Berry phase estimation has a universal adiabatic error-cancellation mechanism that exactly cancels O(T^{-1}) phase error via ±H evolution and suppresses residuals to O(T^{-M}) via randomization for any M.
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Randomized sparse-QSVT reduces gate counts by up to 10x for inhomogeneous many-term Hamiltonians at moderate error (around 10^{-3}), but deterministic QSVT becomes cheaper for higher precision.
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Adiabatic Error Cancellation in Berry Phase Estimation
Berry phase estimation has a universal adiabatic error-cancellation mechanism that exactly cancels O(T^{-1}) phase error via ±H evolution and suppresses residuals to O(T^{-M}) via randomization for any M.
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When is randomization advantageous in quantum simulation?
Randomized sparse-QSVT reduces gate counts by up to 10x for inhomogeneous many-term Hamiltonians at moderate error (around 10^{-3}), but deterministic QSVT becomes cheaper for higher precision.