Adiabatic Error Cancellation in Berry Phase Estimation
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915950669856768 |
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| author | Kiumi, Chusei |
| author_facet | Kiumi, Chusei |
| contents | In this work, we show that Berry phase estimation admits a natural and universal adiabatic error-cancellation mechanism, making it a promising candidate for practical quantum computing before full fault tolerance. Combining finite-runtime evolutions under $\pm H$ along the loop cancels the leading $O(T^{-1})$ phase error exactly, and Richardson extrapolation further reduces the residual error to an oscillatory term with endpoint-controlled coefficient $O(\|\dot H(0)\|^2Δ(0)^{-4}T^{-2})$. Beyond this deterministic cancellation, we establish that, for suitable smooth runtime distributions, runtime randomization suppresses the remaining oscillatory contribution to $O(T^{-M})$ for any fixed $M$, leading to a randomized Hadamard-test algorithm for Berry phase estimation over the full range $[0,2π)$ with improved runtime scaling under standard sample complexity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20952 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Adiabatic Error Cancellation in Berry Phase Estimation Kiumi, Chusei Quantum Physics In this work, we show that Berry phase estimation admits a natural and universal adiabatic error-cancellation mechanism, making it a promising candidate for practical quantum computing before full fault tolerance. Combining finite-runtime evolutions under $\pm H$ along the loop cancels the leading $O(T^{-1})$ phase error exactly, and Richardson extrapolation further reduces the residual error to an oscillatory term with endpoint-controlled coefficient $O(\|\dot H(0)\|^2Δ(0)^{-4}T^{-2})$. Beyond this deterministic cancellation, we establish that, for suitable smooth runtime distributions, runtime randomization suppresses the remaining oscillatory contribution to $O(T^{-M})$ for any fixed $M$, leading to a randomized Hadamard-test algorithm for Berry phase estimation over the full range $[0,2π)$ with improved runtime scaling under standard sample complexity. |
| title | Adiabatic Error Cancellation in Berry Phase Estimation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2604.20952 |