Adiabatic Quantum Phase Estimation

TL;DR

This paper introduces an adiabatic quantum phase estimation protocol that achieves near-optimal Heisenberg-limited scaling, offering robustness against certain errors and requiring minimal hardware capabilities.

Contribution

It presents a simple, robust adiabatic approach to quantum phase estimation that reaches near-optimal scaling with minimal hardware requirements.

Findings

Achieves Heisenberg-limited scaling up to logarithmic factors

Robust against certain dephasing errors due to population encoding

Requires only coupling a single ancilla qubit and pairwise ancilla couplings

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.