Fig. 1: Sketch of the proposed protocol to estimate an unknown Lindbladian, \({{{{{{{\mathcal{L}}}}}}}}\), of a multi-qubit device.
From: Efficient and robust estimation of many-qubit Hamiltonians
In the first step of classical pre-processing, the interaction graph between qubits is identified from the physical connectivity of the device. Then the unknown Lindbladian is written in a general form using an operator basis of Pauli strings, {Pi} and a suitable set of initial states and observables, {(ρj, Oi)} is chosen. In the second step of quantum processing, a time trace (expectation value) of each element of the set is obtained from the preparation and evolution of single qubit Pauli eigenstates on the quantum device followed by measurements in single qubit Pauli basis. In the last step of classical post-processing, each time trace is fitted to a low-degree polynomial to estimate the derivative of the observable. From these, an estimate of the Lindbladian, \({{{{{{{{\mathcal{L}}}}}}}}}_{est}\), is obtained from the Master equation.
