Parameter estimation with cluster states

TL;DR

This paper introduces a parameter estimation scheme using cluster states that achieves Heisenberg-limited precision even under noise, outperforming other methods with fewer qubits.

Contribution

It demonstrates that cluster states enable Heisenberg-limited phase estimation under realistic noise models, surpassing traditional entangled and product states.

Findings

Achieves Heisenberg limit with cluster states under noise.

Remains superior to maximally entangled and product states.

Effective for small cluster states with extended qubit count.

Abstract

We propose a scheme for parameter estimation with cluster states. We find that phase estimation with cluster states under a many-body Hamiltonian and separable measurements leads to a precision at the Heisenberg limit. As noise models we study the dephasing, depolarizing, and pure damping channels. Decoherence reduces the sensitivity but our scheme remains superior over several reference schemes with states such as maximally entangled states and product states. For small cluster states and fixed evolution times it remains at the Heisenberg limit for approximately 2 times as many qubits than alternative schemes.