Paths Towards Quantum Noise Spectroscopy via Randomized Benchmarking

Characterizing noise in quantum systems is essential for identifying errors, developing targeted error protection strategies, and ensuring reliable quantum computation. Two widely used techniques for probing different aspects of quantum operations are Randomized Benchmarking (RB) and Quantum Noise Spectroscopy (QNS). RB is a well-established technique that estimates the average error rate of quantum operations by applying random sequences of gates. The decay in fidelity is averaged over these sequences, providing insight into the noise affecting the system. In contrast, QNS specifically targets time-correlated noise, offering a more detailed spectral breakdown of the noise impacting quantum systems. In this work, we investigate the relationship between RB and QNS by deriving an expression that connects the two. While the Haar-averaged behavior of RB reveals the decay caused by correlated noise, it does not provide meaningful insights for performing QNS. Instead, we explore practical ways to use individual random sequences for noise prediction. We aim to re-establish RB as a promising protocol for noise reconstruction and characterization by employing model-informed techniques drawn from classical signal processing, such as ARMA models.