difficult long-horizon tasks. Their capabilities are undoubtedly impressive, however, a key barrier to the widespread adoption and deployment of CUAs remains their speed and cost. Progress towards faster yet capable CUAs requires reliable evaluation of their speed, but many CUA benchmarks currently face a reproducibility crisis. Benchmarks are based on complex infrastructure with varying machine and container configurations that confound the evaluation of the execution speed of CUAs. Towards addressing this gap, we propose cua-speedrun, which introduces standardized infrastructure and task sets, with a focus on evaluating the speed and efficiency of CUAs. cua-speedrun uses a uniform virtual machine setup and execution pipeline, along with a common agent interface that enables single-agent implementations to operate seamlessly across different benchmarks. Across four different CUA benchmarks, we evaluate how reasoning effort, agent harnesses, and environment latency affect performance, speed, and cost. We find no single model family is optimal for all three; none of the open-weight models are on the frontier, and also, unintuitively, for some models increasing the reasoning effort can speed up task completion, while faster environment input-output can slow down overall task completion time. We also demonstrate that we can effectively reduce the evaluation task set of most CUA benchmarks without degrading overall statistical power, allowing for more efficient benchmarking and comparison. We believe cua-speedrun will enable structured progress towards fast, efficient CUAs, unlocking new real-world use cases and applications. All code, infrastructure, and analysis are available at https://cuaspeedrun.com.

Multi-tenant quantum processors expose a pulse-level attack surface in which coherent crosstalk can mimic benign calibration drift at matched average gate infidelity. We present a structural verification and detection framework based on the residual Pauli transfer matrix (PTM). We prove that products of local unital, trace-preserving channels cannot mix weight-1 and weight-2 Pauli operators, even under coherent drift of arbitrary strength or axis. Building on established PTM-to-Hamiltonian relations, we prove that, for any specified qubit pair in an arbitrarily large system, the first-order map from its nine interaction coefficients to the antisymmetric cross-weight feature is an isometry up to scale. Thus, every interaction direction is locally observable near the identity. We also exhibit cancellation of this feature under large local rotations and prove that the full cross-weight norm is invariant under local unitary composition, providing a structural countermeasure. For calibrated small local rotations, shared randomized-Pauli measurements support periodic verification using the evaluated antisymmetric detector. In simulation, $16{,}384$ randomized settings yield a detection threshold of $\lambda_{\min}\approx0.13$ at a $5\%$ calibrated false-positive target, with approximately $M^{-1/2}$ scaling in the number of settings $M$. Further experiments characterize detection under relaxation, depolarization, native ZZ fluctuations, and time-dependent pulse dynamics. Finally, an FRQI encoding with Pauli-graph quantum Hadamard edge detection reproduces the classical structural edge score to numerical precision.

Let $E/\mathbb{Q}$ be an elliptic curve, and let $p$ be an odd prime of ordinary reduction for $E$, and assume that $E$ admits a rational $p$-isogeny. In this paper we prove Greenberg's conjecture on the vanishing of algebraic Iwasawa $\mu$-invariants of the Selmer groups attached to $E$ over the cyclotomic $\mathbb{Z}_p$-extension of the rational numbers. Via the Iwasawa Main Conjecture for elliptic curves at Eisenstein primes, we also confirm Stevens's conjecture on the behavior of analytic $\mu$-invariants.

Characterising open quantum dynamics requires identifying the environmental degrees of freedom that shape the system's evolution. The memory dimension, defined as the size of the smallest effective memory needed to reproduce this influence, quantifies the dynamically relevant environmental resources and provides a common basis for comparing different many-body environments. Here we introduce a pseudo-control protocol that encodes information about the memory dimension in an experimentally accessible interference matrix, whose rank certifies a lower bound on this dimension without direct access to the environment or full process-tensor tomography. Applied to quantum many-body environments, the protocol allows flexible adjustment of the interaction and interval times, revealing how these parameters, environmental dynamics, and system-environment interactions shape detectable memory. Our approach provides a new operational technique for characterising open quantum dynamics and probing the structure of system-environment interactions through their memory signatures.

Spectrum cartography is crucial for spectrum-aware resource management in low-altitude networks, where uncrewed aerial vehicles (UAVs) collect spectrum measurements to reconstruct power spectral density (PSD) maps. However, limited energy and sensing bandwidth make measurements sparse in space and incomplete in frequency. To collect these measurements efficiently, the UAV actively plans its next move based on the latest map and its uncertainty, which requires rapid online reconstruction. We therefore propose an active online spectrum cartography framework. We first develop online deep-unfolded tensor decomposition (ODU-TD) for rapid map updates. An ensemble of reconstructors then estimates uncertainty to select informative sensing targets, and a learning-based policy determines the UAV movement and sensing bandwidth under the energy budget. Experiments show that ODU-TD achieves an approximately 27-fold speedup over online tensor decomposition and the lowest normalized mean square error (NMSE) among the compared reconstructors under sparse spatial and spectral observations, and the proposed framework reduces the NMSE by at least 55% compared with the representative baselines.

We give a polynomial-time classical algorithm which samples from the syndrome distribution of a surface code state corrupted by coherent nearest-neighbor $ZZ$ crosstalk. Our algorithm complements the known efficient simulation algorithms for coherent single-qubit errors in the surface code. When both single-qubit coherent noise and coherent crosstalk are present, we find a complexity-theoretic obstruction to efficient simulation: unless the polynomial hierarchy collapses, there is no efficient classical algorithm for sampling from the syndrome distribution, even up to a constant multiplicative error. This is obtained by connecting the syndrome distribution under coherent noise to the output distribution of certain IQP circuits associated with a non-planar graph.

The $f$-routing protocol is a leading candidate for quantum position verification (Kent, Munro, and Spiller, Physical Review A, 2011), but security guarantees for explicit functions remain limited. We prove unconditional resource lower bounds for uniform attackers. Our techniques bypass communication-complexity bounds central to previous works, which are inherently at most linear in the input length. We show that, for input length $n$ and a sufficiently small constant $\epsilon>0$, a uniform strategy running in time $T$ and succeeding with probability at least $1-\epsilon$ on every input implies the following computational bounds on $f$. 1. If the strategies are arbitrary quantum channels, then $f\in \mathrm{QSZK}(\mathrm{poly}(T))$, where $\mathrm{QSZK}(T)$ is the class of languages having quantum statistical zero-knowledge proofs in which the verifier runs in time $T$ and the simulator in time $\mathrm{poly}(T)$. 2. If the strategies are Clifford+T circuits using at most $t$ magic gates, then $f\in \mathrm{DTIME}(\mathrm{poly}(T2^t))$. 3. If the strategies are explicit Pauli-sparse unitaries acting on at most $T$ qubits and having at most $s$ nonzero Pauli coefficients, then $f\in \mathrm{DTIME}(\mathrm{poly}(Ts))$. Time and space hierarchies then yield explicit functions secure against superlinear and even all polynomial-time adversaries under our computational restrictions. These bounds exceed the bounded-storage qubit bound $q\leq\log n$ of Bluhm, Christandl, and Speelman (Nature Physics, 2022) for the inner product function $f=\mathrm{IP}$, at the cost of restricting adversarial computation and increasing honest evaluation complexity.

We present an efficient quantum algorithm for the non-uniform Chebyshev transform. It is defined as the projection of a function onto Chebyshev polynomials sampled at given nodes that are uniform in $x\in[-1,1]$, and hence non-uniform in the angle $\theta=\arccos x$, a setting that QFT-based quantum Chebyshev transforms cannot handle. Our construction is based on an improvement of an existing Non-uniform Quantum Fourier Transform (NUQFT) whereby we remove the conditioning from non-uniform node sampling. Hence, error bounds are independent of the geometry-dependent parameter $\kappa$ of prior work. We use the fact that Chebyshev transform matrix is the average of two Type-II non-uniform DFTs, which we implement with a single controlled NUQFT circuit. We provide explicit oracle constructions, including the row-access oracle previously left as an assumption. The resulting $\varepsilon$-accurate block encoding has $O(1)$ normalization and uses $O(L)$ qubits and $\widetilde O(L^2)$ gates, where $L=\log N+\log(1/\varepsilon)$. We give an end-to-end implementation with complexity analysis, including the success probability and output-state error.

We develop a resurgent transseries approach to mock theta functions and show that the associated Mordell–Appell integrals underlie their modular and resurgent structure. From these integrals, we recover the modular transformation laws, obtain uniqueness characterizations of the mock theta vectors, provide a canonical crossing of their natural boundary, and produce new mock theta functions. After representing the Mordell–Appell integrals as Laplace transforms of elementary resurgent functions, we rotate the Laplace contour to a Stokes line. Their Stokes phenomena and their modular transformation laws reproduce those of the associated unary series and, combined with our uniqueness results, those of the mock theta functions. Conversely, we regard these modular transformation laws as functional equations governing the mock theta vectors. For Ramanujan's order-$3$ pair $(f,\omega)$ and the distinguished mock theta vectors of orders $5$, $7$, and $11$, satisfying the full $SL(2,\mathbb Z)$ transformation laws, we prove that these functional equations uniquely determine a holomorphic solution in the unit disk under canonical minimal-growth normalization. This unique solution is precisely the classical mock theta vector. We show that the normalization is essential: for orders $5$, $7$, and $11$ we determine explicit nontrivial solutions of the homogeneous problem, yielding new mock theta functions with faster-growing coefficients. Finally, we give two intrinsic and natural constructions for crossing the natural boundary $|q|=1$. The first continues the modular functional equations and takes their unique holomorphic solutions on the other side. The second acts on the resurgent asymptotic series at the cusp: we replace $\tau$ by $-\tau$ and apply Écalle–Borel summation. We prove that the constructions agree, giving a canonical and explicit boundary crossing.

We develop a signal processing framework for signals indexed by the product of two directed acyclic graphs (DAGs) and described by a linear structural equation model (SEM). Such a setup arises whenever (linear) causal relations act along two domains, as in component versus manufacturing stage or gene versus experimental condition. Disregarding the factorization of the underlying graph and the native two-axis causal structure requires inverting a weighted transitive closure matrix whose size is the product of the two factor sizes for Fourier analysis. Recognizing that standard graph products fail to yield factorizable transitive closures, we introduce a new DAG product under which separability holds. We motivate the new operator in the vertex domain, and show that it also renders the SEM, the Fourier modes, the causal shifts, and the filters on the product DAG separable across its constituent graph factors.

The 2-switch-degree $\text{deg}(G)$ of a graph $G$ is the number of 2-switches that can be performed on $G$; equivalently, it is the degree of $G$ as a vertex of the realization graph $\mathcal{G}(d)$ of its degree sequence $d$. We classify the prime graphs of 2-switch-degree at most 4, where a graph is prime if it is indecomposable with respect to the Tyshkevich composition and every vertex takes part in some 2-switch. From this classification we derive a sharp dichotomy that recovers the global shape of $\mathcal{G}(d)$ from a single one of its local degrees: if $d$ has a realization $X$ with $\text{deg}(X)=k\le3$, then $\mathcal{G}(d)$ is vertex-transitive and $k$-regular if and only if neither $T_{221}$ nor $\overline{T_{221}}$ is an induced subgraph of $X$. Moreover, for every $k\geq 4$ some prime graph of degree $k$ carries a 2-switch raising its degree to $2k-2$. As a further consequence, up to isomorphism there are only 10 realization graphs of prime graphs with degree at most 4.

We give the first exponential quantum advantage in the general interactive three-party Numbers-on-Forehead (NOF) model for a decision problem. Previous separations hold only for restricted protocols like one-way communication for a relation. We construct an explicit partial Boolean function, the Interleaved Unitary Product problem, that requires only $O(\log n)$ NOF quantum communication but $\widetilde{\Omega}(n^{1/32})$ randomized communication. This function builds on the two-party unitary product problem of Arunachalam, Girish, and Lifshitz (TQC 2024). The main technical obstacle is that discrepancy, the standard lower-bound method for NOF, also lower-bounds quantum communication. We instead develop a regularity-based argument for randomized NOF lower bounds, building on the approach of Kelley, Lovett, and Meka and adapting the regularity decomposition of Abboud, Fischer, Kelley, Lovett, and Meka (STOC 2024) to cylinder intersections. Combined with matrix-product estimates of Arunachalam, Girish, and Lifshitz, this yields our randomized lower bound.

This paper describes a skill-based agentic framework for power-system studies using Model Context Protocol (MCP)-connected engineering tools. A custom MCP server was developed to expose Siemens PTI PSSE functions for power-flow analysis, dynamic simulation, result extraction, and model-validation workflows. Two implementation pathways built on a programmable OpenAI Agents software development kit (SDK) and a Claude Code command-line interface (CLI) were evaluated, both using reusable skills, subagents, MCP tools, data-repository connections, and local shell/Python execution. Both frontier-model-based implementations successfully executed representative study tasks. Success was evaluated based on task completion, output accuracy, and the need for human expert interventions. Results based on public datasets show that agentic systems can greatly accelerate power system dynamic simulation process for transmission planning studies leveraging industry-grade simulation platforms. This points toward a shift in transmission planning practice, where agentic systems could handle routine simulation setup and result extraction, allowing engineers to focus expert judgment on scenario design and interpretation rather than tool operation.

Protocols for quantum state tomography can be characterized either by their sample complexity or by the tomographic rate function that governs the large deviation behaviour of error estimates. We establish a framework for the analysis of covariant protocols which allows us to compare these measures. First, we derive the rate functions for several protocols, including random purification-based protocols and the sample-optimal protocol of Haah et al. These rate functions are expressed in terms of a new family of divergences which includes the reverse sandwiched Rényi divergence and Keyl's annealed quantum relative entropy as special cases. We show that these rate functions obey a strict ordering, even though the sample complexity of each protocol is order optimal. We consider a different version of sample complexity based on Wasserstein distance rather than trace distance, and show that the ordering of the rate functions implies analogous strict inequalities for the Wasserstein-type sample complexity. Thus the tomographic rate function is a more fine-grained indicator of the performance of a tomography protocol than the usual sample complexity.

Efficiently testing whether a quantum state possesses a given structure is both a fundamental and a practical task in quantum information. Among the most important structured families are Gaussian states, which underpin quantum optics and many-body physics while defining paradigmatic regimes of efficient classical simulation. Despite the central role of Gaussian states, optimal tests of Gaussianity have remained unknown. Here we give optimal and robust algorithms for testing fermionic and bosonic Gaussian states, with sample complexity independent of system size, particle number, and energy. Remarkably, the protocols implement experimentally feasible measurements associated with known exact symmetry characterizations of Gaussianity, using Bell sampling on two copies for fermions and passive interferometry with photon counting on three copies for bosons. We further obtain tolerant testers requiring joint measurements on a larger, but still constant, number of copies. At the heart of our analysis is a unified approach—which we call the gradient-flow method—that applies across all structured families considered here and underlies our optimal testers: representation theory turns approximate satisfaction of the defining symmetry into quantitative control of the gradient of the rejection probability, allowing a continuous descent from the input state to the target family whose length bounds their distance.

Multi-Agent Path Finding (MAPF) aims to find collision-free paths for multiple agents in a shared environment. Classical MAPF assumes that all static obstacles are known in advance, but real-world environments can change unexpectedly due to fallen objects, spills, or other local disturbances. When such changes are spatially correlated, an observation can inform traversability estimates beyond the observed location. Prior approaches address uncertainty in traversability through contingent plans or replanning based on direct observations, but do not leverage this spatial dependence to infer the traversability of nearby unobserved locations. As a result, they cannot use one observation to anticipate nearby unobserved obstacles that may cause costly rerouting later. We focus on Belief-Aware MAPF, where map discrepancies are fixed during execution but initially unknown, and observations can be informative beyond the observed location. We propose Multi-Agent Gaussian belief Inference for Coordination (MAGIC), a framework that updates a shared belief about traversability online based on agents' observations. MAGIC uses a Gaussian Markov Random Field and Gaussian Belief Propagation to approximately infer traversability and construct detour-aware costs for standard MAPF planners. Our experiments on MAPF benchmarks show that MAGIC reduces the executed sum of costs compared to existing approaches on 96.3% of instances, across several planner families and teams of up to 800 agents, demonstrating its applicability to large-scale MAPF problems.

A fundamental problem in physics as well as engineering is equilibration. For example, the regulation of thermal and quantum fluctuations enables thermal and quantum annealing of complex systems. A key question is how different subsystems, such as electrons, nuclear spins and phonons equilibrate on their own as well as with each other. Level crossings play a special role in the dynamics of coupled degrees of freedom, for it is here that entanglement can be maximized to speed up relaxation. Here we use optical methods to establish the electronuclear level scheme, including avoided and unavoided crossings, and to examine equilibration of a rare earth ion (Ho$^{3+}$) in a salt (LiYF$_4$), a model system with quantum fluctuations which can be tuned via an external magnetic field transverse to the crystallographic long axis of the tetragonal host. We track the state of the system by monitoring the populations of the levels as a function of swept longitudinal fields, and discover that at low temperatures, depending on the experimental protocol, vastly different non-equilibrium states arise. We find evidence that nuclear spin excitations diffuse and equilibrate without the assistance of phonons, and tend to acquire higher effective temperatures than the electronic spins and the yet cooler lattice. A theory of thermally assisted tunneling rules out the standard scenario of phonon -assisted tunneling, and instead suggests that fast dynamics at level anti-crossings are facilitated entirely by nuclear spin diffusion. This provides a new understanding of thermalization and related slow relaxation phenomena in dense, multi-component interacting quantum systems.

Autobidding has become a dominant paradigm in online advertising by enabling advertisers to set high-level goals while algorithms handle real-time bid optimization. A prominent example is the Return-on-Spend (RoS) value maximizer, which maximizes total value subject to an aggregate value-per-spend constraint. While most work on mechanism design for autobidders focuses on one-sided markets, many real-world platforms involve strategic behavior on both sides. We initiate the study of two-sided markets with autobidders. We first establish a stark negative result: for the challenging objective of liquid gains from trade (LGFT) in the prior-free setting, broad classes of utility-truthful, budget-balanced mechanisms have unbounded Price of Anarchy (PoA) once value-maximizing agents are present, even in double-auction environments. We then give two positive results. In the prior-free repeated double-auction setting, McAfee's Trade Reduction mechanism has unbounded PoA for LGFT but achieves constant PoA for liquid welfare under RoS bidding, showing that off-the-shelf mechanisms retain meaningful welfare guarantees. With distributional information regarding the private costs and values, we design a two-sided mechanism that is incentive compatible for each agent under its corresponding objective, individually rational, ex-ante weakly budget balanced, and achieves first-best liquid welfare, equivalently optimal LGFT, whenever at least one side of the market consists of RoS value maximizers. This result applies to matching markets with general downward-closed feasibility constraints. It contrasts sharply with the Myerson–Satterthwaite impossibility theorem~\citep{MS83}, which rules out first-best efficiency with incentive compatibility, individual rationality, and budget balance even in bilateral trade when both the buyer and the seller are quasi-linear utility maximizers.

Measurement compatibility asks whether a family of quantum measurements can be simulated by one parent measurement followed by classical post-processing. We extend this measurement compatibility to the notion of \emph{$d$-compatibility} for measurements, channels, and instruments whose parent passes a $d$-dimensional quantum system and unlimited classical information to the post-processing. We formulate $d$-compatibility as a common linear factorization of operator spaces and operator systems and show that $d$-compatible families form a closed set, even with infinitely many settings and a separable infinite-dimensional input. To certify $d$-incompatibility, we define the compatibility functional as the smallest product of completely bounded norms over common factorizations through a $d$-dimensional register. Using factorization theory of operator spaces, we show that measure-and-prepare channels defined in terms of mutually unbiased bases and pinching channels defined in terms of Heisenberg-Weyl operators are $d$-incompatible in certain regimes of $d$. We also link $d$-compatibility of multi-instruments to the preparability of Choi assemblages using channel-state duality, and use this connection to show that for bipartite states the (in)compatibility of instruments can be used to certify Schmidt numbers and the implementability of the instrument using one-way LOCC protocols. Finally, our compatibility functional also bounds the generalized robustness of compatibility, which we interpret through a memory-bounded nontransient preparation game.

Real-world time-series applications increasingly require models that can handle time series forecasting, context-conditioned prediction, and language-based temporal reasoning. Yet current time-series foundation models remain fragmented across these capabilities: numerical specialists often provide the strongest forecasts, while language-based models offer broader contextual understanding and analysis. A central challenge is to unify these heterogeneous capabilities without reducing their individual performance. We introduce OpenTSLM TeeMoE, a generalist time-series language model that can forecast directly from observed time series, reason over textual context and temporal patterns, and synthesize and refine predictions from external numerical forecasting specialists. We independently train three low-rank experts for forecast aggregation, native forecasting, and temporal analysis over a shared backbone. A learned LoRA mixture-of-experts controller then weights their frozen parameter updates for each request. Our proposed model achieves strong performance on widely used benchmarks for time series forecasting, context-conditioned prediction, and language-based temporal reasoning, ranking among the top three on GIFT-Eval by mean MASE rank, Context is Key by RCRPS, and TimeSeriesExam by accuracy.

Distribution network reconfiguration (DNR) is a combinatorial optimization problem that seeks a low-loss network topology subject to topological and electrical operating constraints. In this work, we propose a two-stage quantum-classical method for DNR. First, an iterative linear-ramp Quantum Alternating Operator Ansatz (LR-QAOA) searches topologically feasible subspaces constructed using a novel cycle-edge encoding. The encoding guarantees that every represented configuration is a spanning tree while allowing the size and coverage of each subspace to be adjusted to the available qubit budget. Second, the resulting sample distribution is used to guide a mixed-integer second-order-cone programming (MISOCP) solver. The method is evaluated on six distribution networks ranging from 33 to 417 buses through ideal simulation and execution on trapped-ion quantum hardware. For the 417-bus network, quantum hardware sampling identifies a configuration within approximately $1.4\%$ of the literature reference loss. Across all six test systems, the MISOCP solver guided by hardware-derived distributions reaches an incumbent within $1\%$ of the target with a lower median solver time than the corresponding unguided solver. These findings establish a concrete framework for applying current quantum hardware to DNR, with the potential to become increasingly competitive as hardware improves.

Subgraph detection asks whether an $n$-vertex graph, accessed through queries to its adjacency matrix, contains a copy of a fixed graph $H$. We prove the first unconditional superlinear lower bounds on the bounded-error quantum query complexity of this problem, answering a longstanding open question. A copy of $H$ is a certificate of constant size, so the adversary method with nonnegative weights cannot prove superlinear lower bounds. For every fixed $r\ge 4$, detecting the clique $K_r$ requires $n^{\lambda_r-o(1)}$ queries, where $\lambda_4=19/18$, the exponents $\lambda_r$ increase strictly with $r$, and $\lambda_r\ge 2-4\sqrt{2/r}+O(1/r)$. More generally, we prove superlinear lower bounds for detecting every fixed connected graph $H$ with chromatic number $c\ge 4$. These bounds approach quadratic as $c$ grows: for sufficiently large $c$, detection requires $n^{2-O(\sqrt{\log\log c/c})-o(1)}$ queries. Chromatic number alone does not characterize the quantum query complexity of subgraph detection: we show that detecting the complete bipartite graph $K_{r,r}$ requires $n^{\beta_r-o(1)}$ queries, where $\beta_{10}=181/180$ and $\beta_r\ge 2-O(1/\sqrt{r})$. Our main technical result is a lower bound for finding an all-ones certificate from a known family when the input bits are sampled independently. Its proof combines Zhandry's compressed oracle [CRYPTO 2019] with conditioning on a randomly planted certificate, adapting an argument of Belovs [FOCS 2026]. Our hard instances are built from graphs containing many copies of the desired subgraph with limited overlap. For cliques, we use a construction of Gowers and Janzer [CPC 2021]; for complete bipartite graphs, we use a random construction.

Quantum list recovery (QLR) and quantum list decoding (QLD) seek short lists of logically distinct Pauli corrections consistent with a syndrome and prescribed error constraints. For CSS codes, two issues arise: treating the \(X\)- and \(Z\)-sectors separately can multiply their output list sizes, while distinct classical candidates can collapse after stabilizer quotienting. We study combinatorial upper and lower bounds for balanced folded quantum Reed–Solomon (FQRS) codes and balanced random CSS codes, both studied by Bergamaschi, Golowich, and Gunn (STOC 24). Let \(R\in(0,1)\) be the quantum rate and \(R_1=(1+R)/2\) the common component rate. As the radius \(\rho=(1-R)/2-\gamma\) approaches the quantum Singleton bound, we have, deterministically for FQRS codes and w.h.p. for balanced random CSS codes, \[ L^\star_{\rm QLR} = \ell^{\Theta(R_1/\gamma)}, \qquad L^\star_{\rm QLD} = \Theta\!\left(\frac{1-R}{\gamma}\right) \qquad (\gamma\downarrow0). \] The asymptotically exact QLD radius tradeoff is \[ \rho_L^\star = \frac{L}{L+1}\frac{1-R}{2}. \] These conclusions extend to the average-radius setting. For achievability, building on the work of Brakensiek, Chen, Dhar, and Zhang (STOC 2026), we establish a pairing lemma for joint \(X/Z\) candidate lists that preserves the one-sector coefficient and avoids a product loss in list size. For the QLD converse, we prove a quantum generalized Singleton bound based on the classical projection-and-patching argument with stabilizer distinctness. For the QLR lower bounds, we adapt the folded Reed–Solomon construction of Chen and Zhang (STOC 2025) so that the candidates remain stabilizer distinct. For random CSS codes, we show classical bad lists survive the stabilizer quotient with high probability.

Linear-fractional rotational interval exchange transformations appear naturally when investigating circle diffeomorphisms with breaks using the renormalization group approach. Earlier, we achieved an important rigidity result on circle diffeomorphisms with a single break by means of establishing a time-reversing duality for the corresponding commuting pairs of linear-fractional maps. In this paper, we extend the established duality to the case of multiple breaks, where a commuting pair from the previous case is replaced by a `commuting collection' of an even number of linear-fractional maps, which act according to a rotational interval exchange scheme of special type, while satisfying certain commutation relations.

In this paper, we present a polynomial-time quantum algorithm for computing a minimum-sized generating set of solvable black-box groups. Next, we consider the class $\Gamma_d$ of black-box groups, where every non-abelian composition factor is isomorphic to a subgroup of the symmetric group $S_d$ for a fixed $d$. We design polynomial-time quantum algorithms to compute the direct product decomposition of abelian factor groups and solve the constructive membership problem for factor groups of groups from $\Gamma_d$. With the help of these algorithms, we design a quantum algorithm for computing a chief series of black-box groups from $\Gamma_d$. Using the chief series, we construct a polynomial-time quantum algorithm for computing minimum generating sets of black-box groups from $\Gamma_d$. Finally, we show that the minimum generating set problem for general black-box groups is in $\textrm{NP} \cap \textrm{coAM}$.

Device-independent self-testing certifies a multipartite quantum state from the correlations it produces alone, without assumptions on the inner workings of the devices. Most existing self-tests, however, break down as soon as the parties can exchange messages. We consider a relaxed setting in a quantum network, where in the honest version of the protocol, the parties never communicate, yet certification remains sound even in an untrusted case where the untrusted devices secretly exchange classical messages within a bounded distance in the network. We show that the code space of the toric code, distributed over a network with the geometry of a torus, can be self-tested in this setting in a noise-robust way, against communication up to distances proportional to the network diameter. We also develop an algorithmic method for constructing such protocols and extend our results to the surface code and cluster states, robust to one round of nearest-neighbor classical communication