Projective measurement of energy on an ensemble of qubits with unknown frequencies

TL;DR

This paper presents a method for performing projective energy measurements on an ensemble of non-interacting qubits with unknown frequencies using only a single probe qubit and global control, simplifying experimental requirements.

Contribution

It introduces a scheme to measure energy projectively on large qubit ensembles with unknown frequencies using only one probe and global manipulations, avoiding individual addressing.

Findings

Single probe qubit suffices for energy measurement in non-interacting qubit ensembles.

The scheme requires only global control fields, not individual qubit addressing.

Feasibility of the protocol demonstrated for large, unknown-frequency systems.

Abstract

In projective measurements of energy, a target system is projected to an eigenstate of the system Hamiltonian, and the measurement outcomes provide the information of corresponding eigen-energies. Recently, it has been shown that such a measurement can be in principle realized without detailed knowledge of the Hamiltonian by using probe qubits. However, in the previous approach for the energy measurement, the necessary size of the dimension for the probe increases as we increase the dimension of the target system, and also individual addresibility of every qubit is required, which may not be possible for many experimental settings with large systems. Here, we show that a single probe qubit is sufficient to perform such a projective measurement of energy if the target system is composed of non-interacting qubits whose resonant frequencies are unknown. Moreover, our scheme requires only global manipulations where every qubit is subjected to the same control fields. These results indicate the feasibility of our energy projection protocols.