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| Format: | Preprint |
| Publié: |
2026
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| Accès en ligne: | https://arxiv.org/abs/2605.02051 |
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| _version_ | 1866918479821537280 |
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| author | Kotukh, Yevgen |
| author_facet | Kotukh, Yevgen |
| contents | We present Stochastic Commutator Synthesis, a hybrid quantum gate compilation framework that integrates Kuperberg's sub-cubic Solovay-Kitaev exponent c near 1.44042 with the error-tailoring machinery of randomized compilation. Classical Solovay-Kitaev implementations produce known word lengths and accumulate coherent approximation errors that degrade fault-tolerant threshold estimates. Kuperberg's 2023-2025 result reduces this via doubly exponential convergence and higher-order commutator decompositions. SCS augments this geometric backbone with a Gibbs-sampled stochastic choice of commutator factors at each recursion level, converting coherent synthesis residuals into incoherent, Pauli-twirl-compatible noise -- a property exploited by RC. Combined with RL-guided pre-synthesis, SCS achieves consistent T-count reductions of 10-25 percent and demonstrates fidelity gains of up to 35 percent on multi-fold Forrelation circuits on trapped-ion hardware such as Sandia QSCOUT. We situate SCS within the complexity-theoretic landscape established by the Raz-Tal oracle separation, arguing that low-error, noise-robust compilation of Forrelation-type circuits constitutes a practical pathway toward demonstrating this separation on physical hardware. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02051 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sub-Cubic Quantum Gate Synthesis via Stochastic Commutator Decomposition Kotukh, Yevgen Quantum Physics We present Stochastic Commutator Synthesis, a hybrid quantum gate compilation framework that integrates Kuperberg's sub-cubic Solovay-Kitaev exponent c near 1.44042 with the error-tailoring machinery of randomized compilation. Classical Solovay-Kitaev implementations produce known word lengths and accumulate coherent approximation errors that degrade fault-tolerant threshold estimates. Kuperberg's 2023-2025 result reduces this via doubly exponential convergence and higher-order commutator decompositions. SCS augments this geometric backbone with a Gibbs-sampled stochastic choice of commutator factors at each recursion level, converting coherent synthesis residuals into incoherent, Pauli-twirl-compatible noise -- a property exploited by RC. Combined with RL-guided pre-synthesis, SCS achieves consistent T-count reductions of 10-25 percent and demonstrates fidelity gains of up to 35 percent on multi-fold Forrelation circuits on trapped-ion hardware such as Sandia QSCOUT. We situate SCS within the complexity-theoretic landscape established by the Raz-Tal oracle separation, arguing that low-error, noise-robust compilation of Forrelation-type circuits constitutes a practical pathway toward demonstrating this separation on physical hardware. |
| title | Sub-Cubic Quantum Gate Synthesis via Stochastic Commutator Decomposition |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2605.02051 |