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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

Tradeoffs on the volume of fault-tolerant circuits

Anirudh Krishna, Gilles Zémor

Year

2025

Journal

arXiv preprint

DOI

arXiv:2510.03057

arXiv

2510.03057

Dating back to the seminal work of von Neumann [von Neumann, Automata Studies, 1956], it is known that error correcting codes can overcome faulty circuit components to enable robust computation. Choosing an appropriate code is non-trivial as it must balance several requirements. Increasing the rate of the code reduces the relative number of redundant bits used in the fault-tolerant circuit, while increasing the distance of the code ensures robustness against faults. If the rate and distance were the only concerns, we could use asymptotically optimal codes as is done in communication settings. However, choosing a code for computation is challenging due to an additional requirement: The code needs to facilitate accessibility of encoded information to enable computation on encoded data. This seems to conflict with having large rate and distance. We prove that this is indeed the case, namely that a code family cannot simultaneously have constant rate, growing distance and short-depth gadgets to perform encoded CNOT gates. As a consequence, achieving good rate and distance may necessarily entail accepting very deep circuits, an undesirable trade-off in certain architectures and applications.

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