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Description
This work explores the application of the Quantum Phase Estimation (QPE) algorithm for the non-destructive measurement of the average photon number $\langle n \rangle$ in a free field, using qubits to capture the decay dynamics of the quantum field. The protocol is implemented with 5 qubits, achieving high precision in estimating the phase associated with $\langle n \rangle$, with uncertainties of $1/2^{32}$. An effective Hamiltonian model of system evolution and dynamics is simulated using the Monte Carlo method, reproducing decay via quantum jumps. The obtained results are compared with semiclassical solutions, highlighting QPE capability to distinguish quantum characteristics of the field. This study demonstrates the feasibility of QPE for non-destructive quantum measurements, motivating the implementation of the protocol in available experimental platforms.
