Adiabatic Error Cancellation in Berry Phase Estimation

• URL: http://arxiv.org/abs/2604.20952v1
• Date: Wed, 22 Apr 2026 18:00:00 GMT
• Title: Adiabatic Error Cancellation in Berry Phase Estimation
• Abstract summary: Berry phase estimation admits a natural and universal adiabatic error-cancellation mechanism.<n>We show that it is a promising candidate for practical quantum computing before full fault tolerance.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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