Quantum Phase Estimation Algorithm with Gaussian Spin States

Quantum phase estimation (QPE) is one of the most important subroutines in quantum computing. In general applications, current QPE algorithms either suffer an exponential time overload or require a set of--notoriously quite fragile--GHZ states. These limitations have so far prevented the demonstration of QPE beyond proof of principles. Here we propose a new QPE algorithm based on a cascade of Gaussian spin states (GSSs) and a suitable adaptive measurement protocol. GSSs are renownedly resilient and have been created experimentally in a variety of platforms, from hundreds of ions up to millions of cold and ultracold neutral atoms. We show that our protocol achieves a QPE sensitivity overcoming previous schemes, including that obtained with GHZ states, scales linearly with time, and is robust against certain sources of noise and decoherence, such as detection noise, in particular. Our work paves the way toward an efficient implementation of the QPE, as well as applications of atomic squeezed states for quantum computation.