Compressed quantum metrology for the Ising Hamiltonian

TL;DR

This paper demonstrates that quantum metrology protocols for Hamiltonians with phase transitions, like the 1D Ising model, can be efficiently simulated on smaller quantum computers without losing Heisenberg scaling precision.

Contribution

It introduces a method to simulate quantum metrology protocols for the Ising Hamiltonian on exponentially smaller quantum computers while preserving optimal precision.

Findings

Efficient simulation of metrology protocols on smaller quantum computers.

Achieved Heisenberg scaling precision of O(1/N^2).

Provided explicit quantum circuit for simulation.

Abstract

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, i.e., O(1/N^2) precision and derive the explicit circuit that accomplishes the simulation.