Bayesian quantum noise spectroscopy

Abstract

Quantum computers promise a considerable speedup over classical computers in solving various classes of problems by exploiting the properties of superposition. Today, the prospects of quantum computers are more promising than ever before, but there are still major challenges ahead. The realisation of quantum computers is plagued by the sensitivity of quantum systems to unwanted perturbations. This indicates the importance of qubits noise characterisation and mitigation protocols.

We will start by discussing and quantifying mitigation, specifically the CPMG dynamical decoupling sequence. We find that the ubiquitous 1/f dephasing noise contributes a Gaussian decay in a qubit’s fidelity. Under a CPMG-n sequence, the qubits has a characteristic decay time of T_phi ∝ n^0.566.

We then demonstrate noise spectroscopy using Bayesian inference and frequentist methods. We find that the Bayesian results offer more insight into the quantities that we are estimating by directly giving us the probability density function of those quantities. We can also obtain the frequentist results by taking the maximum a posteriori probability (MAP) estimates of the Bayesian results.

We end by showing how Bayesian inference can be used to compare two models used to describe the same physical phenomenon.