Iteration-free variational quantum eigensolver algorithm

We present a variant of the variational quantum eigensolver algorithm that only requires the execution of a set of quantum circuits once rather than at every iteration during the parameter optimization process, thereby significantly reducing the number of needed circuit executions. This iteration-free algorithm relies on an ansatz operator of a particular form that lets the quantum processing unit probe all needed probability mass functions and the classical processing unit perform all the remaining calculations, including those that depend on the variational parameters. If the ansatz requirements can be met, it will provide a large degree of control over the parameter space and allow for the consideration of physically motivated parameter constraints, which could be helpful in striking the right balance between computational cost and accuracy.