One Coordinate at a Time: Convergence Guarantees for Rotosolve in Variational Quantum Algorithms
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arXiv
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| Formato: | Preprint |
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2026
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| author | Pramanik, Sayantan Chandra, M Girish |
| author_facet | Pramanik, Sayantan Chandra, M Girish |
| contents | In this paper, we resolve an open question in the field of optimization algorithms for training parametrized quantum circuits: Does the popular Rotosolve algorithm converge? Until now, interpolation-based coordinate descent methods such as Rotosolve have mostly been treated as heuristics, lacking any formal convergence guarantees. We rigorously analyze Rotosolve, and show that it converges to $\varepsilon$-stationary points if the optimization landscape is non-convex and smooth; and to $\varepsilon$-suboptimal points if the objective function additionally obeys the Polyak-Lojasiewicz (PL) condition. Further, we derive explicit worst-case rates of convergence in the finite quantum measurement regime. These rates are contrasted against those from a similar coordinate-based method: Randomized Coordinate Descent (RCD). Although in the worst case their rates are, prima facie, equivalent, we present arguments for a more nuanced comparison between the two. We highlight that Rotosolve is hyperparameter-free, and implicitly uses first and second derivatives in its updates. Finally, we supplement our theoretical findings with numerical experiments from Quantum Machine Learning; and compare the performance of Rotosolve against RCD, Stochastic Gradient Descent, Simultaneous Perturbation Stochastic Approximation, and Randomized Stochastic Gradient Free methods. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_25613 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | One Coordinate at a Time: Convergence Guarantees for Rotosolve in Variational Quantum Algorithms Pramanik, Sayantan Chandra, M Girish Quantum Physics In this paper, we resolve an open question in the field of optimization algorithms for training parametrized quantum circuits: Does the popular Rotosolve algorithm converge? Until now, interpolation-based coordinate descent methods such as Rotosolve have mostly been treated as heuristics, lacking any formal convergence guarantees. We rigorously analyze Rotosolve, and show that it converges to $\varepsilon$-stationary points if the optimization landscape is non-convex and smooth; and to $\varepsilon$-suboptimal points if the objective function additionally obeys the Polyak-Lojasiewicz (PL) condition. Further, we derive explicit worst-case rates of convergence in the finite quantum measurement regime. These rates are contrasted against those from a similar coordinate-based method: Randomized Coordinate Descent (RCD). Although in the worst case their rates are, prima facie, equivalent, we present arguments for a more nuanced comparison between the two. We highlight that Rotosolve is hyperparameter-free, and implicitly uses first and second derivatives in its updates. Finally, we supplement our theoretical findings with numerical experiments from Quantum Machine Learning; and compare the performance of Rotosolve against RCD, Stochastic Gradient Descent, Simultaneous Perturbation Stochastic Approximation, and Randomized Stochastic Gradient Free methods. |
| title | One Coordinate at a Time: Convergence Guarantees for Rotosolve in Variational Quantum Algorithms |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2604.25613 |