Variational Quantum Algorithm for Quantum Sensor Evaluation

The Quantum Fisher information (QFI) quantifies the ultimate precision of estimating a parameter from a quantum state via the quantum Cramér-Rao bound. Thus, the estimation of the QFI is needed in order to assess the quality of a quantum system as a quantum sensor. However, estimation of the QFI for a mixed quantum state is, in general, a computationally demanding task. In this presentation, we present two recent works addressing this issue. First, we discuss a generalized notion of QFI called the Truncated Quantum Fisher Information (TQFI). This quantity lower bounds the standard QFI and, under certain conditions, is efficiently computable on a quantum computer. Next, we discuss our new variational quantum algorithm called Variational Quantum Fisher Information Estimation (VQFIE) which estimates the lower and upper bounds on the QFI and thus outputs a range in which the actual QFI lies. We show that the algorithm can also be used to variationally prepare the state that maximizes the QFI, for the application of quantum sensing. We simulate the algorithm for a magnetometry setup and demonstrate good performance over a range of scenarios. Finally, we compare our contributions to recent literature and discuss the benefits of our methods.