Adiabatic Quantum Phase Estimation

Quantum phase estimation (QPE) is a central algorithmic primitive that estimates eigenvalues of a Hamiltonian up to precision ε in Heisenberg-limited time T=Θ(1/ε). 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 = Oleft\(frac{1}ε logleft(δ^-1right\)right) in both the precision ε and failure probability δ. 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.