Adiabatic Error Cancellation in Berry Phase Estimation

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)^-4T^-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.