Measurement reduction and Hamiltonian trimming for the contextual subspace variational quantum eigensolver

We investigate several optimization strategies to reduce the quantum resources required for implementation of the contextual subspace variational quantum eigensolver (CS-VQE), given limited capacity of near-term quantum devices. While there are already well established methods for the reduction of measurement settings, notably Pauli grouping methods based on qubit-wise commutation, global commutation, and anti-commutation discussed in the literature, we are interested in combined analyses of sample complexity in CS-VQE under two regimes: fixed total samples for a given simulation and total samples to be bounded by a fixed target error. We develop a method of measurement reduction called Hamiltonian trimming, in which low contribution terms are removed from the Hamiltonian to reduce the required sampling while causing minimal or negligible error to the energy estimate. In our case study of hydrogen sulfide (H2S) under CS-VQE at varying bond lengths, we find that using a combination of these techniques reduces the quantum resource of sampling from the order of 10⁷ to 10⁵ while maintaining target error below chemical accuracy of 1.6e-3 Hartrees.