Compressed quantum metrology for the Ising Hamiltonian
W. L. Boyajian, Michalis Skotiniotis, Wolfgang Dür, Barbara Kraus · Physical Review A · 2016
We show how quantum metrology protocols that seek to estimate the parameters of a Hamiltonian that exhibits a quantum phase transition can be efficiently simulated on an exponentially smaller quantum computer. Specifically, by exploiting the fact that the ground state of such a Hamiltonian changes drastically around its phase-transition point, we construct a suitable observable from which one can estimate the relevant parameters of the Hamiltonian with Heisenberg scaling precision. We then show how, for the one-dimensional Ising Hamiltonian with transverse magnetic field acting on $N$ spins, such a metrology protocol can be efficiently simulated on an exponentially smaller quantum computer while maintaining the same Heisenberg scaling for the squared error, i.e., $O({N}^{\ensuremath{-}2})$ precision, and derive the explicit circuit that accomplishes the simulation.