Rubén Darío Guerrero

Rubén Darío Guerrero

We cast the design of parameterized quantum circuits as a four-player potential game whose state is a circuit directed acyclic graph (DAG) and whose players encode trainability, non-stabilizerness, task performance, and hardware cost. Per-player restricted action sets factorize the move space into append, remove, retype, and rewire operations; a block-coordinate $\varepsilon$-Nash residual $δ_\text{Nash}$ certifies that no single player can improve unilaterally. A single weight sweep on MaxCut $K_4$ traces a Pareto frontier from a Clifford endpoint $(M_2/n,\langle H\rangle)=(0,4.00)$ to a non-Clifford endpoint $(0.48,3.30)$. On three four-qubit hardware topologies (heavy-hex, $2\times 2$ grid, Rydberg all-to-all), Nash search achieves the highest mean potential; on the $2\times 2$ grid Nash reaches the theoretical ceiling $Φ_\text{max}=4.10$ on two of five seeds while the simulated-annealing baseline does so on one; paired Wilcoxon tests over five seeds cannot reject the null on any single topology ($p\ge 0.22$). On LiH/STO-3G, seeding Nash from a 58-gate Givens-doubles ansatz produces a 48-operation, depth-25 circuit retaining $97.7\%$ of the correlation energy while simultaneously reducing gate count, increasing non-stabilizerness, and controlling trainability. The framework is complementary to energy-only searches such as ADAPT-VQE and k-UpCCGSD, which reach chemical accuracy with fewer operations but do not optimize the other three axes.

Rubén Darío Guerrero

Automated code generation can systematically exceed expert hand-optimization for recurrence relations-computational primitives ubiquitous in orthogonal polynomials, special functions, numerical integration, and molecular integral evaluation. We present RECURSUM, a Python-based domain-specific language generating optimized C++ for arbitrary recurrence relations via three backends: template metaprogramming for compile-time evaluation, a novel LayeredCodegen backend with architectural optimizations, and runtime loop-based evaluation. The DSL uses einsum-inspired notation to specify recurrences, validity constraints, and base cases in 10-30 lines of Python, generating 650+ lines of production C++. LayeredCodegen achieves 9.8x speedup over expert hand-written implementations and 1.9x over template metaprogramming for McMurchie-Davidson Hermite coefficients. Architecture analysis reveals three quantifiable effects: (1) zero-copy output parameters eliminate return-by-value overhead (70-80% of speedup), (2) guaranteed function inlining eliminates compiler-refused overhead (15-20%), (3) exact-sized stack buffers achieve 100% cache efficiency vs 27% for MAX-sized arrays (5-10%). We validate on 24 recurrence types spanning pure mathematics (Legendre, Chebyshev, Hermite, Laguerre polynomials), numerical analysis (Clenshaw, Golub-Welsch), and quantum chemistry (McMurchie-Davidson, Rys quadrature, Boys function). Production benchmarks show speedups propagate to complete algorithms, with generated code matching expert baselines within 3.3%. RECURSUM demonstrates that systematic code generation serves as the performance ceiling for recurrence algorithms. By eliminating the dual expertise barrier (domain knowledge + C++ metaprogramming), the framework democratizes high-performance scientific computing-establishing a paradigm where automated generation systematically exceeds manual optimization.

Rubén Darío Guerrero

The semiconductor industry faces a computational crisis in extreme ultraviolet (EUV) lithography optimization, where traditional methods consume billions of CPU hours while failing to achieve sub-nanometer precision. We present a physics-constrained adaptive learning framework that automatically calibrates electromagnetic approximations through learnable parameters $\boldsymbolθ = \{θ_d, θ_a, θ_b, θ_p, θ_c\}$ while simultaneously minimizing Edge Placement Error (EPE) between simulated aerial images and target photomasks. The framework integrates differentiable modules for Fresnel diffraction, material absorption, optical point spread function blur, phase-shift effects, and contrast modulation with direct geometric pattern matching objectives, enabling cross-geometry generalization with minimal training data. Through physics-constrained learning on 15 representative patterns spanning current production to future research nodes, we demonstrate consistent sub-nanometer EPE performance (0.664-2.536 nm range) using only 50 training samples per pattern. Adaptive physics learning achieves an average improvement of 69.9\% over CNN baselines without physics constraints, with a significant inference speedup over rigorous electromagnetic solvers after training completion. This approach requires 90\% fewer training samples through cross-geometry generalization compared to pattern-specific CNN training approaches. This work establishes physics-constrained adaptive learning as a foundational methodology for real-time semiconductor manufacturing optimization, addressing the critical gap between academic physics-informed neural networks and industrial deployment requirements through joint physics calibration and manufacturing precision objectives.