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arXiv · 2605.22770

Adiabatic Quantum Phase Estimation

Alexander Schmidhuber·Seth Lloyd
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Abstract

Quantum phase estimation (QPE) is a central algorithmic primitive that estimates eigenvalues of a Hamiltonian up to precision $\epsilon$ in Heisenberg-limited time $T=\Theta(1/\epsilon)$. Standard gate-based implementations of QPE require deep controlled time-evolution circuits and are not native to analog hardware. Here, we present a simple adiabatic protocol for QPE that achieves (up to logarithmic factors) the optimal Heisenberg-limited scaling $T = O\left( \frac{1}{\epsilon} \log\left(\delta^{-1}\right)\right)$ in both the precision $\epsilon$ and failure probability $\delta$. By encoding eigenvalues in populations of computational basis states rather than complex phases, our approach is naturally robust against certain dephasing errors. The adiabatic protocol only requires the ability to couple a single ancilla qubit to the system Hamiltonian as well as pairwise couplings within the ancilla register.

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Alexander Schmidhuber, Seth Lloyd. 2026-05-21. Adiabatic Quantum Phase Estimation. https://arxiv.org/abs/2605.22770

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