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Understanding the mathematical reasoning capabilities of Large Language Models (LLMs) is a central topic in the study of artificial intelligence. This new domain necessitates the creation of datasets of reasoning tasks for both training and benchmarking the performance of LLMs. To this end, we introduce the Karp dataset: The first dataset composed of detailed proofs of NP-completeness reductions. The reductions vary in difficulty, ranging from simple exercises of undergraduate courses to more challenging reductions from academic papers. We compare the performance of state-of-the-art models on this task and demonstrate the effect of fine-tuning with the Karp dataset on reasoning capacity., Comment: Accepted to the 4th workshop on mathematical reasoning and AI at NeurIPS 2024

Windblown sand creates multiscale bedforms on Earth, Mars, and other planetary bodies. According to conventional wisdom, decameter-scale dunes and decimeter-scale ripples emerge via distinct mechanisms on Earth: a hydrodynamic instability related to a phase shift between the turbulent flow and the topography, and a granular instability related to a synchronization of hopping grains with the topography. Here, we report the reproducible creation of coevolving centimeter and decimeter-scale ripples on fine-grained monodisperse sand beds in ambient-air and low-pressure wind-tunnels, revealing two adjacent mesoscale growth instabilities. Their morphological traits and our quantitative grain-scale numerical simulations authenticate the smaller structures as impact ripples but point at a hydrodynamic origin for the larger ones. This suggests that the aeolian transport layer would have to partially respond to the topography on a scale comparable to the average hop length, hence faster than previously thought, but consistent with the phase lag of the inferred aeolian sand flux relative to the wind. Hydrodynamic modelling supports the existence of hydrodynamic aerodynamic ripples on Earth, connecting them mechanistically to megaripples and to the debated Martian ripples. We thereby propose a unified framework for mesoscale granular bedforms found across the Solar System.

Fisheries scientists use regression models to estimate population quantities, such as biomass or abundance, for use in climate, habitat, stock, and ecosystem assessments. However, these models are sensitive to the chosen probability distribution used to characterize observation error. Here, we introduce the generalized gamma distribution (GGD), which has not been widely used in fisheries science. The GGD has useful properties: (1) it reduces to the lognormal distribution when the shape parameter approaches zero; (2) it reduces to the gamma distribution when the shape and scale parameters are equal; and (3) the coefficient of variation is independent of the mean. We assess the relative performance and robustness of the GGD to estimate biomass density across different observation error types in a simulation experiment. When fit to data generated from the GGD, lognormal, gamma, and Tweedie families, the GGD had low bias and high predictive accuracy. Finally, we fit spatiotemporal index standardization models using the R package sdmTMB to 15 species from three trawl surveys from the Gulf of Alaska and coast of British Columbia, Canada. When the Akaike information criterion (AIC) weight was compared among fits using the lognormal, gamma, and Tweedie families the GGD was the most commonly selected model.

A remarkable characteristic of quantum computing is the potential for reliable computation despite faulty qubits. This can be achieved through quantum error correction, which is typically implemented by repeatedly applying static syndrome checks, permitting correction of logical information. Recently, the development of time-dynamic approaches to error correction has uncovered new codes and new code implementations. In this work, we experimentally demonstrate three time-dynamic implementations of the surface code, each offering a unique solution to hardware design challenges and introducing flexibility in surface code realization. First, we embed the surface code on a hexagonal lattice, reducing the necessary couplings per qubit from four to three. Second, we walk a surface code, swapping the role of data and measure qubits each round, achieving error correction with built-in removal of accumulated non-computational errors. Finally, we realize the surface code using iSWAP gates instead of the traditional CNOT, extending the set of viable gates for error correction without additional overhead. We measure the error suppression factor when scaling from distance-3 to distance-5 codes of $\Lambda_{35,\text{hex}} = 2.15(2)$, $\Lambda_{35,\text{walk}} = 1.69(6)$, and $\Lambda_{35,\text{iSWAP}} = 1.56(2)$, achieving state-of-the-art error suppression for each. With detailed error budgeting, we explore their performance trade-offs and implications for hardware design. This work demonstrates that dynamic circuit approaches satisfy the demands for fault-tolerance and opens new alternative avenues for scalable hardware design., Comment: 11 pages, 5 figures, Supplementary Information

Quantum error correction is essential for bridging the gap between the error rates of physical devices and the extremely low logical error rates required for quantum algorithms. Recent error-correction demonstrations on superconducting processors have focused primarily on the surface code, which offers a high error threshold but poses limitations for logical operations. In contrast, the color code enables much more efficient logic, although it requires more complex stabilizer measurements and decoding techniques. Measuring these stabilizers in planar architectures such as superconducting qubits is challenging, and so far, realizations of color codes have not addressed performance scaling with code size on any platform. Here, we present a comprehensive demonstration of the color code on a superconducting processor, achieving logical error suppression and performing logical operations. Scaling the code distance from three to five suppresses logical errors by a factor of $\Lambda_{3/5}$ = 1.56(4). Simulations indicate this performance is below the threshold of the color code, and furthermore that the color code may be more efficient than the surface code with modest device improvements. Using logical randomized benchmarking, we find that transversal Clifford gates add an error of only 0.0027(3), which is substantially less than the error of an idling error correction cycle. We inject magic states, a key resource for universal computation, achieving fidelities exceeding 99% with post-selection (retaining about 75% of the data). Finally, we successfully teleport logical states between distance-three color codes using lattice surgery, with teleported state fidelities between 86.5(1)% and 90.7(1)%. This work establishes the color code as a compelling research direction to realize fault-tolerant quantum computation on superconducting processors in the near future.

Ultrafast X-ray spectroscopy has been revolutionized in recent years due to the advent of fourth-generation X-ray facilities. In solid-state materials, core excitons determine the energy and line shape of absorption features in core-level spectroscopies such as X-ray absorption spectroscopy. The screening of core excitons is an inherent many-body process that can reveal insight into charge-transfer excitations and electronic correlations. Under non-equilibrium conditions such as after photoexcitation, however, core-exciton screening is still not fully understood. Here we demonstrate the dynamic Coulomb screening of core excitons induced by photoexcited carriers by employing X-ray transient absorption (XTA) spectroscopy with picosecond time resolution. Our interpretation is supported by state-of-the-art ab initio theory, combining constrained and real-time time-dependent density functional theory with many-body perturbation theory. Using ZnO as an archetypal wide band-gap semiconductor, we show that the Coulomb screening by photoexcited carriers at the Zn K-edge leads to a decrease in the core-exciton binding energy, which depends nonlinearly on both the excitation density and the distribution of photoexcited carriers in reciprocal space. The effect of Coulomb screening dominates over Pauli blocking in the XTA spectra. We show that dynamic core-exciton screening is also observed at other X-ray absorption edges and theoretically predict the effect of core-exciton screening on the femtosecond time scale for the case of ZnO, a major step towards hard X-ray excitonics. The results have implications for the interpretation of ultrafast X-ray spectra in general and their use in tracking charge carrier dynamics in complex materials on atomic length scales., Comment: 43 pages, 37 figures

Mechanical systems have emerged as a compelling platform for applications in quantum information, leveraging recent advances in the control of phonons, the quanta of mechanical vibrations. Several experiments have demonstrated control and measurement of phonon states in mechanical resonators integrated with superconducting qubits, and while entanglement of two mechanical resonators has been demonstrated in some approaches, a full exploitation of the bosonic nature of phonons, such as multi-phonon entanglement, remains a challenge. Here, we describe a modular platform capable of rapid multi-phonon entanglement generation and subsequent tomographic analysis, using two surface acoustic wave resonators on separate substrates, each connected to a superconducting qubit. We generate a mechanical Bell state between the two mechanical resonators, achieving a fidelity of $\mathcal{F} = 0.872\pm 0.002$, and further demonstrate the creation of a multi-phonon entangled state (N=2 N00N state), shared between the two resonators, with fidelity $\mathcal{F} = 0.748\pm 0.008$. This approach promises the generation and manipulation of more complex phonon states, with potential future applications in bosonic quantum computing in mechanical systems. The compactness, modularity, and scalability of our platform further promises advances in both fundamental science and advanced quantum protocols, including quantum random access memory and quantum error correction., Comment: 25 pages, 9 figures

Magnetic transition-metal dichalcogenides (TMDs) have been of particular interest due to their unique magnetic properties and layered structure that can be promising for a wide range of spintronic applications. One of the most exciting compounds in this family of magnets is chromium telluride, Cr$_{1+x}$Te$_2$, which has shown rich magnetic phases with varied Cr concentrations. An emergent antiferromagnetic (AFM) ordering has been found in Cr$_{1.25}$Te$_2$ (equivalently, Cr$_{5}$Te$_8$), which is induced by intercalating 0.25 Cr atom per unit cell within the van der Waals (vdW) gaps of CrTe$_2$. In this work, we report an increased N\'eel Temperature ($T_\mathrm{N}$) of the AFM phase in Cr$_{1+x}$Te$_2$ by slightly reducing the concentration of Cr intercalants. Moreover, the intercalated Cr atoms form a metastable 2$\times$2 supercell structure that can be manipulated by electron beam irradiation. This work offers a promising approach to tuning magnetic and structural properties by adjusting the concentration of self-intercalated magnetic atoms., Comment: 5 figures, 1 table

The Cavendish torsion balance is the instrument of choice for measuring weak forces, such as gravity. Although torsion balances have extremely high sensitivity for measuring forces over ranges of a few cm and more, their dynamics make it difficult to extend this range to much less than fractions of mm. In particular forces such as the Casimir force are usually studied using atomic force microscopes. We present results of our studies of a simple torsion balance with a 3-wire suspension. This device should be able to maintain parallelism between flat plates of areas of a few $\sim\mathrm{cm^2}$ at separations of much less of 10's of $\mathrm{\mu m}$. In this paper we describe our experimental investigation into the coupling of ground tilt to the torsional rotation of the novel device. We show that, like the Cavendish torsion balance, the 3-wire torsion balance is highly insensitive to tilts. We also demonstrate that this tilt sensitivity is itself insensitive to shifts in the centre of mass position of the suspended mass. We discuss simple models of the 3-wire torsion balance that show that it is only the static wire lengths that determine the coupling of tilts and horizontal accelerations. We also discuss designs of torsion balances where sensitivity and noise rejection to tilts are optimised.

This work presents a novel, dimensionless model that results in a dimensionless algebraic equation that can be used to quantify the pressure drop associated with the steady state, isothermal flow through a straight, horizontal pipeline, of a compressible gas mixture whose thermodynamic behavior is described for comparison purposes by ideal gas (IG) and nonideal gas generic cubic (GC) equation of state (EOS) models. A solution strategy, that uses the aforementioned dimensionless algebraic equation, is then presented that quantifies the pipeline pressure drop for hydrogen containing mixtures. Two case studies are presented to illustrate the pressure drop dependence on the hydrogen mole fraction of a binary, methane hydrogen mixture, and a natural gas hydrogen mixture with a real life natural gas composition containing eight species., Comment: 45 pages, 9 figures

We present a novel application of a qubit-coupled phonon detector to search for new physics, e.g., ultralight dark matter (DM) and high-frequency gravitational waves. The detector, motivated by recent advances in quantum acoustics, is composed of superconducting transmon qubits coupled to high-overtone bulk acoustic resonators ($h$BARs) and operates in the GHz - 10 GHz frequency range. New physics can excite $O(10 \, \mu \text{eV})$ phonons within the $h$BAR, which are then converted to qubit excitations via a transducer. We detail the design, operation, backgrounds, and expected sensitivity of a prototype detector, as well as a next-generation detector optimized for new physics signals. We find that a future detector can complement current haloscope experiments in the search for both dark photon DM and high-frequency gravitational waves. Lastly we comment on such a detector's ability to operate as a $10 \, \mu\text{eV}$ threshold athermal phonon sensor for sub-GeV DM detection., Comment: 17 pages main text, 8 pages appendices, 5 pages references, 10 Figures

One of the most challenging problems in the computational study of localization in quantum manybody systems is to capture the effects of rare events, which requires sampling over exponentially many disorder realizations. We implement an efficient procedure on a quantum processor, leveraging quantum parallelism, to efficiently sample over all disorder realizations. We observe localization without disorder in quantum many-body dynamics in one and two dimensions: perturbations do not diffuse even though both the generator of evolution and the initial states are fully translationally invariant. The disorder strength as well as its density can be readily tuned using the initial state. Furthermore, we demonstrate the versatility of our platform by measuring Renyi entropies. Our method could also be extended to higher moments of the physical observables and disorder learning.

In an attempt to simulate black hole echoes (generated by potential quantum-gravitational structure) in numerical relativity, we recently described how to implement a reflecting boundary outside of the horizon of a black hole in spherical symmetry. Here, we generalize this approach to spacetimes with no symmetries and implement it numerically using the generalized harmonic formulation. We cast the evolution equations and the numerical implementation into a Summation By Parts (SBP) scheme, which seats our method closer to a class of provably numerically stable systems. We implement an embedded boundary numerical framework that allows for arbitrarily shaped domains on a rectangular grid and even boundaries that evolve and move across the grid. As a demonstration of this framework, we study the evolution of gravitational wave scattering off a boundary either inside, or just outside, the horizon of a black hole. This marks a big leap toward the goal of a generic framework to obtain gravitational waveforms for behaviors motivated by quantum gravity near the horizons of merging black holes., Comment: 14 pages, 6 figures, final published version

Lattice gauge theories (LGTs) can be employed to understand a wide range of phenomena, from elementary particle scattering in high-energy physics to effective descriptions of many-body interactions in materials. Studying dynamical properties of emergent phases can be challenging as it requires solving many-body problems that are generally beyond perturbative limits. We investigate the dynamics of local excitations in a $\mathbb{Z}_2$ LGT using a two-dimensional lattice of superconducting qubits. We first construct a simple variational circuit which prepares low-energy states that have a large overlap with the ground state; then we create particles with local gates and simulate their quantum dynamics via a discretized time evolution. As the effective magnetic field is increased, our measurements show signatures of transitioning from deconfined to confined dynamics. For confined excitations, the magnetic field induces a tension in the string connecting them. Our method allows us to experimentally image string dynamics in a (2+1)D LGT from which we uncover two distinct regimes inside the confining phase: for weak confinement the string fluctuates strongly in the transverse direction, while for strong confinement transverse fluctuations are effectively frozen. In addition, we demonstrate a resonance condition at which dynamical string breaking is facilitated. Our LGT implementation on a quantum processor presents a novel set of techniques for investigating emergent particle and string dynamics.

About 40 transneptunian binaries (TNBs) have fully determined orbits with about 10 others being solved except for breaking the mirror ambiguity. Despite decades of study almost all TNBs have only ever been analyzed with a model that assumes perfect Keplerian motion (e.g., two point masses). In reality, all TNB systems are non-Keplerian due to non-spherical shapes, possible presence of undetected system components, and/or solar perturbations. In this work, we focus on identifying candidates for detectable non-Keplerian motion based on sample of 45 well-characterized binaries. We use MultiMoon, a non-Keplerian Bayesian inference tool, to analyze published relative astrometry allowing for non-spherical shapes of each TNB system's primary. We first reproduce the results of previous Keplerian fitting efforts with MultiMoon, which serves as a comparison for the non-Keplerian fits and confirms that these fits are not biased by the assumption of a Keplerian orbit. We unambiguously detect non-Keplerian motion in 8 TNB systems across a range of primary radii, mutual orbit separations, and system masses. As a proof of concept for non-Keplerian fitting, we perform detailed fits for (66652) Borasisi-Pabu, possibly revealing a $J_2 \approx 0.44$, implying Borasisi (and/or Pabu) may be a contact binary or an unresolved compact binary. However, full confirmation of this result will require new observations. This work begins the next generation of TNB analyses that go beyond the point mass assumption to provide unique and valuable information on the physical properties of TNBs with implications for their formation and evolution., Comment: Accepted to AJ

Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this exponential suppression only occurs if the physical error rate is below a critical threshold. In this work, we present two surface code memories operating below this threshold: a distance-7 code and a distance-5 code integrated with a real-time decoder. The logical error rate of our larger quantum memory is suppressed by a factor of $\Lambda$ = 2.14 $\pm$ 0.02 when increasing the code distance by two, culminating in a 101-qubit distance-7 code with 0.143% $\pm$ 0.003% error per cycle of error correction. This logical memory is also beyond break-even, exceeding its best physical qubit's lifetime by a factor of 2.4 $\pm$ 0.3. We maintain below-threshold performance when decoding in real time, achieving an average decoder latency of 63 $\mu$s at distance-5 up to a million cycles, with a cycle time of 1.1 $\mu$s. To probe the limits of our error-correction performance, we run repetition codes up to distance-29 and find that logical performance is limited by rare correlated error events occurring approximately once every hour, or 3 $\times$ 10$^9$ cycles. Our results present device performance that, if scaled, could realize the operational requirements of large scale fault-tolerant quantum algorithms., Comment: 10 pages, 4 figures, Supplementary Information

Superconducting qubits provide a promising approach to large-scale fault-tolerant quantum computing. However, qubit connectivity on a planar surface is typically restricted to only a few neighboring qubits. Achieving longer-range and more flexible connectivity, which is particularly appealing in light of recent developments in error-correcting codes, however usually involves complex multi-layer packaging and external cabling, which is resource-intensive and can impose fidelity limitations. Here, we propose and realize a high-speed on-chip quantum processor that supports reconfigurable all-to-all coupling with a large on-off ratio. We implement the design in a four-node quantum processor, built with a modular design comprising a wiring substrate coupled to two separate qubit-bearing substrates, each including two single-qubit nodes. We use this device to demonstrate reconfigurable controlled-Z gates across all qubit pairs, with a benchmarked average fidelity of $96.00\%\pm0.08\%$ and best fidelity of $97.14\%\pm0.07\%$, limited mainly by dephasing in the qubits. We also generate multi-qubit entanglement, distributed across the separate modules, demonstrating GHZ-3 and GHZ-4 states with fidelities of $88.15\%\pm0.24\%$ and $75.18\%\pm0.11\%$, respectively. This approach promises efficient scaling to larger-scale quantum circuits, and offers a pathway for implementing quantum algorithms and error correction schemes that benefit from enhanced qubit connectivity.

Wildfire smoke is a health hazard as it contains a mixture of carcinogenic volatile compounds and fine particulate matter. In particular, exposure to polycyclic aromatic hydrocarbons (PAHs) is a major concern, since these compounds have been recognized as important contributors to the overall carcinogenic risk of smoke exposure. In this work, gas and particle-phase PAH emissions from the combustion of Eastern White Pine (pinus strobus) were quantified using time-of-flight mass spectrometry over a range of burn conditions representative of wildfires and prescribed fires. These experiments allow for controlling conditions of fuel moisture, heat flux, and oxygen concentration to understand their impact on PAH emissions. We find that optimal conditions for fuel moisture content of 20 - 30%, heat load onto the sample of 60 - 70 kW/m$^2$, and oxygen concentrations of the burn environment of 5 - 15% can reduce the emissions of the heavy molar weight PAHs by up to 77%. Our analysis shows that the relative carcinogenic risk can be reduced by more than 50% under optimal conditions, offering a way for reducing emission exposure from forest treatment activities., Comment: Submitted to Atmospheric Pollution Research

Artin, Tate and Van den Bergh initiated the field of noncommutative projective algebraic geometry by fruitfully studying geometric data associated to noncommutative graded algebras. More specifically, given a field $\mathbb K$ and a graded $\mathbb K$-algebra $A$, they defined an inverse system of projective schemes $\Upsilon_A = \{{\Upsilon_d(A)}\}$. This system affords an algebra, $\mathbf B(\Upsilon_A)$, built out of global sections, and a $\mathbb K$-algebra morphism $\tau: A \to \mathbf B(\Upsilon_A)$. We study and extend this construction. We define, for any natural number $n$, a category ${\tt PSys}^n$ of projective systems of schemes and a contravariant functor $\mathbf B$ from ${\tt PSys}^n$ to the category of associative $\mathbb K$-algebras. We realize the schemes ${\Upsilon_d(A)}$ as ${\rm Proj \ } {\mathbf U}_d(A)$, where ${\mathbf U}_d$ is a functor from associative algebras to commutative algebras. We characterize when the morphism $\tau: A \to \mathbf B(\Upsilon_A)$ is injective or surjective in terms of local cohomology modules of the ${\mathbf U}_d(A)$. Motivated by work of Walton, when $\Upsilon_A$ consists of well-behaved schemes, we prove a geometric result that computes the Hilbert series of $\mathbf B(\Upsilon_A)$. We provide many detailed examples that illustrate our results. For example, we prove that for some non-AS-regular algebras constructed as twisted tensor products of polynomial rings, $\tau$ is surjective or an isomorphism., Comment: 35 pages

Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators. Unlocking the full potential of such systems toward this goal requires flexible initial state preparation, precise time evolution, and extensive probes for final state characterization. We present a quantum simulator comprising 69 superconducting qubits which supports both universal quantum gates and high-fidelity analog evolution, with performance beyond the reach of classical simulation in cross-entropy benchmarking experiments. Emulating a two-dimensional (2D) XY quantum magnet, we leverage a wide range of measurement techniques to study quantum states after ramps from an antiferromagnetic initial state. We observe signatures of the classical Kosterlitz-Thouless phase transition, as well as strong deviations from Kibble-Zurek scaling predictions attributed to the interplay between quantum and classical coarsening of the correlated domains. This interpretation is corroborated by injecting variable energy density into the initial state, which enables studying the effects of the eigenstate thermalization hypothesis (ETH) in targeted parts of the eigenspectrum. Finally, we digitally prepare the system in pairwise-entangled dimer states and image the transport of energy and vorticity during thermalization. These results establish the efficacy of superconducting analog-digital quantum processors for preparing states across many-body spectra and unveiling their thermalization dynamics.

Multi-view stereo omnidirectional distance estimation usually needs to build a cost volume with many hypothetical distance candidates. The cost volume building process is often computationally heavy considering the limited resources a mobile robot has. We propose a new geometry-informed way of distance candidates selection method which enables the use of a very small number of candidates and reduces the computational cost. We demonstrate the use of the geometry-informed candidates in a set of model variants. We find that by adjusting the candidates during robot deployment, our geometry-informed distance candidates also improve a pre-trained model's accuracy if the extrinsics or the number of cameras changes. Without any re-training or fine-tuning, our models outperform models trained with evenly distributed distance candidates. Models are also released as hardware-accelerated versions with a new dedicated large-scale dataset. The project page, code, and dataset can be found at https://theairlab.org/gicandidates/ .

The dynamics of quantum information in many-body systems with large onsite Hilbert space dimension admits an enlightening description in terms of effective statistical mechanics models. Motivated by this fact, we reveal a connection between three separate models: the classically chaotic $d$-adic R\'{e}nyi map with stochastic control, a quantum analog of this map for qudits, and a Potts model on a random graph. The classical model and its quantum analog share a transition between chaotic and controlled phases, driven by a randomly applied control map that attempts to order the system. In the quantum model, the control map necessitates measurements that concurrently drive a phase transition in the entanglement content of the late-time steady state. To explore the interplay of the control and entanglement transitions, we derive an effective Potts model from the quantum model and use it to probe information-theoretic quantities that witness both transitions. The entanglement transition is found to be in the bond-percolation universality class, consistent with other measurement-induced phase transitions, while the control transition is governed by a classical random walk. These two phase transitions merge as a function of model parameters, consistent with behavior observed in previous small-size numerical studies of the quantum model., Comment: 14+3 pages, 13+1 figures, 3+4 tables