Quantum noise spectroscopy by qudit spectators

Abstract: Quantum noise spectroscopy is a well-known method for detecting environmental noise spectrum and has various applications in quantum sensing, quantum network design, and quantum computing. In this work, a protocol for quantum noise spectroscopy by qudit spectators (arbitrary d-level quantum systems) is presented for noises with stochastic and stationary Gaussian distributions. The protocol uses Weyl basis decomposition, consisting of generalized Pauli matrices, as the theoretical tool, and the Alvarez-Suter noise spectroscopy method, by which the qudit is being exposed to a series of pulse sequences, and the noise polyspectra is extracted by multiple measurements of an observable of the qudit. The formalism is further developed and simulated for three theoretical frameworks: The first two frameworks utilize a simplified Weyl basis and are capable of detecting Z-type dephasing noise. One is specifically modeled for a qutrit (d=3), and the second framework is designed for all qudits and has been tested through simulations of a ququad (d=4) and a quoct (d=8). The third framework employs the full Weyl basis, enabling it to identify all types of XYZ-dephasing noise. The simulations for this framework have been conducted for a quoct (d=8) implemented by the Antimony atom. The analytical protocol for noise spectroscopy that has been introduced transforms qudit systems into quantum spectators, and the presented simulations demonstrate the accuracy and reliability of this noise spectroscopy protocol.