quantum computing developers

Abstract: An autonomous research laboratory could conduct an entire study, from formulating questions to preparing manuscripts. Artificial intelligence (AI) offers one route towards this goal. Recent AI systems take on several research roles, but may draw conclusions that the evidence does not support. Here, we present an autonomous research laboratory in which agents based on large language models assess one another's work and can stop or redirect investigations. They can generate and reject research questions, require separate theoretical checks and conduct experiments designed to challenge their claims. We demonstrate these capabilities by investigating ensembles of quantum spins in diamond. The agents derived the minimum number of calibration settings needed to predict responses to a defined family of microwave pulse sequences. They checked the result computationally and designed experiments to distinguish competing predictions. An initial experiment agreed with the theoretical predictions, but repeated reference measurements showed that the signal was drifting during data collection. The agents therefore treated the result as inconclusive and revised the measurement protocol without relaxing the acceptance criteria. The revised experiment met those criteria and supported the theoretical predictions. This study demonstrates that collaborating AI agents can select research questions, derive theoretical results and test their predictions experimentally.

Abstract: We prove two universality theorems for neural networks consisting of a single neuron. First we prove a strong form of the Bovdi--Geche universality conjecture on neurons over finite fields, where the activation function is a certain modification of the discrete logarithm, using the Weil bound on multiplicative character sums over finite fields. Then we show a generalisation of Aizenberg's universality theorem for complex binary neurons with a weight vector independent of the target function, positively answering another question in the literature. The proof of the latter uses an equidistribution theorem for the dilates of certain maps into tori.

Abstract: We present the Infinity Machine, a self-improving AI agent that we use for research on problems whose answers aprogram or data can check. Each candidate solution is produced by a full tool-using agent that works for up to an hour in a fresh sandbox; proposers see only a public score, and a private split decides what counts. The harness itself(prompts, tools, skills, playbook, meta agent) is an editable genome, changed only through a kernel-enforced gate with held-out and cost checks. An autonomous mode goes from a plain-text goal to a verified report with no human step: an agent picks an open problem and writes its verifier, the kernel calibrates it, an adversarial agent audits it, and an agent that never sees the verifier re-checks the result. Across fourteen problems in six days, for about $180 of model usage, the system produced four results beyond the published state of the art on catalogued open problems in quantum information: a certified depolarizing-channel threshold point p = 0.064966, a qutrit positivity frontier of 0.2910672, a 44-gate depth-6 Golay state preparation, and a stabilizer-rank bound chi(T^7) <= 10. It also cut SABRE qubit-routing overhead from 68,559 to 12,087 added gates. In hardware, it cut the energy per MAC of an open 8x8 INT8 systolic tile by 77.7% through a full open RTL-to-GDS flow, bit-exact. Three fully autonomous runs ended in honestties with public records; one audit caught a stale record, and one agent-written score pointing the wrong way went unnoticed. We report the failures as carefully: the one self-derived harness generation was rejected on cost, proposers gamed lenient scorers four times, and operator changes were decisive for several results.

Abstract: QRecoupling.jl is a Julia package for numerical, exact and symbolic evaluation of classical and quantum recoupling coefficients and generic finite sums of quantum factorials, with one interface across the classical limit, principal unitary levels and real or complex deformation. A compact factorial rule and its cyclotomic exponents expose factor cancellation, polynomial structure and level support. The package covers quantum Clebsch-Gordan coefficients, 3j and 6j symbols and user-defined sums. Its adaptive numerical evaluation is combined with exact decisions for sums that cancel to zero. Classical 3j and 6j symbols are evaluated at a speed comparable to that of WIGXJPF, which is based on prime factorization tables, at the smallest spins, and about 6 and 10 times faster at spin cutoff 500. Under real, root-of-unity and complex deformation, the largest relative error measured against independent high-precision references is $3.5 \times 10^{-14}$ for spins up to 400. Fusion matrices with 401 channels are computed about 100 times faster than by loops over their entries.

Abstract: Partially optimal assignments (also called persistencies) allow combinatorial optimization problems to be reduced by fixing a subset of variables to values consistent with at least one optimal solution. For the quadratic unconstrained binary optimization (QUBO) problem, such assignments can be computed efficiently via autarkies of quadratic posiforms. However, the largest autarky domain and thus the number of fixed variables can depend on the specific posiform representation. We show that every quadratic posiform with the greatest possible constant term (the roof-dual bound) yields the largest autarky domain obtainable from any quadratic posiform. By computing such a roof-dual-optimal quadratic posiform and a corresponding autarky with largest domain in polynomial time, one can therefore attain the maximum partial optimality obtainable by quadratic posiform autarkies in polynomial time. This justifies the computation of roof-dual-optimal quadratic posiforms and corresponding autarkies in popular polynomial-time algorithms and establishes that finding additional partial optimality in QUBO requires going beyond autarkies of quadratic posiforms.

Abstract: Cancer detection using AI methods and image databases faces several challenges, including limited and imbalanced image datasets, long algorithm training times, and high-complexity feature generation. In particular, many cancer image datasets contain very few malignant examples compared to benign ones, limiting the amount of minority-class data available for training. Although classical AI and especially deep learning methods have had some success in providing cancer diagnostics, Quantum Machine Learning (QML) methods may offer advantages through high-dimensional feature representations, generative data augmentation, and the exploitation of feature correlations through quantum properties such as entanglement. In this paper, we propose using a generative QML method on the compressed breast ultrasound image dataset (BUSI) to generate synthetic images and hence augmented datasets for classifier training. In particular, we train a convolutional neural network with real, synthetic, and a combination of real and synthetic images. We test the algorithm on real images and provide comparative results for all three training cases. Our results show that the classifier trained entirely on synthetic images achieved an AUC-ROC of 0.802 (80.2%), compared with 0.760 (76.0%) for the real-data baseline.

Abstract: We determine the hundredths digit of the real Grothendieck constant by proving $1.773 \leq K_G \leq 1.7799$. Furthermore, numerical heuristics suggest the estimate $K_G \approx 1.779$. We start by simplifying the Gaussian duality theory of $K_G$, based on Hermite projection games and Krivine rounding schemes. The bounds are obtained by a heuristic primal/dual search for these objects, followed by rigorous {\em certification} of their values. The search and certification are performed using AI tools, and in particular the rigorous certificates are very large (analytical reductions to thousands of numerical inequalities).

Abstract: We give a deterministic polynomial-time algorithm for the Bilu--Linial signing problem on bipartite graphs. For every finite simple bipartite graph of maximum degree at most an integer $Δ\ge3$, the algorithm assigns signs to its edges so that the signed adjacency matrix has operator norm strictly less than $2\sqrt{Δ-1}$. Our algorithm builds on the randomized recursive repair framework of Jadbabaie, Saberi, and Sra~\cite{JSS26}, with deterministic rules for sign selection and vertex deletion.

Abstract: Multimodal vision-language systems typically fuse image and text embeddings through classical operators such as concatenation, attention, bilinear pooling, or tensor interactions. We propose Quantum Entangled Multimodal Fusion Networks (QEMFN), a hybrid quantum-classical framework that introduces parameterized entanglement as a structured inductive bias for multimodal fusion. Pretrained visual and textual features are projected into compact latent spaces, encoded as angle-parameterized quantum states, processed through intra-modal and paired cross-modal entangling circuits, and measured to produce fused representations for retrieval. Under matched parameter budgets and identical frozen CLIP backbones, QEMFN outperforms classical fusion baselines on COCO-5k and Flickr30k, including multilayer perceptron, tensor fusion, FiLM, cross-attention, compact transformer, and a dequantized paired-topology analogue. An ablation suite isolates the quantum module's contribution from the surrounding classical projections, and quantum-centric analyses report Meyer-Wallach entangling capability, expressibility, gradient variance against barren-plateau bounds, and entropy-performance correlation under controls for training progress alongside an intervention study on the entangling component. QEMFN is executed under shot-based estimation, a noise-modeled fake backend, and a real superconducting device with zero-noise extrapolation. This work does not claim quantum computational advantage; the contribution is the framework together with a controlled empirical and quantum-centric evaluation that positions trainable entanglement as an interpretable, hardware-executable fusion mechanism at scales accessible on contemporary devices.

Abstract: Explicit R-matrices of quantum groups are routinely transcribed from the literature, yet whether they satisfy an identity depends on basis order, tensor placement, the coproduct and, for superalgebras, the Koszul sign rule. quantum-group is a Python package that builds such matrices exactly with SymPy and returns every identity as an exact residual matrix, whose nonzero entries locate the convention that disagrees. It covers U_q(sl_2) modules, tensor products and the fundamental R-matrix, and the graded Yang--Baxter equation for GL_q(2|1). Applied to the thesis it was written for, it exposed an R-matrix that satisfies the Yang--Baxter equation but intertwines the opposite coproduct.

Abstract: Variational autoencoders are powerful representation learning models that map complex data into low-dimensional latent spaces, enabling the discovery of interpretable and disentangled factors. Such representations can facilitate the interpretation and controllable generation of data describing complex scientific systems. Understanding how these factors are organized and encoded in latent space is therefore important for developing reliable representation learning models. Recently, quantum variational autoencoders (QVAEs) have been proposed as quantum representation models, demonstrating informative latent representations and improved latent-space occupancy through quantum regularization. However, it remains unclear whether and how QVAEs can learn disentangled and interpretable latent factors. A key challenge in investigating quantum latent factors is that a small number of qubits spans an exponentially large Hilbert space, making the notion of an individual quantum latent dimension nontrivial. Here, we investigate what constitutes an individual quantum latent dimension and whether it can encode a distinct factor. We develop theoretical insights into quantum latent dimensions and support them with empirical studies on representative synthetic problems, including MNIST variants. Across three datasets, we demonstrate that QVAEs can discover factorized and semantically interpretable latent representations, with individual qubits functioning as meaningful latent factors. These results establish a foundation for understanding quantum latent spaces and their potential for structured and interpretable representation learning.

Abstract: Gaussian-process limits are powerful in describing overparameterized machine learning models, yet their validity in structured tensor-network architectures remains unclear. Here we analytically present a moment-based approach that identifies precise conditions for the emergence and breakdown of Gaussian universality in tensor-network learning models, with a focus on matrix product states. We prove that in the large bond dimension limit, the learning models with both local and global observables converge to Gaussian processes, with explicit finite-size bounds on higher-order moment deviations. Whereas in the large physical dimension limit, the Gaussian universality no longer persists: while the models with local observables retain Gaussian-process behavior, those global cases exhibit persistent non-Gaussian corrections. Our results reveal that Gaussian-process behavior in tensor-network learning is controlled not only by parameter number, but also by architectural scaling, observable locality, and the spectral properties.

Abstract: We ask whether a neural network can learn a structure-preserving map from a compressed latent space to a Hilbert-space representation. Using an 8-dimensional autoencoder bottleneck on MNIST and $n$-qubit product-state targets from PCA-based angle encoding, we report four findings. Although the target angles are generated by a nonlinear sigmoid transformation of the latent projections, the resulting mapping is well approximated by a linear function over the observed latent distribution: linear regression from $z$ to the true target angles achieves $R^{2} = 0.98$, while regression to the MLP's recovered angles achieves $R^{2} = 0.91$. The learned map's primary direction is strongly aligned with the target-induced direction, with cosine similarity $0.989$, while remaining nearly orthogonal to the input's principal direction, with cosine similarity $0.002$. The map is genuinely rank-4: removing any singular direction degrades inner-product preservation by $2.5$--$5.9\times$ despite a singular-value spectrum with two dominant and two small values. The learned subspace does not coincide with the PCA basis used to construct the target, and different random seeds recover the same primary direction but diverge in higher ranks. Finally, kernel ridge regression with an RBF kernel outperforms a tuned MLP (IP error $0.0144$ vs.\ $0.0197$), suggesting that for approximately linear structure-preserving mappings, classical kernel methods may be a simpler and more effective alternative.

Abstract: We study the transverse field Ising model, defined by the Hamiltonian $H =\frac{1}{2}\sum_{i, j\in [n]} J_{ij} Z_i Z_j +\sum_{i=1}^n h_i^z Z_i + η\sum_{i} X_i$ where $J $ is the symmetric interaction matrix, and $η$ is the transverse field strength. Let $Δ(J)=λ_{\max}(J)-λ_{\min}(J)$ be the spectral width of $J.$ When the inverse temperature $β\geq0$ satisfies $Δ(J)\cdot\frac{\tanh(βη)}η\leq1$, we give a randomized classical algorithm that approximates the partition function $Z(β)=\operatorname{Tr}(e^{-βH})$ to a given relative error $ε\in(0,1)$ in time polynomial in $n$, $β$, the model parameters, and $ε^{-1}$. When $ Δ(J) \cdot \frac{\tanh(βη)}η > 1 ,$ we show that approximating $ Z(β)$ within an $\exp(o(n))$-multiplicative factor is $\textbf{NP}$-hard, and thus unlikely to admit an efficient classical or quantum algorithms under standard complexity theoretic assumptions. Furthermore, in the regime $Δ(J)\cdot \frac{\tanh(βη)}η\leq 1,$ we provide an efficient randomized classical algorithm that approximates Pauli string observables of the Gibbs state $ ρ_β= \frac{e^{-βH}}{\operatorname{Tr}(e^{-βH})}$ within an arbitrarily small additive error. In the special case when the observable is also diagonal in the $X$-basis, i.e. $P \in \{I, X\}^{\otimes n}$, the algorithm further achieves arbitrarily small relative error.

Abstract: Error-correcting codes (ECCs) are essential across diverse applications, from wireless communications and storage to quantum computing, yet each application imposes distinct design requirements on the parity-check matrix (PCM). To address these on-demand requirements in a unified framework, we propose ZeroCode, a reinforcement learning (RL)-based approach that constructs PCMs sequentially from the all-zero matrix. ZeroCode formulates construction as a discrete sequential decision-making problem and uses proximal policy optimization with action masking to select valid edges. ZeroCode achieves a gain of approximately 1 dB over the prior RL-based construction method at a bit error rate (BER) of $10^{-4}$ for the (32,16) code and outperforms existing genetic, differentiable, and classical code-design methods in our experiments. Beyond optimizing decoding performance, the masking mechanism allows on-demand structural constraints, such as a maximum degree, 4-cycle-free structure, and quasi-cyclic structure, to be flexibly incorporated. Moreover, a single policy rollout yields a library of PCMs with varying edge counts, offering trade-offs between decoding performance and complexity without retraining. Overall, ZeroCode addresses diverse code-design requirements within a unified framework, providing solutions with optimized decoding performance under given constraints.

Abstract: We reply to the comments by M. Sienicki and K. Sienicki (arXiv:2512.07881) and by K. Sienicki (arXiv:2601.06104) on our work on quantum-mechanical statistics in human language (arXiv:2407.14924) and on quantum structure in AI-generated language (arXiv:2511.21731). We thank the authors for their careful reading and address what we consider to be the main points of criticism: the exploratory nature of the protocol used in the experiments with large language models; the role of marginal-law violations, and of the Contextuality-by-Default criterion, in the identification of entanglement; the limited diagnostic value of a Bose-Einstein fit taken in isolation; the meaning of assigning the lowest energy levels to the most frequent words; and the relation between the vector spaces used by LLMs and quantum state spaces. We also correct a typographical error in Table 3 of arXiv:2511.21731, which does not affect the reported CHSH value.

Abstract: On a seven-compound drug-response model, warm-start quantum approximate optimization (QAOA) on IonQ Forte-1 returned valid assignments more often than random bitstrings, but this alone did not show effective optimization. Ideal QAOA raised optimum probability above uniform feasible sampling in only four of twelve reference circuits. Hardware often fell below its own noiseless circuits, while greedy search solved all hardware models within 200 objective evaluations. Expanded simulations showed a gain over feasible sampling in 28 of 35 CAMA-1 panels and none of four 647-V panels. Annealing solved all these panels in every seed. A Grover mixer preserved feasibility and improved optimum probability over feasible sampling in all ten tested models. We analyzed 25 completed tasks containing 5,300 shots from 18 circuits and 14 instances. The encodings use 6-35 qubits and at most 4,900 feasible assignments, which we enumerated to establish exact optima. Noiseless references now cover both the original six circuits and six wider circuits. At 35 qubits, with 4,900 feasible assignments, ideal feasibility was 35.85%, compared with 7 of 200 valid hardware outputs. Its ideal optimum probability was below both sampling controls. The circuits sample assignments in a model built from measured single-agent and pairwise responses.

Abstract: Gowers, Green, Manners, and Tao (Annals '25) recently resolved Marton's polynomial Freiman-Ruzsa conjecture. We give an algorithmic counterpart to their result: given uniform sampling and membership-oracle access to a set $A \subseteq \mathbb{F}_2^n$ with doubling constant at most $K$, our algorithm outputs a subspace of size at most $|A|$ whose $K^{O(1)}$ translates cover $A$. The algorithm runs in $\textsf{poly}(n,K)$ time. As applications, we obtain polynomial-time algorithms for a variety of learning problems, including quadratic Goldreich-Levin, improper agnostic tomography of stabilizer states, and tomography of quantum states with bounded stabilizer extent.

Abstract: We give an FPRAS for the permanent of an $n\times n$ $0/1$ matrix with running time $\widetilde{O}(n^{3.5}\varepsilon^{-2})$. Our algorithm extends to a strongly polynomial FPRAS for arbitrary nonnegative matrices, as in previous works. Jerrum, Sinclair, and Vigoda (2004) gave the first FPRAS for the permanent of a nonnegative matrix. The running time was subsequently improved to $\widetilde{O}(n^7)$ by Bezáková, Štefankovič, Vazirani, and Vigoda (2008), and recently to $\widetilde{O}(n^6)$ by Chen, Vigoda, and Yang (2026). We introduce a multicommodity-flow bound inspired by electrical flows, replacing the usual path-length factor by routing energy. For a boosted version of the classical JSV chain, we prove a relaxation-time bound of $O(n^3\log n)$ and show that stationary trajectories of this length estimate all stationary hole-pattern probabilities, yielding an $\widetilde O(n^5)$-time FPRAS algorithm. Our new hole-weighted slide (HWS) chain improves both bounds to $O(n^2\log n)$, yielding an $\widetilde O(n^4)$-time algorithm. Finally, we obtain the claimed $\widetilde O(n^{3.5})$ running time by using a subset of $\widetilde{O}(\sqrt{n})$ checkpoint temperatures in an iterated sequence of warm-starts to obtain initializations at every temperature.

Abstract: We give a deterministic polynomial-time algorithm that, given rational Hermitian matrices $H_1,\dots,H_N$ of rank at most one, finds signs $s\in\{\pm1\}^N$ with $\|\sum_i s_i H_i\|\le 13\|\sum_i H_i^2\|^{1/2}$. As a corollary, for vectors $v_i$ with $\sum_i v_iv_i^*=I$ and $\|v_i\|^2\leδ$, the signs yield a partition $[N] = S_1 \cup S_2$ such that each part satisfies $\|\sum_{i \in S_j} v_i v_i^* - \frac{I}{2}\| \leq \frac{13}{2}\sqrtδ$ for $j = 1,2$. This gives a deterministic polynomial-time algorithm for the Kadison--Singer problem, in Weaver's equivalent discrepancy-theoretic $\mathsf{KS}_2$ formulation, with a universal constant.

Abstract: Regularization choice changes the recovery phase diagrams of annealing-based binary compressed sensing. We develop a regularization-selection method that combines systematic parameter search with random forest regression. Under noiseless Gaussian measurements with known sparsity, reference parameters are selected from a candidate grid by minimizing mean squared reconstruction error over repeated simulated annealing (SA) trials. The fitted model predicts these reference values from signal dimension, sampling ratio, and sparsity. With predicted regularization, the SA recovery transition broadly follows the asymptotic reference boundary for box-constrained $\ell_1$ recovery at the larger signal dimensions examined. Without retraining, the same predictor supplies identical regularization values to SA and a quantum--classical hybrid solver. On matched problem instances, the hybrid solver yields smaller mean squared reconstruction errors than SA in parts of the evaluated parameter space. The resulting rule reuses the searched information for subsequent reconstruction without repeating candidate searches at each setting. The results quantify empirical performance under the stated finite candidate grid and solver settings; they do not constitute a solver-independent recovery guarantee or a time-to-solution comparison.

Abstract: The Komlós conjecture is a classic problem in discrepancy theory; it asks whether an absolute constant $K$ exists such that given any $n$ vectors $a_1,\ldots,a_n$ inside the $m$-dimensional Euclidean ball, regardless of how large $m,n$ are, there is always a selection of signs $\varepsilon_1,\ldots,\varepsilon_n$ guaranteeing $$\|\varepsilon_1a_1+\ldots+\varepsilon_na_n\|_\infty \leq K.$$ We show that if the $\varepsilon_i$'s are allowed to take not just the values of $\pm 1$ but any unit modulus complex number, which we refer to as complex discrepancy, then the above inequality holds for a finite, explicit constant $K_{\mathbb{C}}$. Here, the $\ell^\infty$ norm of the resulting vector in $\mathbb{C}^m$ is the largest modulus of its entries, and thus the complex discrepancy of real vectors is equivalent to their rank-$2$ vector discrepancy. Therefore, our result resolves the Komlós problem for Gaussian discrepancy -- a discrepancy measure introduced by Chewi, Gerber, Rigollet and Turner. Our paper builds upon the recent work of Bansal and Jiang on the Beck-Fiala and Komlós conjectures, which we approach from the formalism of Burkholder and the Bellman function method from probability and harmonic analysis. Our work was in part motivated by the realization that the complex discrepancy of the columns of any unitary matrix is equal to 1, a fact that follows from a straightforward calculation based on Idel and Wolf's generalization of the Sinkhorn normal form for unitary matrices.

Abstract: A long-standing open question in query complexity asks whether there is a total Boolean function f with R(f) << C(f), where R(f) and C(f) denote its bounded-error randomized query complexity and certificate complexity, respectively. We construct a function with R(f) = O~(sqrt{C(f)}), which is optimal up to log factors. The same function also has $Q(f) = O~(C(f)^{1/4}), where Q(f) is the bounded-error quantum query complexity of f, which is also nearly optimal.

Abstract: Rigorous empirical validation of quantum machine learning on natural language tasks remains scarce. We evaluate a 10-qubit hybrid quantum-classical variational circuit (2,148 parameters) for paraphrase detection across three benchmarks: MRPC, Quora Question Pairs (QQP), and adversarial PAWS. On QQP (n = 10 seeds), the circuit achieves 75.53% +/- 0.75%. accuracy, statistically outperforming parameter-matched classical baselines (DeepMLP: p = 0.015, Cohen's d = 1.20; F1: p < 0.001, d = 2.32) and surpassing DistilBERT-4bit with 31,191 fewer parameters. On MRPC the optimal 2-layer variant reaches 92% of BERT-base accuracy at 54,000 lower parameter cost. Circuit depth analysis reveals a dataset-depth scaling effect; entanglement analysis via the Meyer-Wallach measure identifies multi-qubit entanglement as the primary performance driver (r = 0.85 across four variants). Adversarial evaluation on PAWS reveals emergent robustness: 98.2% recall versus 81.6% classical (+16.6 pp, d = 1.24, p < 0.001), without adversarial training. These results constitute the first systematic parameter-matched multi-benchmark empirical validation of hybrid variational circuits for NLP. All results are from classical simulation; hardware validation is future work.

Abstract: Field temporal prediction and source identification constitute canonical problems in dynamical systems. Conventional approaches to these problems depend on a thorough understanding of the governing partial differential equations (PDEs). Recently, deep learning, as represented by neural operators, has provided a data-driven paradigm for addressing such tasks. However, most existing global neural operators for PDEs require large training datasets and many learnable parameters, with limited interpretability and generalization. We propose the local gradient neural operator (LGNO) as a lightweight and interpretable alternative for field temporal evolution prediction and source identification in typical mechanical problems. The method builds on priors from nonlinear gradient discretization and uses multilayer perceptron convolutional layers to learn translation-invariant local kernels that resemble discrete stencils. A zero consistent stencil factorization separates coefficient learning from field reconstruction, rendering the learned operators more transparent. For problems with symmetries, network folding shares equivalent components and reduces parameter counts. We evaluate the method on PDE benchmarks covering linear and nonlinear, static and dynamic, and low and high dimensional cases. Results show that LGNO maintains accuracy, parameter efficiency, and rollout stability across these tasks, and further exhibits wide applicability to mechanical problems including diffusion, flow, and quantum phenomena.