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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2511.19551 |
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| _version_ | 1866912727411195904 |
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| author | Zubarev, Mikhail |
| author_facet | Zubarev, Mikhail |
| contents | Variational quantum algorithms face a fundamental trainability crisis: barren plateaus render optimization exponentially difficult as system size grows. While recent Lie algebraic theory precisely characterizes when and why these plateaus occur, no practical optimization method exists with finite-sample guarantees for navigating them. We present the sequential plateau-adaptive regime-testing algorithm (SPARTA), the first measurement-frugal scheduler that provides explicit, anytime-valid risk control for quantum optimization. Our approach integrates three components with rigorous statistical foundations: (i) a $χ^2$-calibrated sequential test that distinguishes barren plateaus from informative regions using likelihood-ratio supermartingales; (ii) a probabilistic trust-region exploration strategy with one-sided acceptance to prevent false improvements under shot noise; and (iii) a theoretically-optimal exploitation phase that achieves the best attainable convergence rate. We prove geometric bounds on plateau exit times, linear convergence in informative basins, and show how Lie-algebraic variance proxies enhance test power without compromising statistical calibration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19551 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | SPARTA: $χ^2$-calibrated, risk-controlled exploration-exploitation for variational quantum algorithms Zubarev, Mikhail Quantum Physics Variational quantum algorithms face a fundamental trainability crisis: barren plateaus render optimization exponentially difficult as system size grows. While recent Lie algebraic theory precisely characterizes when and why these plateaus occur, no practical optimization method exists with finite-sample guarantees for navigating them. We present the sequential plateau-adaptive regime-testing algorithm (SPARTA), the first measurement-frugal scheduler that provides explicit, anytime-valid risk control for quantum optimization. Our approach integrates three components with rigorous statistical foundations: (i) a $χ^2$-calibrated sequential test that distinguishes barren plateaus from informative regions using likelihood-ratio supermartingales; (ii) a probabilistic trust-region exploration strategy with one-sided acceptance to prevent false improvements under shot noise; and (iii) a theoretically-optimal exploitation phase that achieves the best attainable convergence rate. We prove geometric bounds on plateau exit times, linear convergence in informative basins, and show how Lie-algebraic variance proxies enhance test power without compromising statistical calibration. |
| title | SPARTA: $χ^2$-calibrated, risk-controlled exploration-exploitation for variational quantum algorithms |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2511.19551 |