quantum computing developers

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.