Fig. 2: Flow chart for ExcitationSolve for fixed ansätze.
From: Fast gradient-free optimization of excitations in variational quantum eigensolvers
In this iterative algorithm, the k-th iteration updates a single parameter θj through repeated sweeps over all N parameters until convergence. To reflect the flexibility in the sweep order, we use separate indices j and k. Per iteration, the parameter is shifted to four different positions \({\theta }_{j,1}^{(k)},{\theta }_{j,2}^{(k)},{\theta }_{j,3}^{(k)},{\theta }_{j,4}^{(k)}\), and the quantum computer (QC) is used to obtain the corresponding energy values. This is the only part requiring the quantum hardware (purple). All remaining steps are efficiently computed classically. The energy associated with the unshifted current parameter value \({\theta }_{j}^{(k)}\) is re-used from the previous iteration k − 1.
