Structured Scaling of AI Discovery Across Diverse Scientific Domains — part 2/12

Cleaned-text code points [15628, 31592). Bibliography omitted here; source.md includes it.

Quantum computing is an increasingly important computing paradigm that stores and processes information via quantum-mechanical systems [ 99 ] . Whereas a classical bit has a definite value of either 0 or 1, a quantum bit, or qubit , can be in a coherent superposition of both states. By manipulating such states and creating correlations between qubits through entangling operations, quantum computers can obtain polynomial or exponential speedups for selected problem classes [ 125 , 50 , 35 , 52 , 13 , 37 , 84 , 7 ] . At the center of this paradigm is the quantum algorithm, which specifies how quantum operations transform input states into desired outputs. In the circuit model, a quantum algorithm is represented by a quantum circuit: an ordered sequence of elementary operations, called gates , applied to logical qubits [ 99 ] . One-qubit gates update the state of a single qubit, while two-qubit gates create interactions between a pair of qubits. A logical circuit may specify two-qubit gates between arbitrary pairs of logical qubits, but a real device can apply a direct two-qubit gate only when the corresponding physical qubits satisfy the hardware’s interaction constraints, thus creating a compilation problem of how to assign logical qubits to physical qubits and update that assignment over time so that every required two-qubit gate becomes executable. The additional operations introduced in this process are costly and error-prone, making overhead reduction the central optimization goal.

This optimization problem is computationally challenging and takes different forms on different hardware platforms [ 61 , 128 , 28 , 15 , 133 , 80 , 132 , 137 ] . We use SimpleTES to address two representative hardware settings, superconducting platforms and neutral-atom architectures. In superconducting devices, physical qubits occupy fixed chip locations and allowed two-qubit interactions form a sparse coupling graph; compilation must choose an initial layout and insert SWAP gates when interacting logical qubits are mapped to non-adjacent physical qubits [ 76 , 176 ] . In zoned neutral-atom devices, atoms are kept in a storage zone or moved to an entangling zone for Rydberg gates; compilation must choose placement snapshots whose transitions can be realized through AOD-mediated movement. Together, these settings contrast fixed-graph routing with geometry-limited atom placement and rearrangement, while retaining the same high-level goal of minimizing extra hardware work. We apply SimpleTES within fixed compilation scaffolds that isolate editable policy components, with necessary correctness checks applied. For superconducting circuits, SimpleTES edits the initial layout and online SWAP selection rule; candidate routers are compared against SABRE [ 76 ] and LightSABRE [ 176 ] , with added SWAP overhead as the cost. For zoned neutral-atom compilation, SimpleTES edits only the placer in a fixed scheduler–reuse-analyzer–placer–router pipeline, with the remaining modules held fixed; candidate placers are compared against a reuse-aware ZAC-style baseline [ 80 ] , with total execution time as the objective. Formal problem definitions, hardware constraints, and optimization objectives for both compilation tasks are given in Supplementary H.1 . Benchmark suites, baselines, and evaluation metrics are provided in Supplementary H.2 .

Across both settings, SimpleTES achieves substantial overhead reductions relative to established baselines, driven by a shared design principle: place important logical qubits near useful hardware locations before expensive routing or rearrangement becomes unavoidable. In superconducting routing, the best policy reduces topology-averaged added SWAP overhead by 21.7% relative to SABRE and 14.9% relative to LightSABRE , with the largest reductions on Q20 reaching 33.3% and 24.5%, respectively; it implements the shared principle by mapping high-traffic logical qubits toward high-degree physical qubits, refining the assignment by local search, and scoring online SWAPs using a broader candidate neighborhood, look-ahead information, and immediate gate executability ( Figure 2 b,c). In zoned neutral-atom compilation, the best placer discovered by SimpleTES reduces the geometric mean of total execution time by 33.2% relative to the ZAC-style baseline; it implements the same principle through the sequence of placement snapshots passed to the fixed AOD router, preserving relative qubit order, reducing travel distance without losing AOD parallelism, and refining placements through reverse-time passes ( Figure 2 d–f). Further details of the best discovered programs and the additional superconducting routing policy obtained using SimpleTES with Gemini are provided in Supplementary H.3 and H.4 .

### SimpleTES improves optimizers for fuel-efficient deep-space trajectories

Deep-space missions often reach distant targets by using planets as moving gravitational waypoints rather than flying directly. A gravity assist (GA) uses a planetary flyby to reshape the spacecraft’s heliocentric path with little propellant, whereas a deep-space maneuver (DSM) uses an engine burn to adjust the path [ 98 ] . Designing such missions is difficult because route choices and timing choices are tightly coupled: the optimizer must choose which bodies to encounter, which transfer branches to use, and where maneuvers may be inserted, while also setting launch and encounter epochs and maneuver variables [ 148 , 121 ] . We formulate this as an evaluation-driven discovery task in which each candidate produced by SimpleTES is an executable mission-design program. Given mission windows, a target body, allowed flyby bodies, and endpoint conditions, the program proposes complete multi-gravity-assist trajectories ( Figure 3 a); an independent patched-conic evaluator reconstructs the trajectory from ephemerides [ 38 ] , transfer arcs [ 62 ] , flybys [ 95 ] , DSMs, and endpoint costs, rejects constraint violations, and scores feasible designs by verified propulsive cost.

We benchmark SimpleTES on five historical mission-window benchmarks and a prospective Jupiter exploration window. For the historical benchmarks, the comparison is not to flown mission Δ ​ v \Delta v budgets, which incorporate operational choices, navigation margins, and mission-specific high-fidelity modeling. Instead, each reference trajectory is constructed from the historical encounter sequence and nominal timing, then evaluated under the same orbital-dynamics model, feasibility constraints, and cost definition used to score SimpleTES . Across the historical mission windows, the best verified trajectories found by the discovered optimizers reduce propulsive cost in every case, by 2.1–23.1% relative to these same-evaluator references ( Figure 3 b). In the prospective 2028–2030 Jupiter exploration window, where no encounter sequence is prescribed, the discovered optimizer synthesizes an evaluator-feasible no-DSM Earth–Venus–Earth–Earth–Jupiter trajectory reaching Jupiter in 2035 ( Figure 3 a).

Inspection of the evolved optimizers shows that the gains arise from reusable policies for coupled discrete–continuous mission design. The clearest sequence-level changes occur for Galileo and Rosetta ( Figure 3 c): the Galileo optimizer finds Earth–Venus–Venus–Venus–Earth–Jupiter rather than the reference Earth–Venus–Earth–Earth–Jupiter sequence, while the Rosetta optimizer finds Earth–Earth–Earth–67P rather than Earth–Earth–Mars–Earth–Earth–67P. For Mariner 10, Voyager 2, and Cassini, the programs independently recover the reference encounter order and lower cost by refining the continuous trajectory variables within that sequence, showing that improvements do not require a different encounter sequence. Across cases, the evolved programs generate and prioritize candidate encounter sequences, allocate finite computation to promising time-of-flight regions, explore multiple transfer branches, combine global search with local refinement of encounter epochs and maneuver variables, and retain DSMs only when they reduce verified cost. Together, these results show that the evolved optimizers allocate finite computation both across encounter sequences and within each sequence’s continuous design space.

### SimpleTES discovers better scientific algorithms

Scientific algorithms are the computational methods that solve scientific problems: optimization solvers, forecasters, and learned models whose quality is judged by task-specific scientific objectives. These algorithms are usually produced by hand, often after years of accumulated domain expertise and engineering. We apply SimpleTES to three such problems and find that the same evaluation-driven search procedure discovers algorithms that improve over strong baselines: a geometry-aware lasso path solver that preserves strict correctness guarantees while outperforming the expert-engineered glmnet on real datasets; a whole-brain neural-activity forecaster that outperforms a prior proprietary-model search result; and a single-cell RNA-seq denoising algorithm that generalizes across datasets. We discuss the first two in detail below. Full denoising results are reported in the Supplementary Information, where an algorithm evolved exclusively on the Pancreas dataset matches the previous state of the art on held-out PBMC ( 0.71 0.71 ) and establishes a new best on held-out Tabula Muris Senis Lung ( 0.74 0.74 versus 0.73 0.73 ) (Supplementary M ).

##### SimpleTES discovers a geometry-aware lasso solver that surpasses glmnet .

The lasso regularization path is a core computational primitive in high-dimensional statistics, used in cross-validation, model selection, and large-scale regression workflows from genomics to finance. The de facto solver, glmnet [ 39 ] , encodes more than a decade of expert coordinate-descent engineering: warm starts, sequential strong-rule screening [ 142 ] , active-set inner loops, KKT verification, and a precision-matched switch between the covariance ( p < 500 p<500 ) and naive residual ( p ≥ 500 p\geq 500 ) updates. We ask whether evaluation-driven search, starting from a faithful C++ port of glmnet itself, can produce a strictly faster solver while preserving the same correctness guarantees. The evaluator is exact: candidate programs are self-contained C++ binaries, and a candidate is valid only if its per- λ \lambda objective gap relative to sklearn ’s solution stays below 10 − 6 10^{-6} on a held-out problem, with any failure forcing the score to zero. Evolution operates exclusively on synthetic problems, scored by the geometric mean of solve times across 17 procedurally generated instances that span sample-to-feature ratio, design-matrix sparsity, active-set density, and feature correlation. Because no real dataset is ever exposed to the search, the gains reported on real data below reflect generalization rather than tuning to the test set.

Across the 11 real-world datasets in Supplementary Table 16 , none seen during the search, SimpleTES discovers a solver that is 2.17 × 2.17\times faster than glmnet on average and 14.08 × 14.08\times faster than sklearn , with every reported solution passing the held-out correctness check. What makes the discovered solver notable is not just raw speed but geometry awareness : it reads the shape of each problem and adapts its algorithm accordingly. Where glmnet applies coordinate descent uniformly, SimpleTES ’s solver detects the problem regime and switches solver family to match it. For moderate-dimensional, tall designs ( p ≤ 2000 p\leq 2000 and n ≥ p / 4 n\geq p/4 ) it abandons coordinate descent for an exact LARS homotopy solver that traces the regularization path analytically, updating the active set at each kink with rank-one inverse Gram updates [ 34 ] ; for wide or sparse designs ( p > 2000 p>2000 or n < p / 4 n<p/4 ) it retains coordinate descent with strong-rule screening. This geometry-dependent switching is exactly what the speedups track: the gains peak at 9.56 × 9.56\times over glmnet on the tall DNA design ( 1700 × 180 1700\times 180 , the only case with n ≫ p n\gg p ), where the LARS branch fires on a small active set, settle at 1.30 1.30 – 1.50 × 1.50\times on wide biological designs where p ≫ n p\gg n , and reach 1.36 1.36 – 1.76 × 1.76\times on large mixed-shape datasets such as RCV1 and Gisette. The vs- sklearn gains are largest on the biological datasets, up to 50.77 × 50.77\times on TCGA BRCA. In effect, the discovered program recombines two well-known but historically separate lasso solver families into a single geometry-aware policy that selects the right one for each input, arrived at from no prior beyond the starting code and the evaluator. That the speedups hold on unseen real data suggests it exploits genuine problem structure rather than fitting the synthetic surrogate distribution.

##### SimpleTES discovers new state-of-the-art predictor for Zebrafish whole-brain neural-activity.

Forecasting the neural activity of an entire vertebrate brain is a central challenge for understanding how brains turn sensory input and internal state into behavior [ 3 ] . Continuous whole-brain recording at single-cell resolution is limited by motion artifact [ 175 ] , photobleaching and phototoxicity [ 72 ] , and the trade-off between imaging speed and field-of-view [ 109 ] . Predictive models bridge this gap by learning from recorded activity and stimulus context to forecast future brain states. The Zebrafish Activity Prediction Benchmark (ZAPBench) [ 88 ] , built from a two-hour light-sheet recording of a larval zebrafish exposed to a sequence of visual stimuli, provides activity traces for 71,721 71{,}721 neurons over 7,879 7{,}879 time steps across nine stimulus conditions, with the task of predicting neural activities up to 32 32 steps ahead from only 4 4 steps of context. The strongest previously reported forecaster was discovered by Empirical Research Assistance (ERA) [ 9 ] , a tree-search method guided by a proprietary frontier model; ERA and SimpleTES differ in both the search algorithm and the underlying model, and we ask whether SimpleTES with an open-sourced model can discover competitive forecasters on the same task under similar computational limits.

SimpleTES achieves the strongest forecasting performance on ZAPBench, outperforming prior methods at every evaluated horizon ( Figure 4 d): its horizon-averaged test MAE of 0.0259 0.0259 at 32 steps improves over ERA ( 0.0283 0.0283 ; 8.5 % 8.5\% relative reduction) and the strongest ZAPBench baseline, the volumetric U-Net ( 0.0292 0.0292 ; 11.3 % 11.3\% relative reduction). Its whole-brain prediction closely matches both the spatial organization and magnitude of the recorded population response ( Figure 4 a); the neuron-by-time raster preserves the dominant temporal structure of the recorded activity ( Figure 4 b). The prediction error varies across stimulus conditions ( Figure 4 c), and grows over the forecast horizon ( Figure 4 e). The discovered program ( Figure 4 f) shows that SimpleTES improves performance by automatically identifying a compact, well-matched combination of forecasting modules and their parameterization. The decisive change is to reformulate the prediction target: rather than regressing absolute future activity, the network predicts a residual added back through an identity skip connection, echoing residual learning [ 53 ] and last-value normalization from NLinear-style models [ 168 ] . Around this residual predictor it adds an explicit linear-trend baseline, combines it with the nonlinear forecasts using per-horizon closed-form least-squares weights, and feeds the nonlinear predictor a rich per-neuron descriptor including first-order differences, window slopes, per-step population statistics, and data-driven identity features from each neuron’s low-rank SVD loadings and coupling to the brain-wide mean.

### SimpleTES improves AI foundations