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Paper 1

LLM-Guided Evolutionary Search for Algebraic T-Count Optimization

Daniil Fisher, Valentin Khrulkov, Mikhail Saygin, Ivan Oseledets, Stanislav Straupe

Year

2026

Journal

arXiv preprint

DOI

arXiv:2603.29894

arXiv

2603.29894

Reducing the non-Clifford cost of fault-tolerant quantum circuits is a central challenge in quantum compilation, since T gates are typically far more expensive than Clifford operations in error-corrected architectures. For Clifford+T circuits, minimizing T-count remains a difficult combinatorial problem even for highly structured algebraic optimizers. We introduce VarTODD, a policy-parameterized variant of FastTODD in which the correctness-preserving algebraic transformations are left unchanged while candidate generation, pooling, and action selection are exposed as tunable heuristic components. This separates the quality of the algebraic rewrite system from the quality of the search policy. On standard arithmetic benchmarks, fixed hand-designed VarTODD policies already match or improve strong FastTODD baselines, including reductions from 147 to 139 for GF(2^9) and from 173 to 163 for GF(2^10) in the corresponding benchmark branches. As a proof of principle for automated tuning, we then optimize VarTODD policies with GigaEvo, an LLM-guided evolutionary framework, and obtain additional gains on harder instances, reaching 157 for GF(2^10) and 385 for GF(2^16). These results identify policy optimization as an independent and practical lever for improving algebraic T-count reduction, while LLM-guided evolution provides one viable way to exploit it.

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Paper 2

Quantum feature-map learning with reduced resource overhead

Jonas Jäger, Philipp Elsässer, Elham Torabian

Year

2025

Journal

arXiv preprint

DOI

arXiv:2510.03389

arXiv

2510.03389

Current quantum computers require algorithms that use limited resources economically. In quantum machine learning, success hinges on quantum feature maps, which embed classical data into the state space of qubits. We introduce Quantum Feature-Map Learning via Analytic Iterative Reconstructions (Q-FLAIR), an algorithm that reduces quantum resource overhead in iterative feature-map circuit construction. It shifts workloads to a classical computer via partial analytic reconstructions of the quantum model, using only a few evaluations. For each probed gate addition to the ansatz, the simultaneous selection and optimization of the data feature and weight parameter is then entirely classical. Integrated into quantum neural network and quantum kernel support vector classifiers, Q-FLAIR shows state-of-the-art benchmark performance. Since resource overhead decouples from feature dimension, we train a quantum model on a real IBM device in only four hours, surpassing 90% accuracy on the full-resolution MNIST dataset (784 features, digits 3 vs 5). Such results were previously unattainable, as the feature dimension prohibitively drives hardware demands for fixed and search costs for adaptive ansätze. By rethinking feature-map learning beyond black-box optimization, this work takes a concrete step toward enabling quantum machine learning for real-world problems and near-term quantum computers.

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